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D21_out

Magma V2.12-16    Sun Jan 14 2007 21:05:56 on bayeux   [Seed = 1572010376]
Type ? for help.  Type -D to quit.

> load D21;
Loading "D21"
[
    -8*x^4*y + 27*x^3*y^3 - 3*x^3*y^2 - 15*x^3*y - x^3 + 3*x^2*y^3 + 3*x^2*y^2 -
        3*x^2*y - 3*x^2 + 8*x*y^4 - 15*x*y^3 + 3*x*y^2 + 7*x*y - 3*x + y^3 -
        3*y^2 + 3*y - 1,
    3*x^2*y^2 - 2*x^2*y - x^2 + 2*x*y^2 - 6*x*y - y^2 + 1,
    x^4*y - x^4 - 3*x^3*y^2 - 11*x^3*y - 2*x^3 + 3*x^2*y^3 - 3*x^2*y^2 - x*y^4 -
        11*x*y^3 + 10*x*y + 2*x - y^4 + 2*y^3 - 2*y + 1,
    x^2*y - x*y^2 + x*y + 2*x - 2*y - 1,
    2*x^4*y + 2*x^4 + x^3*y^2 + 6*x^3*y + 5*x^3 - 3*x^2*y^2 + 3*x^2 + 3*x*y^2 -
        2*x*y - x - y^2 + 2*y - 1,
    -3*x^2*y - x^2 + 2*x*y^3 - 3*x*y^2 - 2*x*y - x + y^4 - y^3,
    x^2*y^3 + 3*x^2*y^2 + 3*x^2*y + x^2 + 2*x*y^4 - 6*x*y^3 + 2*x*y + 2*x -
        2*y^4 + 5*y^3 - 3*y^2 - y + 1,
    x^4 + 2*x^3*y + x^3 + 3*x^2*y + 3*x*y^2 - 2*x*y - y^2 + y
]

----- CURVE ----- 1
-8*x^4*y + 27*x^3*y^3 - 3*x^3*y^2 - 15*x^3*y - x^3 + 3*x^2*y^3 + 3*x^2*y^2 -
    3*x^2*y - 3*x^2 + 8*x*y^4 - 15*x*y^3 + 3*x*y^2 + 7*x*y - 3*x + y^3 - 3*y^2 +
    3*y - 1
Genus= 1
[
    [ 1, -1 ],
    [ 0, 1 ],
    [ 1, 1 ],
    [ -1, -1 ],
    [ -1, 0 ]
]
Elliptic Curve defined by y^2 + 55190517760*x*y +
30061330177525962931961856000*y = x^3 - 747391789170176819200*x^2 -
765411624993527882435477601433681920000*x -
131471071371312765694449633282384062218322929778688000000 over Rational Field
Mapping from: CrvPln: D to CrvEll: E
with equations :
31477366451994624000*X^2*Y^7 - 22383905032529510400*X^2*Y^6*Z +
    43368816000525926400*X*Y^7*Z + 5246227741999104000*Y^8*Z -
    2763445065744384000*X^4*Y^3*Z^2 - 81426636015324364800*X^2*Y^5*Z^2 +
    5716876979758694400*X*Y^6*Z^2 + 11191952516264755200*Y^7*Z^2 +
    1351017587697254400*X^4*Y^2*Z^3 - 2187727343714304000*X^3*Y^3*Z^3 +
    11462539845618892800*X^2*Y^4*Z^3 - 85290661459682918400*X*Y^5*Z^3 +
    1748742580666368000*Y^6*Z^3 + 4114462653441638400*X^4*Y*Z^4 +
    4766942738409062400*X^3*Y^2*Z^4 + 41500611992538316800*X^2*Y^3*Z^4 -
    10493415013534924800*X*Y^4*Z^4 - 27090397410125414400*Y^5*Z^4 +
    7468977913803571200*X^3*Y*Z^5 + 2797988129066188800*X^2*Y^2*Z^5 +
    44289964355774054400*X*Y^3*Z^5 - 14897175822296678400*Y^4*Z^5 +
    514307831680204800*X^3*Z^6 + 1816389413004902400*X^2*Y*Z^6 +
    3337243728701030400*X*Y^2*Z^6 + 16728437943120691200*Y^3*Z^6 +
    1491108900057907200*X^2*Z^7 - 2368118896617062400*X*Y*Z^7 +
    7439712262933708800*Y^2*Z^7 + 1439294305075200000*X*Z^8 -
    829993049260032000*Y*Z^8 + 462493236697497600*Z^9
-786548511686128752968859648000*X^2*Y^7 +
    87394279076236528107651072000*X^2*Y^6*Z -
    1009650368692370127470985216000*X*Y^7*Z -
    131091418614354792161476608000*Y^8*Z +
    2271070690496224172414337024000*X^2*Y^5*Z^2 -
    543539515894714592812597248000*X*Y^6*Z^2 -
    281823406674700329975545856000*Y^7*Z^2 +
    20459931818487929762742272000*X^5*Y*Z^3 +
    15344948863865947322056704000*X^4*Y^2*Z^3 +
    36204534486696411113979904000*X^2*Y^4*Z^3 +
    2272435009328613055398936576000*X*Y^5*Z^3 -
    38968390970866988985876480000*Y^6*Z^3 -
    575979589313851371693277184000/9*X^4*Y*Z^4 -
    163016926606153714889654272000/3*X^3*Y^2*Z^4 -
    3572160582108039615283724288000/3*X^2*Y^3*Z^4 +
    6044606029589572724530872320000/9*X*Y^4*Z^4 +
    618026340768865482977574912000*Y^5*Z^4 +
    2557491477310991220342784000*X^4*Z^5 -
    516165369624594346498064384000/3*X^3*Y*Z^5 -
    250356338228172953445466112000/3*X^2*Y^2*Z^5 -
    3841257130417241907997442048000/3*X*Y^3*Z^5 +
    467427517255452649580396544000*Y^4*Z^5 -
    46102847456457635355688960000/9*X^3*Z^6 -
    142466822712156886826745856000/3*X^2*Y*Z^6 -
    423396905777597151759564800000/3*X*Y^2*Z^6 -
    3929243545557455227162984448000/9*Y^3*Z^6 -
    87923242062192494956773376000/3*X^2*Z^7 +
    573311173141775818443194368000/9*X*Y*Z^7 -
    627571659006849897843392512000/3*Y^2*Z^7 -
    99053738940195459913744384000/3*X*Z^8 +
    70778169361568726329065472000/3*Y*Z^8 - 102511761386265451209687040000/9*Z^9
-Y^8*Z - 2*Y^7*Z^2 + Y^6*Z^3 + 4*Y^5*Z^4 + Y^4*Z^5 - 2*Y^3*Z^6 - Y^2*Z^7
Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 2*x over Rational Field
Elliptic curve isomorphism from: CrvEll: E to CrvEll: M
Taking (x : y : 1) to (1/932662709688729600*x + 37/8 :
1/900714012809766679609344000*y + 379/12590946580797849600*x + 115/8 : 1)

----- CURVE ----- 2
3*x^2*y^2 - 2*x^2*y - x^2 + 2*x*y^2 - 6*x*y - y^2 + 1
Genus= 1
[
    [ 0, -1 ],
    [ 1, 0 ],
    [ 0, 1 ],
    [ -1, 0 ]
]
Elliptic Curve defined by y^2 + 96*x*y - 3981312*y = x^3 + 42048*x^2 +
833421312*x - 917294284800 over Rational Field
Mapping from: CrvPln: D to CrvEll: E
with equations :
13824*X*Y^3 + 4608*X*Y^2*Z - 13824*X*Y*Z^2 - 50688*Y^2*Z^2 - 4608*X*Z^3 -
    64512*Y*Z^3 - 13824*Z^4
-2654208*X*Y^3 + 1769472*X*Y^2*Z + 884736*X*Y*Z^2 + 12496896*Y^2*Z^2 +
    8183808*Y*Z^3 + 2764800*Z^4
Y^3*Z + 3*Y^2*Z^2 + 3*Y*Z^3 + Z^4
Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 2*x over Rational Field
Elliptic curve isomorphism from: CrvEll: E to CrvEll: M
Taking (x : y : 1) to (1/2304*x + 6 : 1/110592*y + 1/4608*x - 21 : 1)

----- CURVE ----- 3
x^4*y - x^4 - 3*x^3*y^2 - 11*x^3*y - 2*x^3 + 3*x^2*y^3 - 3*x^2*y^2 - x*y^4 -
    11*x*y^3 + 10*x*y + 2*x - y^4 + 2*y^3 - 2*y + 1
Genus= 1
[
    [ 0, -1 ],
    [ 1, -1 ],
    [ 1, 0 ],
    [ 0, 1 ],
    [ -1, 0 ]
]
Elliptic Curve defined by y^2 - 3*x*y = x^3 + 9*x^2 - 162*x over Rational Field
Mapping from: CrvPln: D to CrvEll: E
with equations :
3*X^3*Y^2 - 6*X^2*Y^3 - 6*X*Y^4 - 45*X^2*Y^2*Z - 30*X*Y^3*Z - 6*Y^4*Z -
    3*X^3*Z^2 - 42*X^2*Y*Z^2 + 3*X*Y^2*Z^2 - 3*X^2*Z^3 + 30*X*Y*Z^3 + 3*Y^2*Z^3
    + 3*X*Z^4 + 3*Z^5
9*X^3*Y^2 - 45*X^2*Y^3 + 63*X*Y^4 - 27*X^3*Y*Z - 27*X^2*Y^2*Z + 153*X*Y^3*Z -
    45*Y^4*Z + 18*X^3*Z^2 + 198*X^2*Y*Z^2 + 36*X*Y^2*Z^2 - 54*Y^3*Z^2 +
    18*X^2*Z^3 - 234*X*Y*Z^3 + 36*Y^2*Z^3 - 18*X*Z^4 + 81*Y*Z^4 - 18*Z^5
Y^5 + 2*Y^4*Z - 2*Y^2*Z^3 - Y*Z^4
Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 2*x over Rational Field
Elliptic curve isomorphism from: CrvEll: E to CrvEll: M
Taking (x : y : 1) to (1/9*x : 1/27*y - 1/9*x : 1)

----- CURVE ----- 4
x^2*y - x*y^2 + x*y + 2*x - 2*y - 1
Genus= 1
[
    [ 1, -1 ],
    [ 1, 1 ],
    [ -1, -1 ]
]
Elliptic Curve defined by y^2 = x^3 - 28*x^2 - 384*x + 9216 over Rational Field
Mapping from: CrvPln: D to CrvEll: E
with equations :
6*X^2 - 6*Y^2
-24*X^2 + 48*X*Y - 24*Y^2 - 72*X*Z + 72*Y*Z + 48*Z^2
1/8*X^2 - 1/8*Y^2 - 1/4*X*Z - 1/4*Y*Z
and inverse
8*u^2 - u*v - 96*u*w - 4608*w^2
8*u^2 + u*v - 96*u*w - 4608*w^2
-u*v + 48*v*w
Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 2*x over Rational Field
Elliptic curve isomorphism from: CrvEll: E to CrvEll: M
Taking (x : y : 1) to (1/16*x - 1 : 1/64*y - 1/32*x + 1/2 : 1)

----- CURVE ----- 5
2*x^4*y + 2*x^4 + x^3*y^2 + 6*x^3*y + 5*x^3 - 3*x^2*y^2 + 3*x^2 + 3*x*y^2 -
    2*x*y - x - y^2 + 2*y - 1
Genus= 1
[
    [ 1, -1 ],
    [ 0, 1 ],
    [ -1, 0 ]
]
Elliptic Curve defined by y^2 + 2*x*y - 48*y = x^3 + 28*x^2 + 288*x over
Rational Field
Mapping from: CrvPln: D to CrvEll: E
with equations :
12*X^3*Y^4 + 6*X^2*Y^5 + 42*X^3*Y^3*Z + 51*X^2*Y^4*Z - 18*X*Y^5*Z +
    50*X^3*Y^2*Z^2 + 132*X^2*Y^3*Z^2 - 48*X*Y^4*Z^2 + 24*Y^5*Z^2 + 22*X^3*Y*Z^3
    + 138*X^2*Y^2*Z^3 - 12*X*Y^3*Z^3 + 33*Y^4*Z^3 + 2*X^3*Z^4 + 54*X^2*Y*Z^4 +
    48*X*Y^2*Z^4 - 18*Y^3*Z^4 + 3*X^2*Z^5 + 30*X*Y*Z^5 - 32*Y^2*Z^5 - 6*Y*Z^6 -
    Z^7
-24*X^3*Y^4 - 12*X^2*Y^5 - 24*X^3*Y^3*Z - 96*X^2*Y^4*Z + 24*X*Y^5*Z +
    28*X^3*Y^2*Z^2 - 78*X^2*Y^3*Z^2 - 84*X*Y^4*Z^2 - 36*Y^5*Z^2 + 24*X^3*Y*Z^3 +
    102*X^2*Y^2*Z^3 - 156*X*Y^3*Z^3 - 60*Y^4*Z^3 - 4*X^3*Z^4 + 90*X^2*Y*Z^4 +
    84*X*Y^2*Z^4 - 54*Y^3*Z^4 - 6*X^2*Z^5 + 132*X*Y*Z^5 + 50*Y^2*Z^5 + 98*Y*Z^6
    + 2*Z^7
-Y^5*Z^2 - 2*Y^4*Z^3 + 2*Y^2*Z^5 + Y*Z^6
Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 2*x over Rational Field
Elliptic curve isomorphism from: CrvEll: E to CrvEll: M
Taking (x : y : 1) to (1/4*x + 2 : 1/8*y - 4 : 1)

----- CURVE ----- 6
-3*x^2*y - x^2 + 2*x*y^3 - 3*x*y^2 - 2*x*y - x + y^4 - y^3
Genus= 1
[
    [ -1, 1 ],
    [ 1, -1 ],
    [ 0, 1 ],
    [ -1, 0 ],
    [ 0, 0 ]
]
Elliptic Curve defined by y^2 - 6*x*y + 48*y = x^3 + 20*x^2 + 384*x over
Rational Field

Mapping from: CrvPln: D to CrvEll: E
with equations :
24*X*Y^2*Z - 16*X*Y*Z^2 - 8*Y^2*Z^2 - 8*X*Z^3 + 16*Y*Z^3 - 8*Z^4
96*X*Y^2*Z - 48*Y^3*Z + 32*X*Y*Z^2 + 16*Y^2*Z^2 + 80*Y*Z^3 - 48*Z^4
-Y^4 + 2*Y^3*Z - 2*Y*Z^3 + Z^4
Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 2*x over Rational Field
Elliptic curve isomorphism from: CrvEll: E to CrvEll: M
Taking (x : y : 1) to (1/4*x + 2 : 1/8*y - 1/2*x + 2 : 1)

----- CURVE ----- 7
x^2*y^3 + 3*x^2*y^2 + 3*x^2*y + x^2 + 2*x*y^4 - 6*x*y^3 + 2*x*y + 2*x - 2*y^4 +
    5*y^3 - 3*y^2 - y + 1
Genus= 1
[
    [ 1, -1 ],
    [ 0, 1 ],
    [ -1, 0 ]
]
Elliptic Curve defined by y^2 - 2*x*y + 48*y = x^3 + 28*x^2 + 288*x over
Rational Field
Mapping from: CrvPln: D to CrvEll: E
with equations :
4*X*Y^4 + 16*X*Y^3*Z - 28*Y^4*Z + 24*X*Y^2*Z^2 - 16*Y^3*Z^2 + 16*X*Y*Z^3 +
    24*Y^2*Z^3 + 4*X*Z^4 + 16*Y*Z^4 + 4*Z^5
16*X*Y^4 + 48*X*Y^3*Z - 160*Y^4*Z + 48*X*Y^2*Z^2 + 16*X*Y*Z^3 + 96*Y^2*Z^3 +
    64*Y*Z^4
Y^5 + 2*Y^4*Z - 2*Y^2*Z^3 - Y*Z^4
Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 2*x over Rational Field
Elliptic curve isomorphism from: CrvEll: E to CrvEll: M
Taking (x : y : 1) to (1/4*x + 2 : 1/8*y - 1/4*x + 2 : 1)

----- CURVE ----- 8
x^4 + 2*x^3*y + x^3 + 3*x^2*y + 3*x*y^2 - 2*x*y - y^2 + y
Genus= 1
[
    [ -1, 1 ],
    [ 1, -1 ],
    [ 0, 1 ],
    [ -1, 0 ],
    [ 0, 0 ]
]
Elliptic Curve defined by y^2 - 6*x*y + 48*y = x^3 + 20*x^2 + 384*x over
Rational Field
Mapping from: CrvPln: D to CrvEll: E
with equations :
4*X^3 + 8*X^2*Y + 8*X^2*Z + 12*X*Y*Z - 4*Y^2*Z - 4*Y*Z^2 + 8*Z^3
8*X^3 + 16*X^2*Y + 16*X^2*Z + 8*X*Y*Z - 40*Y^2*Z - 16*X*Z^2 - 8*Y*Z^2 + 48*Z^3
Y^2*Z - Z^3
Elliptic Curve defined by y^2 + x*y = x^3 + x^2 - 2*x over Rational Field
Elliptic curve isomorphism from: CrvEll: E to CrvEll: M
Taking (x : y : 1) to (1/4*x + 2 : 1/8*y - 1/2*x + 2 : 1)

=========================================================
Curve # 1
Curve over Rational Field defined by
531441*z^28 + 314928*z^27 - 2879550*z^26 + 1568808*z^25 - 2125764*z^24*w^2 + 
    20211525*z^24 - 5511240*z^23*w^2 - 3907440*z^23 + 8290188*z^22*w^2 - 
    80277480*z^22 + 27932364*z^21*w^2 + 20528640*z^21 - 42557076*z^20*w^2 + 
    237748770*z^20 + 6377292*z^19*w^4 - 111820824*z^19*w^2 - 56896992*z^19 + 
    8739252*z^18*w^4 + 110515428*z^18*w^2 - 497437524*z^18 - 22709808*z^17*w^4 +
    260375472*z^17*w^2 + 32204304*z^17 - 20985480*z^16*w^4 - 154646172*z^16*w^2 
    + 635059602*z^16 + 51168024*z^15*w^4 - 345730680*z^15*w^2 + 51671520*z^15 - 
    4782969*z^14*w^6 + 30516696*z^14*w^4 + 124020396*z^14*w^2 - 464816232*z^14 -
    2480058*z^13*w^6 - 60342624*z^13*w^4 + 262613016*z^13*w^2 - 60046272*z^13 + 
    11055285*z^12*w^6 - 30617352*z^12*w^4 - 55218348*z^12*w^2 + 191841453*z^12 +
    3877308*z^11*w^6 + 29427840*z^11*w^4 - 102407976*z^11*w^2 + 9179568*z^11 - 
    8780913*z^10*w^6 + 12990240*z^10*w^4 + 18134604*z^10*w^2 - 47879262*z^10 - 
    619974*z^9*w^6 - 5139504*z^9*w^4 + 17523216*z^9*w^2 + 5744520*z^9 + 
    2821157*z^8*w^6 - 1693656*z^8*w^4 - 5851440*z^8*w^2 + 7850601*z^8 - 
    787384*z^7*w^6 + 1134216*z^7*w^4 - 2985984*z^7*w^2 - 361584*z^7 - 
    343235*z^6*w^6 + 1031400*z^6*w^4 - 557928*z^6*w^2 + 46656*z^6 + 
    14426*z^5*w^6 + 84672*z^5*w^4 + 12636*z^5*w^2 + 16384*z^4*w^8 - 
    34777*z^4*w^6 + 18792*z^4*w^4 - 3888*z^4*w^2 - 4292*z^3*w^6 - 108*z^3*w^4 - 
    83*z^2*w^6 + 108*z^2*w^4 - 26*z*w^6 - w^6
Genus =  7
Bad primes =  [ 2, 3, 17, 23, 162847 ]
Weil primes =  [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 
149, 151, 157, 163, 167, 173, 179, 181, 191, 193 ]
Looking for local solutions ...
Local solutions everywhere.
Looking for rational points slow ...
Rational points h(z),h(w) <= 20
{
    [ -1, -2 ],
    [ 1, 2 ],
    [ -1, 2 ],
    [ 1, 0 ],
    [ 1, -2 ],
    [ -1, 0 ],
    [ 0, 0 ]
}
Coleman bound =  23  at p= 19
=========================================================
Curve # 2
Curve over Rational Field defined by
81*z^16 - 108*z^15 + 306*z^14 + 3816*z^13 - 162*z^12*w^2 + 7047*z^12 - 
    108*z^11*w^2 - 4572*z^11 - 171*z^10*w^2 - 21024*z^10 - 3966*z^9*w^2 + 
    144*z^9 + 81*z^8*w^4 - 10177*z^8*w^2 + 29583*z^8 + 216*z^7*w^4 - 
    6808*z^7*w^2 + 10332*z^7 + 108*z^6*w^4 + 1642*z^6*w^2 - 8982*z^6 - 
    120*z^5*w^4 + 356*z^5*w^2 + 1224*z^5 - 74*z^4*w^4 - 1660*z^4*w^2 + 3321*z^4 
    + 40*z^3*w^4 + 148*z^3*w^2 - 468*z^3 + 12*z^2*w^4 - 95*z^2*w^2 + 36*z^2 - 
    8*z*w^4 + 10*z*w^2 + w^4 - w^2
Genus =  7
Bad primes =  [ 2, 3, 5, 17, 23, 61, 17929 ]
Weil primes =  [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 
149, 151, 157, 163, 167, 173, 179, 181, 191, 193 ]
Looking for local solutions ...
Local solutions everywhere.
Looking for rational points fast ...
Rational points h(z) <= 400
{
    [ -2, -9 ],
    [ 0, -1 ],
    [ 0, 0 ],
    [ 1, -1 ],
    [ 1, 9 ],
    [ -2, 9 ],
    [ -1, 0 ],
    [ 1, -9 ],
    [ 0, 1 ],
    [ 1, 1 ]
}
Coleman bound =  26  at p= 19
=========================================================
Curve # 3
Curve over Rational Field defined by
46656*z^26 + 361584*z^25 + 7850601*z^24 - 5744520*z^23 - 46656*z^22*w^2 - 
    47879262*z^22 + 1597968*z^21*w^2 - 9179568*z^21 - 10362249*z^20*w^2 + 
    191841453*z^20 + 1257282*z^19*w^2 + 60046272*z^19 + 33479811*z^18*w^2 - 
    464816232*z^18 + 37021536*z^17*w^2 - 51671520*z^17 + 15552*z^16*w^4 - 
    145976904*z^16*w^2 + 635059602*z^16 + 1870128*z^15*w^4 - 35660736*z^15*w^2 -
    32204304*z^15 - 2912328*z^14*w^4 + 248373216*z^14*w^2 - 497437524*z^14 + 
    3055104*z^13*w^4 - 37087632*z^13*w^2 + 56896992*z^13 - 15323904*z^12*w^4 - 
    168538482*z^12*w^2 + 237748770*z^12 + 18331488*z^11*w^4 + 20772612*z^11*w^2 
    - 20528640*z^11 - 1728*z^10*w^6 + 11390328*z^10*w^4 + 72175374*z^10*w^2 - 
    80277480*z^10 + 190080*z^9*w^6 - 24750576*z^9*w^4 + 11212992*z^9*w^2 + 
    3907440*z^9 - 1133200*z^8*w^6 + 3642624*z^8*w^4 - 31500576*z^8*w^2 + 
    20211525*z^8 + 1867616*z^7*w^6 + 4491504*z^7*w^4 - 1737936*z^7*w^2 - 
    1568808*z^7 - 838064*z^6*w^6 + 2602152*z^6*w^4 + 3524472*z^6*w^2 - 
    2879550*z^6 - 240256*z^5*w^6 - 2706912*z^5*w^4 + 2558304*z^5*w^2 - 
    314928*z^5 + 64*z^4*w^8 - 31024*z^4*w^6 + 440640*z^4*w^4 - 1068957*z^4*w^2 +
    531441*z^4 + 256*z^3*w^8 + 275680*z^3*w^6 - 286848*z^3*w^4 + 65610*z^3*w^2 +
    384*z^2*w^8 - 93584*z^2*w^6 + 144936*z^2*w^4 - 59049*z^2*w^2 + 256*z*w^8 + 
    3520*z*w^6 - 3888*z*w^4 + 64*w^8 - 64*w^6
Genus =  7
Bad primes =  [ 2, 3, 13, 17, 23, 4271 ]
Weil primes =  [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 
149, 151, 157, 163, 167, 173, 179, 181, 191, 193 ]
Looking for local solutions ...
Local solutions everywhere.
Looking for rational points slow ...
Rational points h(z),h(w) <= 20
{
    [ 0, -1 ],
    [ 0, 0 ],
    [ 1, 0 ],
    [ 1, -1 ],
    [ -1, 0 ],
    [ 0, 1 ],
    [ 1, 1 ]
}
Coleman bound =  23  at p= 19
=========================================================
Curve # 4
Curve over Rational Field defined by
36*z^14 + 468*z^13 + 3321*z^12 - 1224*z^11 - 144*z^10*w^2 - 8982*z^10 - 
    432*z^9*w^2 - 10332*z^9 - 472*z^8*w^2 + 29583*z^8 + 1040*z^7*w^2 - 144*z^7 +
    1672*z^6*w^2 - 21024*z^6 - 784*z^5*w^2 + 4572*z^5 + 16*z^4*w^4 - 
    3256*z^4*w^2 + 7047*z^4 + 2896*z^3*w^2 - 3816*z^3 - 392*z^2*w^2 + 306*z^2 - 
    128*z*w^2 + 108*z - 64*w^2 + 81
Genus =  7
Bad primes =  [ 2, 3, 5, 17, 23, 37, 83 ]
Weil primes =  [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 
149, 151, 157, 163, 167, 173, 179, 181, 191, 193 ]
Looking for local solutions ...
Local solutions everywhere.
Looking for rational points fast ...
Rational points h(z) <= 400
{
    [ 0, 9/8 ],
    [ -3, 18 ],
    [ -3, -18 ],
    [ 1/2, -9/8 ],
    [ 1, 2 ],
    [ -1, 2 ],
    [ -1, -18 ],
    [ -1, 18 ],
    [ 1, 0 ],
    [ -1, -2 ],
    [ 1/2, 9/8 ],
    [ 1, -2 ],
    [ 0, -9/8 ]
}
Coleman bound =  29  at p= 19
=========================================================
Curve # 5
Curve over Rational Field defined by
36*z^22 + 612*z^21 + 5409*z^20 + 15012*z^19 - 9*z^18*w^2 + 7956*z^18 - 
    162*z^17*w^2 - 39852*z^17 - 1525*z^16*w^2 - 67212*z^16 - 5312*z^15*w^2 + 
    19044*z^15 - 8391*z^14*w^2 + 105588*z^14 + 1778*z^13*w^2 + 27612*z^13 + 
    z^12*w^4 + 6971*z^12*w^2 - 71802*z^12 - 12*z^11*w^4 - 6756*z^11*w^2 - 
    32436*z^11 + 66*z^10*w^4 - 5785*z^10*w^2 + 24588*z^10 - 220*z^9*w^4 + 
    4290*z^9*w^2 + 11196*z^9 + 495*z^8*w^4 + 729*z^8*w^2 - 5868*z^8 - 
    792*z^7*w^4 - 2648*z^7*w^2 - 1620*z^7 + 924*z^6*w^4 + 251*z^6*w^2 + 1224*z^6
    - 792*z^5*w^4 + 558*z^5*w^2 + 432*z^5 + 495*z^4*w^4 - 415*z^4*w^2 + 81*z^4 -
    220*z^3*w^4 + 60*z^3*w^2 + 66*z^2*w^4 - 18*z^2*w^2 - 12*z*w^4 + w^4
Genus =  7
Bad primes =  [ 2, 3, 5, 17, 23, 2767117 ]
Weil primes =  [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 
149, 151, 157, 163, 167, 173, 179, 181, 191, 193 ]
Looking for local solutions ...
Local solutions everywhere.
Looking for rational points fast ...
Rational points h(z) <= 400
{
    [ 1/2, -9/8 ],
    [ -3, -18 ],
    [ 1, 0 ],
    [ 1/2, 9/8 ],
    [ -3, 18 ],
    [ 0, 0 ],
    [ -1, 0 ]
}
Coleman bound =  25  at p= 19
=========================================================
Curve # 6
Curve over Rational Field defined by
6561*z^20 - 22356*z^19 + 14508*z^18 + 69228*z^17 - 6561*z^16*w^2 - 31572*z^16 + 
    27702*z^15*w^2 - 372996*z^15 - 68391*z^14*w^2 + 398916*z^14 + 33804*z^13*w^2
    + 952812*z^13 - 10549*z^12*w^2 - 1746018*z^12 + 3888*z^11*w^4 + 
    262770*z^11*w^2 - 657900*z^11 - 216*z^10*w^4 - 1022947*z^10*w^2 + 
    2756340*z^10 + 5184*z^9*w^4 + 812696*z^9*w^2 - 649116*z^9 - 20400*z^8*w^4 + 
    1065549*z^8*w^2 - 1723716*z^8 + 144336*z^7*w^4 - 1497990*z^7*w^2 + 
    1060020*z^7 - 576*z^6*w^6 - 50976*z^6*w^4 + 111419*z^6*w^2 + 203868*z^6 + 
    1728*z^5*w^6 - 180816*z^5*w^4 + 489324*z^5*w^2 - 372924*z^5 - 5520*z^4*w^6 +
    101616*z^4*w^4 - 203191*z^4*w^2 + 120537*z^4 - 2016*z^3*w^6 + 960*z^3*w^4 + 
    3934*z^3*w^2 - 6768*z^3 + 2160*z^2*w^6 - 5640*z^2*w^4 + 3663*z^2*w^2 + 
    576*z^2 - 768*z*w^6 + 1872*z*w^4 - 1168*z*w^2 + 64*w^8 - 192*w^6 + 192*w^4 -
    64*w^2
Genus =  7
Bad primes =  [ 2, 3, 5, 17, 19, 23, 41, 137, 461 ]
Weil primes =  [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 
149, 151, 157, 163, 167, 173, 179, 181, 191, 193 ]
Looking for local solutions ...
Local solutions everywhere.
Looking for rational points slow ...
Rational points h(z),h(w) <= 20
{
    [ 1, -9 ],
    [ -1, 4 ],
    [ 0, -1 ],
    [ 1, 9 ],
    [ 1, 0 ],
    [ -1, -4 ],
    [ 0, 1 ],
    [ -1, 0 ],
    [ 0, 0 ]
}
Coleman bound =  33  at p= 29
=========================================================
Curve # 7
Curve over Rational Field defined by
576*z^22 + 6768*z^21 + 120537*z^20 + 372924*z^19 - 432*z^18*w^2 + 203868*z^18 - 
    4860*z^17*w^2 - 1060020*z^17 - 90280*z^16*w^2 - 1723716*z^16 - 
    261272*z^15*w^2 + 649116*z^15 + 108*z^14*w^4 - 65040*z^14*w^2 + 2756340*z^14
    + 1404*z^13*w^4 + 719804*z^13*w^2 + 657900*z^13 + 23808*z^12*w^4 + 
    256052*z^12*w^2 - 1746018*z^12 + 100296*z^11*w^4 - 239208*z^11*w^2 - 
    952812*z^11 - 9*z^10*w^6 - 228900*z^10*w^4 + 219884*z^10*w^2 + 398916*z^10 +
    90*z^9*w^6 + 50652*z^9*w^4 - 397860*z^9*w^2 + 372996*z^9 - 1101*z^8*w^6 + 
    45120*z^8*w^4 - 297168*z^8*w^2 - 31572*z^8 + 20472*z^7*w^6 + 28848*z^7*w^4 +
    175864*z^7*w^2 - 69228*z^7 - 70674*z^6*w^6 + 17604*z^6*w^4 - 40264*z^6*w^2 +
    14508*z^6 + 105852*z^5*w^6 - 121164*z^5*w^4 - 32796*z^5*w^2 + 22356*z^5 + 
    64*z^4*w^8 - 84258*z^4*w^6 + 127680*z^4*w^4 - 12604*z^4*w^2 + 6561*z^4 - 
    256*z^3*w^8 + 38328*z^3*w^6 - 59064*z^3*w^4 + 7560*z^3*w^2 + 384*z^2*w^8 - 
    9765*z^2*w^6 + 14580*z^2*w^4 - 2916*z^2*w^2 - 256*z*w^8 + 1146*z*w^6 - 
    972*z*w^4 + 64*w^8 - 81*w^6
Genus =  7
Bad primes =  [ 2, 3, 17, 23, 1088407 ]
Weil primes =  [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 
149, 151, 157, 163, 167, 173, 179, 181, 191, 193 ]
Looking for local solutions ...
Local solutions everywhere.
Looking for rational points slow ...
Rational points h(z),h(w) <= 20
{
    [ -1, 18 ],
    [ 0, 9/8 ],
    [ -1, -18 ],
    [ 1, 0 ],
    [ 0, -9/8 ],
    [ -1, 0 ],
    [ 0, 0 ]
}
Coleman bound =  23  at p= 19
=========================================================
Curve # 8
Curve over Rational Field defined by
81*z^20 - 432*z^19 + 1224*z^18 + 1620*z^17 - 5868*z^16 - 11196*z^15 - 
    576*z^14*w^2 + 24588*z^14 - 384*z^13*w^2 + 32436*z^13 + 2744*z^12*w^2 - 
    71802*z^12 + 3312*z^11*w^2 - 27612*z^11 - 8296*z^10*w^2 + 105588*z^10 - 
    8272*z^9*w^2 - 19044*z^9 + 12528*z^8*w^2 - 67212*z^8 + 18048*z^7*w^2 + 
    39852*z^7 - 33568*z^6*w^2 + 7956*z^6 + 18528*z^5*w^2 - 15012*z^5 + 
    1296*z^4*w^4 - 4888*z^4*w^2 + 5409*z^4 - 1728*z^3*w^4 + 1360*z^3*w^2 - 
    612*z^3 + 864*z^2*w^4 - 696*z^2*w^2 + 36*z^2 - 192*z*w^4 + 176*z*w^2 + 
    16*w^4 - 16*w^2
Genus =  7
Bad primes =  [ 2, 3, 5, 17, 23, 57349 ]
Weil primes =  [ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,
61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 
149, 151, 157, 163, 167, 173, 179, 181, 191, 193 ]
Looking for local solutions ...
Local solutions everywhere.
Looking for rational points fast ...
Rational points h(z) <= 400
{
    [ -2, -9 ],
    [ -1, -4 ],
    [ 0, -1 ],
    [ 0, 0 ],
    [ 1, 0 ],
    [ -1, 4 ],
    [ -2, 9 ],
    [ -1, 0 ],
    [ 0, 1 ]
}
Coleman bound =  25  at p= 19

Total time: 1651.549 seconds, Total memory usage: 50.19MB
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