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triangle_out

Magma V2.14-6     Wed Feb 20 2008 23:17:48 on bayeux   [Seed = 2874209934]
Type ? for help.  Type -D to quit.

------Model------
Genus= 7  degree= 16
Genus= 3  degree= 8
Genus= 3  degree= 7
J(Q)= Jacobian of Hyperelliptic Curve defined by y^2 = -46080*x^7 - 208512*x^6 -
    351616*x^5 - 228512*x^4 + 43776*x^3 + 145800*x^2 + 75816*x + 13122 over 
Rational Field
points= [ (-9 : 373248 : 2), (-3 : 1152 : 2), (-1 : 0 : 2), (-7 : 4608 : 6), (-9
: 0 : 8), (-9 : 0 : 10) ]
Divisors= [ (x + 9/2, -23328, 1), (x + 3/2, -72, 1), (x + 1/2, 0, 1), (x + 9/8, 
0, 1), (x + 9/10, 0, 1), (x^2 + 5/3*x + 3/4, 0, 2), (x^2 + 1/3*x - 3/4, 0, 2) ]

------Torsion------
11 Torsion <= 1280
13 Torsion <= 256
17 Torsion <= 256
19 Torsion <= 256
23 Torsion <= 128
29 Torsion <= 128
31 Torsion <= 128
37 Torsion <= 128
41 Torsion <= 64
Torsion <= 64
11 Torsion <= 16 ? false [ 2, 2, 2, 2, 80 ]
13 Torsion <= 16 ? false [ 2, 2, 12, 48 ]
17 Torsion <= 16 ? false [ 2, 2, 2, 2, 480 ]
19 Torsion <= 16 ? false [ 2, 2, 2, 2, 8, 48 ]
23 Torsion <= 16 ? true [ 2, 2, 4, 952 ]
29 Torsion <= 16 ? true [ 2, 2, 2, 2, 1456 ]
31 Torsion <= 16 ? true [ 2, 2, 2, 4, 1360 ]

------Rank------
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 6 generators
Relations:
    2*$.1 = 0
    2*$.2 = 0
    2*$.3 = 0
    2*$.4 = 0
    2*$.5 = 0
    2*$.6 = 0
Mapping from: Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 6 generators
Relations:
    2*$.1 = 0
    2*$.2 = 0
    2*$.3 = 0
    2*$.4 = 0
    2*$.5 = 0
    2*$.6 = 0 to Univariate Quotient Polynomial Algebra in $.1 over Rational 
Field
with modulus $.1^7 + 181/40*$.1^6 + 2747/360*$.1^5 + 7141/1440*$.1^4 - 
    19/20*$.1^3 - 405/128*$.1^2 - 1053/640*$.1 - 729/2560 given by a rule [no 
inverse]

Total time: 3.629 seconds, Total memory usage: 10.54MB
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