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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 ```