Z/2Z curve from the Fermigier 2-torsion construction (Dujella, Proc. Japan Acad. 78 (2002)), parameter s = 5*13*457 = 29705, each factor a sum of two squares (5 = 1^2+2^2, 13 = 2^2+3^2, 457 = 4^2+21^2); normalized model y^2 = x^3 + 76960218985x^2 - 93128508442464837632x, where a2 = s*17*257*593. Rank exactly 13 by 2-descent: 13 independent points, 2-Selmer upper bound 13, both with the supplied points and with no seeded points. Torsion Z/2Z, root number -1.
Z/2Z curve from the Fermigier 2-torsion construction (Dujella, Proc. Japan Acad. 78 (2002)), parameter s = 5*13*457 = 29705, each factor a sum of two squares (5 = 1^2+2^2, 13 = 2^2+3^2, 457 = 4^2+21^2); normalized model y^2 = x^3 + 76960218985x^2 - 93128508442464837632x, where a2 = s*17*257*593. Rank exactly 13 by 2-descent: 13 independent points, 2-Selmer upper bound 13, both with the supplied points and with no seeded points. Torsion Z/2Z, root number -1, conductor 2*3*17^2*59*157*257^2*307*593^2*619*827*1543*1723*3779, log N = 82.3637888819.
Z/2Z curve from the Fermigier 2-torsion construction (Dujella, Proc. Japan Acad. 78 (2002)), parameter s = 5*13*457 = 29705, each factor a sum of two squares (5 = 1^2+2^2, 13 = 2^2+3^2, 457 = 4^2+21^2); normalized model y^2 = x^3 + 76960218985x^2 - 93128508442464837632x, where a2 = s*17*257*593. Rank exactly 13 by 2-descent: 13 independent points, 2-Selmer upper bound 13, both with the supplied points and with no seeded points, and the same for the 2-isogenous partner y^2 = x^3 - 153920437970x^2 + 6295389339989013780753x. Torsion Z/2Z, root number -1, conductor 2*3*17^2*59*157*257^2*307*593^2*619*827*1543*1723*3779, log N = 82.3637888819.
Fermigier Z/2 construction (Dujella, Proc. Japan Acad. 78 (2002)), parameter s = 5*13*457 = 29705, each factor a sum of two squares (5 = 1^2+2^2, 13 = 2^2+3^2, 457 = 4^2+21^2); normalized model y^2 = x^3 + 76960218985x^2 - 93128508442464837632x, whose minimal model is the curve submitted here. Rank exactly 13 by 2-descent: PARI ellrank returns r1 = r2 = 13 both with the 13 points supplied and with no seeded points, for this curve and for its 2-isogenous partner y^2 = x^3 - 153920437970x^2 + 6295389339989013780753x. Torsion Z/2Z, root number -1, conductor 2*3*17^2*59*157*257^2*307*593^2*619*827*1543*1723*3779, log N = 82.3637888819. Re-verified with the project's local re-run of the site pipeline: on-curve 13/13, GP_CERT status = 1 with bound 13, all listed primes prime and exhausting the conductor.
Steps Unbounded ·
Steps Unbounded ·
Steps Unbounded ·
Steps Unbounded ·