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2026-09-28 12:41:47 UTC · Matej Jurasić

commented on curve #3553

Rank exactly 19, torsion Z/2Z. Specialization at T = 51349/6454 of the rank-9 fibration of X400 (equations as in curve#802).
2026-09-28 12:05:33 UTC · Ritik Jain

submitted curve #3557 — rank ≥ 29, log |Δ| = 346.58
2026-09-28 12:05:29 UTC · Ritik Jain

submitted curve #3556 — rank ≥ 28, log |Δ| = 334.97
2026-09-28 11:04:12 UTC · Tom Fisher

submitted curve #3555 — rank ≥ 5, torsion ℤ/8ℤ, log |Δ| = 197.37
2026-09-28 10:50:01 UTC · Tom Fisher

submitted curve #3554 — rank ≥ 4, torsion ℤ/4ℤ, log |Δ| = 46.65
2026-09-28 10:48:46 UTC · Matej Jurasić

commented on curve #3553

Specialization at T = 51349/6454 of the rank-9 fibration of X400 (equations as in curve#802).
2026-09-28 10:48:46 UTC · Matej Jurasić

submitted curve #3553 — rank ≥ 19, torsion ℤ/2ℤ, log |Δ| = 315.70 ☆ record for ℤ/2ℤ torsion, rank ≥ 19: conductor, Faltings height, naive height
2026-09-28 10:46:05 UTC · Tom Fisher

submitted curve #3552 — rank ≥ 4, torsion ℤ/4ℤ, log |Δ| = 48.68
2026-09-28 10:41:19 UTC · Matej Jurasić

commented on curve #3551

Specialization at T = 7258/7029 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).
2026-09-28 10:41:19 UTC · Matej Jurasić

submitted curve #3551 — rank ≥ 29, log |Δ| = 339.56
2026-09-28 08:36:16 UTC · Matej Jurasić

commented on curve #3550

Specialization at T = 45/11 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).
2026-09-28 08:36:16 UTC · Matej Jurasić

submitted curve #3550 — rank ≥ 23, log |Δ| = 206.04 ★ record for rank ≥ 23: discriminant, Faltings height, naive height
2026-09-28 08:35:18 UTC · Matej Jurasić

commented on curve #3549

Specialization at T = -107/161 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).
2026-09-28 08:35:18 UTC · Matej Jurasić

submitted curve #3549 — rank ≥ 26, log |Δ| = 265.70 ★ record for rank ≥ 26: discriminant, Faltings height, naive height
2026-09-28 05:57:23 UTC · Steps Unbounded

commented on curve #3548

2-isogenous partner of curve#3547 (Fermigier 2-torsion construction; Dujella, Proc. Japan Acad. 78 (2002)). Rank exactly 13 by 2-descent: 13 independent points, 2-Selmer upper bound 13. Torsion Z/2Z, root number -1.
2026-09-28 05:57:21 UTC · Steps Unbounded

commented on curve #3547

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…
2026-09-28 05:54:00 UTC · Steps Unbounded

commented on curve #3547

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…
2026-09-28 05:53:54 UTC · Steps Unbounded

commented on curve #3548

2-isogenous partner of curve#3547 (Fermigier 2-torsion construction; Dujella, Proc. Japan Acad. 78 (2002)). Rank exactly 13 by 2-descent: 13 independent points, 2-Selmer upper bound 13. Torsion Z/2Z, root number -1, conductor 2*3*17^2*59*157*257^2*307*593^2*619*827*1543*1723*3779…
2026-09-28 05:53:54 UTC · Steps Unbounded

submitted curve #3548 — rank ≥ 13, torsion ℤ/2ℤ, log |Δ| = 143.60 ☆ record for ℤ/2ℤ torsion, rank ≥ 13: conductor
2026-09-28 05:51:57 UTC · Steps Unbounded

commented on curve #3547

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…
2026-09-28 05:49:19 UTC · Steps Unbounded

commented on curve #3547

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 s…
2026-09-28 05:49:19 UTC · Steps Unbounded

submitted curve #3547 — rank ≥ 13, torsion ℤ/2ℤ, log |Δ| = 136.61 ☆ record for ℤ/2ℤ torsion, rank ≥ 13: conductor, discriminant, Faltings height
2026-09-28 01:56:19 UTC · wgxli

commented on curve #3545

Specialization at T = 1385746/32591 of the rank-17 fibration of X1092 given by: y^2 + (Lx+B)y = x(x+D)(x+E), where B = pE + qD + pq(L-p-q), L = 67471T^2 - 41284T + 2226804, p = 42194T^2 + 309567T - 510125, q = 50198T^2 + 3823T - 546298, D = 1972452336T^4 + 3250176116T^3 - …
2026-09-28 01:06:10 UTC · wgxli

commented on curve #3546

2-isogenous to curve #3544.
2026-09-28 01:06:09 UTC · wgxli

submitted curve #3546 — rank ≥ 16, torsion ℤ/2ℤ, log |Δ| = 203.92 ☆ record for ℤ/2ℤ torsion, rank ≥ 16: conductor
2026-09-28 01:05:39 UTC · Ritik Jain

submitted curve #3545 — rank ≥ 31, log |Δ| = 458.63
2026-09-28 01:05:09 UTC · wgxli

commented on curve #3544

Construction adapted from S. Kihara, Proc. Japan Acad., 77, Ser. A (2001). Parameters (a, b, c, u) = (408, 1129, 1166, 556). With apologies to @mathandcobb!
2026-09-28 01:05:09 UTC · wgxli

submitted curve #3544 — rank ≥ 16, torsion ℤ/2ℤ, log |Δ| = 197.66 ☆ record for ℤ/2ℤ torsion, rank ≥ 16: conductor, discriminant, Faltings height, naive height
2026-09-28 00:33:30 UTC · Matej Jurasić

commented on curve #3543

Specialization at T = -5/22 of the rank-17 fibration of X1008 (equations as in curve#751).
2026-09-28 00:33:30 UTC · Matej Jurasić

submitted curve #3543 — rank ≥ 18, log |Δ| = 175.30