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2026-09-27 08:24:09 UTC · hdeping

commented on curve #1265

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+txy+(t+2)y=x^3 with torsion Z/6Z, at t=589163/23621.
2026-09-27 08:23:52 UTC · hdeping

commented on curve #1803

Rank 11 with torsion Z/2Z x Z/2Z induced by a rational Diophantine triple, smallest known conductor in its class (Dujella-Peral 2017/2020); witness points from the paper.
2026-09-27 08:23:37 UTC · hdeping

commented on curve #1802

Rank 12 with torsion Z/2Z x Z/2Z induced by a rational Diophantine triple (Dujella-Peral, RACSAM 113 (2019)); witness points from the paper.
2026-09-27 08:23:21 UTC · hdeping

commented on curve #810

Specialization at T = -15/604 of the genus-one fibration with 17 independent sections behind the rank-30/31 records #273/#302 (the 'wgxli' family y^2-(Lx+B)y = x(x+D)(x+E)), with 25 independent rational points.
2026-09-27 08:23:06 UTC · hdeping

commented on curve #813

Specialization at T = -511/4961 of the genus-one fibration with 17 independent sections behind the rank-30/31 records #273/#302 (the 'wgxli' family y^2-(Lx+B)y = x(x+D)(x+E)), with 26 independent rational points.
2026-09-27 08:22:50 UTC · hdeping

commented on curve #807

Fiber T = -683/2288 of the wgxli #302 elliptic K3 fibration (Gonzalez-Rotger 2004 / Elkies 2007), with 26 independent rational points.
2026-09-27 08:22:37 UTC · hdeping

commented on curve #807

Fiber T = -683/2288 of the wgxli #302 elliptic K3 fibration (Gonzalez-Rotger 2004 / Elkies 2007), with 26 independent rational points.
2026-09-27 08:15:46 UTC · Tom Fisher

submitted curve #3476 — rank ≥ 5, torsion ℤ/6ℤ, log |Δ| = 91.19
2026-09-27 08:09:21 UTC · Tom Fisher

submitted curve #3475 — rank ≥ 5, torsion ℤ/6ℤ, log |Δ| = 84.20 ☆ record for ℤ/6ℤ torsion, rank ≥ 5: naive height
2026-09-27 08:01:24 UTC · jesper-petersen

commented on curve #3474

Found by a conductor-oriented search in the standard Z/2Z x Z/4Z family \(y^2=x(x+u^2)(x+v^2)\), using conditions \(u+v=d w^2\) with small squarefree \(d\). Here \((u,v)=(8791,11900)\) and \(u+v=20691=19\cdot33^2\). PARI/GP 2.17.4 gives exact rank 5 and torsion Z/2Z x Z/4Z. Condu…
2026-09-27 08:01:24 UTC · jesper-petersen

submitted curve #3474 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 104.28
2026-09-27 07:20:35 UTC · jesper-petersen

commented on curve #3473

Found by a conductor-oriented search in the standard Z/2Z x Z/4Z family y^2 = x(x+u^2)(x+v^2), using the square-sum condition u+v=w^2. Here (u,v)=(3431,7178), with u+v=10609=103^2. The relevant factorization is u=4773, v=23797, v-u=31249, v+u=103^2. PARI/GP 2.17.4 gives exac…
2026-09-27 07:20:35 UTC · jesper-petersen

submitted curve #3473 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 105.85
2026-09-27 06:36:16 UTC · Steps Unbounded

commented on curve #3472

Z/2Z curve from the Elkies-Klagsbrun rank-9 family y^2=x^3+2A(t,u)x^2+B(t,u)x (Elkies-Klagsbrun 2020), fibre u=2/5, t=1546/487. Found by sweeping t=a/b with |a|,b<=8192 using the lossless conic-Hilbert prefilter of Breddin (Zenodo 10.5281/zenodo.22242109), screened with PARI ellr…
2026-09-27 06:36:16 UTC · Steps Unbounded

submitted curve #3472 — rank ≥ 17, torsion ℤ/2ℤ, log |Δ| = 272.62
2026-09-27 06:36:13 UTC · Steps Unbounded

commented on curve #3471

Z/2Z curve from the Elkies-Klagsbrun rank-9 family y^2=x^3+2A(t,u)x^2+B(t,u)x (Elkies-Klagsbrun 2020), fibre u=2/5, t=-921/2080. Found by sweeping t=a/b with |a|,b<=8192 using the lossless conic-Hilbert prefilter of Breddin (Zenodo 10.5281/zenodo.22242109), screened with PARI ell…
2026-09-27 06:36:13 UTC · Steps Unbounded

submitted curve #3471 — rank ≥ 16, torsion ℤ/2ℤ, log |Δ| = 242.13
2026-09-27 05:43:28 UTC · Michael Rubinstein

commented on curve #3470

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank
2026-09-27 05:43:28 UTC · Michael Rubinstein

submitted curve #3470 — rank ≥ 9, torsion ℤ/2ℤ, log |Δ| = 78.28
2026-09-27 05:43:18 UTC · Michael Rubinstein

commented on curve #3469

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank
2026-09-27 05:43:18 UTC · Michael Rubinstein

submitted curve #3469 — rank ≥ 7, torsion ℤ/3ℤ, log |Δ| = 80.91
2026-09-27 05:43:07 UTC · Michael Rubinstein

commented on curve #3468

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank
2026-09-27 05:43:07 UTC · Michael Rubinstein

submitted curve #3468 — rank ≥ 6, torsion ℤ/3ℤ, log |Δ| = 78.01
2026-09-27 05:42:57 UTC · Michael Rubinstein

commented on curve #3467

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank
2026-09-27 05:42:57 UTC · Michael Rubinstein

submitted curve #3467 — rank ≥ 9, torsion ℤ/2ℤ, log |Δ| = 78.14
2026-09-27 05:42:47 UTC · Michael Rubinstein

commented on curve #3466

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank
2026-09-27 05:42:47 UTC · Michael Rubinstein

submitted curve #3466 — rank ≥ 8, torsion ℤ/3ℤ, log |Δ| = 98.31
2026-09-27 05:42:37 UTC · Michael Rubinstein

commented on curve #3465

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank
2026-09-27 05:42:37 UTC · Michael Rubinstein

submitted curve #3465 — rank ≥ 8, torsion ℤ/2ℤ, log |Δ| = 62.96
2026-09-27 05:42:27 UTC · Michael Rubinstein

commented on curve #3464

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank