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2026-09-26 20:22:56 UTC · David Renshaw

commented on curve #2798

Cremona 2454b1 = LMFDB 2454.a1: https://www.lmfdb.org/EllipticCurve/Q/2454/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 2454, minimal discriminant 14724, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:22:56 UTC · David Renshaw

submitted curve #2798 — rank ≥ 2, torsion ℤ/2ℤ, log |Δ| = 9.60
2026-09-26 20:22:53 UTC · Natanael Wildner Fraga

commented on curve #2797

Dujella - Petricevic - Rathbun (2022). Source: https://dujella.github.io/tors/z9.html (curve entry 6). Published independent points; exact point coordinates checked.
2026-09-26 20:22:53 UTC · Natanael Wildner Fraga

submitted curve #2797 — rank ≥ 4, torsion ℤ/9ℤ, log |Δ| = 261.93
2026-09-26 20:22:49 UTC · Natanael Wildner Fraga

commented on curve #2796

Dujella (2008). Source: https://dujella.github.io/tors/z10.html (curve entry 4). Published independent points; exact point coordinates checked.
2026-09-26 20:22:49 UTC · Natanael Wildner Fraga

submitted curve #2796 — rank ≥ 4, torsion ℤ/10ℤ, log |Δ| = 263.44
2026-09-26 20:22:46 UTC · David Renshaw

commented on curve #2795

Cremona 199728a2 = LMFDB 199728.b2: https://www.lmfdb.org/EllipticCurve/Q/199728/b/2 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 199728, minimal discriminant 51699091083264, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:22:46 UTC · David Renshaw

submitted curve #2795 — rank ≥ 3, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 31.58
2026-09-26 20:22:45 UTC · Natanael Wildner Fraga

commented on curve #2794

Voznyy (2026). Source: https://dujella.github.io/tors/z9.html (curve entry 7). Published independent points; exact point coordinates checked.
2026-09-26 20:22:45 UTC · Natanael Wildner Fraga

submitted curve #2794 — rank ≥ 4, torsion ℤ/9ℤ, log |Δ| = 305.99
2026-09-26 20:22:41 UTC · Natanael Wildner Fraga

commented on curve #2793

Dujella (2008). Source: https://dujella.github.io/tors/z10.html (curve entry 5). Published independent points; exact point coordinates checked.
2026-09-26 20:22:41 UTC · Natanael Wildner Fraga

submitted curve #2793 — rank ≥ 4, torsion ℤ/10ℤ, log |Δ| = 268.46
2026-09-26 20:22:38 UTC · Natanael Wildner Fraga

submitted curve #2792 — rank ≥ 4, log |Δ| = 14.03
2026-09-26 20:22:35 UTC · Natanael Wildner Fraga

commented on curve #2790

2-isogenous to curve#1585 via the rational 2-torsion point x=18. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence i…
2026-09-26 20:22:35 UTC · David Renshaw

commented on curve #2791

Cremona 498675d2 = LMFDB 498675.d2: https://www.lmfdb.org/EllipticCurve/Q/498675/d/2 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 498675, minimal discriminant 6216918890625, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:22:35 UTC · David Renshaw

submitted curve #2791 — rank ≥ 3, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 29.46
2026-09-26 20:22:34 UTC · Natanael Wildner Fraga

submitted curve #2790 — rank ≥ 4, torsion ℤ/2ℤ, log |Δ| = 26.61
2026-09-26 20:22:31 UTC · Natanael Wildner Fraga

commented on curve #2789

2-isogenous image of D-z10-004, rational kernel x=-63094581573040382401/4. Source: https://dujella.github.io/tors/z10.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadrat…
2026-09-26 20:22:31 UTC · Natanael Wildner Fraga

submitted curve #2789 — rank ≥ 4, torsion ℤ/10ℤ, log |Δ| = 250.90
2026-09-26 20:22:27 UTC · Natanael Wildner Fraga

submitted curve #2788 — rank ≥ 4, log |Δ| = 14.64
2026-09-26 20:22:25 UTC · David Renshaw

commented on curve #2787

Cremona 8502b2 = LMFDB 8502.b2: https://www.lmfdb.org/EllipticCurve/Q/8502/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 8502, minimal discriminant 72284004, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:22:25 UTC · David Renshaw

submitted curve #2787 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 18.10
2026-09-26 20:22:24 UTC · Natanael Wildner Fraga

submitted curve #2786 — rank ≥ 4, log |Δ| = 15.03
2026-09-26 20:22:21 UTC · Natanael Wildner Fraga

submitted curve #2785 — rank ≥ 4, log |Δ| = 14.38
2026-09-26 20:22:17 UTC · Natanael Wildner Fraga

commented on curve #2784

Elkies (2006). Source: https://dujella.github.io/tors/z10.html (curve entry 3). Published independent points; exact point coordinates checked.
2026-09-26 20:22:17 UTC · Natanael Wildner Fraga

submitted curve #2784 — rank ≥ 4, torsion ℤ/10ℤ, log |Δ| = 264.27
2026-09-26 20:22:15 UTC · David Renshaw

commented on curve #2783

Cremona 10560bl2 = LMFDB 10560.b2: https://www.lmfdb.org/EllipticCurve/Q/10560/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 10560, minimal discriminant 111513600, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:22:15 UTC · David Renshaw

submitted curve #2783 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 18.53
2026-09-26 20:22:13 UTC · Natanael Wildner Fraga

commented on curve #2782

2-isogenous image of D-z10-006, rational kernel x=6914743098109976052. Source: https://dujella.github.io/tors/z10.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-c…
2026-09-26 20:22:13 UTC · Natanael Wildner Fraga

submitted curve #2782 — rank ≥ 4, torsion ℤ/10ℤ, log |Δ| = 269.10