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2026-09-26 20:43:46 UTC · David Renshaw

commented on curve #3231

Cremona 4352h1 = LMFDB 4352.a2: https://www.lmfdb.org/EllipticCurve/Q/4352/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 4352, minimal discriminant 8704, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:43:46 UTC · David Renshaw

submitted curve #3231 — rank ≥ 2, torsion ℤ/2ℤ, log |Δ| = 9.07
2026-09-26 20:43:43 UTC · Natanael Wildner Fraga

commented on curve #3230

Voznyy (2023). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 6). Published independent points; exact point coordinates checked.
2026-09-26 20:43:43 UTC · Natanael Wildner Fraga

submitted curve #3230 — rank ≥ 18, torsion ℤ/2ℤ, log |Δ| = 314.67
2026-09-26 20:43:40 UTC · Natanael Wildner Fraga

commented on curve #3229

2-isogenous image of D-z2old141516171819-006, rational kernel x=70317727086699237217052. Source: https://dujella.github.io/tors/z2old141516171819.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and tr…
2026-09-26 20:43:39 UTC · Natanael Wildner Fraga

submitted curve #3229 — rank ≥ 18, torsion ℤ/2ℤ, log |Δ| = 322.65
2026-09-26 20:43:36 UTC · Natanael Wildner Fraga

commented on curve #3227

Dujella (2009). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 22). Published independent points; exact point coordinates checked.
2026-09-26 20:43:36 UTC · David Renshaw

commented on curve #3228

Cremona 2080d1 = LMFDB 2080.a1: https://www.lmfdb.org/EllipticCurve/Q/2080/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 2080, minimal discriminant 4160, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:43:36 UTC · Natanael Wildner Fraga

submitted curve #3227 — rank ≥ 16, torsion ℤ/2ℤ, log |Δ| = 234.90
2026-09-26 20:43:36 UTC · David Renshaw

submitted curve #3228 — rank ≥ 2, torsion ℤ/2ℤ, log |Δ| = 8.33
2026-09-26 20:43:32 UTC · Natanael Wildner Fraga

commented on curve #3226

2-isogenous image of D-z2old141516171819-022, rational kernel x=528240160300186247/4. Source: https://dujella.github.io/tors/z2old141516171819.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and trans…
2026-09-26 20:43:32 UTC · Natanael Wildner Fraga

submitted curve #3226 — rank ≥ 16, torsion ℤ/2ℤ, log |Δ| = 234.83
2026-09-26 20:43:29 UTC · Natanael Wildner Fraga

commented on curve #3225

Dujella (2009), Aguirre - Peral (2009). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 27). Published independent points; exact point coordinates checked.
2026-09-26 20:43:28 UTC · Natanael Wildner Fraga

submitted curve #3225 — rank ≥ 16, torsion ℤ/2ℤ, log |Δ| = 264.11
2026-09-26 20:43:26 UTC · David Renshaw

commented on curve #3224

Cremona 2130b1 = LMFDB 2130.a2: https://www.lmfdb.org/EllipticCurve/Q/2130/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 2130, minimal discriminant -63900, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:43:26 UTC · David Renshaw

submitted curve #3224 — rank ≥ 2, torsion ℤ/2ℤ, log |Δ| = 11.07
2026-09-26 20:43:25 UTC · Natanael Wildner Fraga

commented on curve #3223

2-isogenous image of D-z2old141516171819-027, rational kernel x=-12420185912395920417/4. Source: https://dujella.github.io/tors/z2old141516171819.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and tr…
2026-09-26 20:43:25 UTC · Natanael Wildner Fraga

submitted curve #3223 — rank ≥ 16, torsion ℤ/2ℤ, log |Δ| = 259.40
2026-09-26 20:43:21 UTC · Natanael Wildner Fraga

commented on curve #3222

2-isogenous image of D-z2old141516171819-050, rational kernel x=-393203196144086129/4. Source: https://dujella.github.io/tors/z2old141516171819.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and tran…
2026-09-26 20:43:21 UTC · Natanael Wildner Fraga

submitted curve #3222 — rank ≥ 15, torsion ℤ/2ℤ, log |Δ| = 237.81
2026-09-26 20:43:17 UTC · David Renshaw

commented on curve #3220

Cremona 4845c1 = LMFDB 4845.a2: https://www.lmfdb.org/EllipticCurve/Q/4845/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 4845, minimal discriminant -92055, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:43:17 UTC · Natanael Wildner Fraga

commented on curve #3221

Dujella (2009). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 50). Published independent points; exact point coordinates checked.
2026-09-26 20:43:17 UTC · David Renshaw

submitted curve #3220 — rank ≥ 2, torsion ℤ/2ℤ, log |Δ| = 11.43
2026-09-26 20:43:17 UTC · Natanael Wildner Fraga

submitted curve #3221 — rank ≥ 15, torsion ℤ/2ℤ, log |Δ| = 242.68
2026-09-26 20:43:14 UTC · Natanael Wildner Fraga

commented on curve #3219

Dujella (2009). Source: https://dujella.github.io/tors/z2old141516171819.html (curve entry 48). Published independent points; exact point coordinates checked.
2026-09-26 20:43:14 UTC · Natanael Wildner Fraga

submitted curve #3219 — rank ≥ 15, torsion ℤ/2ℤ, log |Δ| = 211.63
2026-09-26 20:43:10 UTC · Natanael Wildner Fraga

commented on curve #3218

2-isogenous image of D-z2old141516171819-048, rational kernel x=8340799720431663/4. Source: https://dujella.github.io/tors/z2old141516171819.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transpo…
2026-09-26 20:43:10 UTC · Natanael Wildner Fraga

submitted curve #3218 — rank ≥ 15, torsion ℤ/2ℤ, log |Δ| = 210.83
2026-09-26 20:43:08 UTC · David Renshaw

commented on curve #3217

Cremona 3717b1 = LMFDB 3717.a2: https://www.lmfdb.org/EllipticCurve/Q/3717/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 3717, minimal discriminant 78057, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:43:08 UTC · David Renshaw

submitted curve #3217 — rank ≥ 2, torsion ℤ/2ℤ, log |Δ| = 11.27