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2026-09-26 20:35:17 UTC · Natanael Wildner Fraga

submitted curve #3057 — rank ≥ 8, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 219.12
2026-09-26 20:35:17 UTC · David Renshaw

submitted curve #3058 — rank ≥ 1, torsion ℤ/8ℤ, log |Δ| = 36.78
2026-09-26 20:35:14 UTC · Natanael Wildner Fraga

commented on curve #3056

Dujella - Peral - Tadic (2019). Source: https://dujella.github.io/tors/z6old678.html (curve entry 25). Published independent points; exact point coordinates checked.
2026-09-26 20:35:13 UTC · Natanael Wildner Fraga

submitted curve #3056 — rank ≥ 8, torsion ℤ/6ℤ, log |Δ| = 193.44
2026-09-26 20:35:10 UTC · Natanael Wildner Fraga

commented on curve #3055

Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 50). Published independent points; exact point coordinates checked.
2026-09-26 20:35:10 UTC · Natanael Wildner Fraga

submitted curve #3055 — rank ≥ 8, torsion ℤ/6ℤ, log |Δ| = 200.74
2026-09-26 20:35:08 UTC · David Renshaw

commented on curve #3054

Cremona 6006bd1 = LMFDB 6006.bb6: https://www.lmfdb.org/EllipticCurve/Q/6006/bb/6 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 6006, minimal discriminant -425928037217050368, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.
2026-09-26 20:35:08 UTC · David Renshaw

submitted curve #3054 — rank ≥ 1, torsion ℤ/8ℤ, log |Δ| = 40.59
2026-09-26 20:35:06 UTC · Natanael Wildner Fraga

commented on curve #3053

2-isogenous image of D-z2z4old678-023, rational kernel x=1402149274312. Source: https://dujella.github.io/tors/z2z4old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; qua…
2026-09-26 20:35:06 UTC · Natanael Wildner Fraga

submitted curve #3053 — rank ≥ 8, torsion ℤ/4ℤ, log |Δ| = 179.07
2026-09-26 20:35:03 UTC · Natanael Wildner Fraga

commented on curve #3052

2-isogenous image of D-z2z4old678-023, rational kernel x=-3382740935541. Source: https://dujella.github.io/tors/z2z4old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; qu…
2026-09-26 20:35:02 UTC · Natanael Wildner Fraga

submitted curve #3052 — rank ≥ 8, torsion ℤ/4ℤ, log |Δ| = 164.07
2026-09-26 20:34:59 UTC · Natanael Wildner Fraga

commented on curve #3051

Voznyy (2021). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 30). Published independent points; exact point coordinates checked. One witness is a half of a published relation, giving a 2-saturated independent set.
2026-09-26 20:34:59 UTC · Natanael Wildner Fraga

submitted curve #3051 — rank ≥ 8, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 230.53
2026-09-26 20:34:58 UTC · David Renshaw

commented on curve #3050

Cremona 7854o4 = LMFDB 7854.p5: https://www.lmfdb.org/EllipticCurve/Q/7854/p/5 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 7854, minimal discriminant -18744614063916048, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.
2026-09-26 20:34:58 UTC · David Renshaw

submitted curve #3050 — rank ≥ 1, torsion ℤ/8ℤ, log |Δ| = 37.47
2026-09-26 20:34:55 UTC · Natanael Wildner Fraga

commented on curve #3049

Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 66). Published independent points; exact point coordinates checked.
2026-09-26 20:34:55 UTC · Natanael Wildner Fraga

submitted curve #3049 — rank ≥ 8, torsion ℤ/6ℤ, log |Δ| = 202.73
2026-09-26 20:34:51 UTC · Natanael Wildner Fraga

commented on curve #3048

Dujella - Eroshkin (2008). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 4). Published independent points; exact point coordinates checked.
2026-09-26 20:34:51 UTC · Natanael Wildner Fraga

submitted curve #3048 — rank ≥ 8, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 210.92
2026-09-26 20:34:48 UTC · David Renshaw

commented on curve #3047

Cremona 43230o1 = LMFDB 43230.n4: https://www.lmfdb.org/EllipticCurve/Q/43230/n/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 43230, minimal discriminant 31777292250000, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:34:48 UTC · David Renshaw

submitted curve #3047 — rank ≥ 2, torsion ℤ/6ℤ, log |Δ| = 31.09
2026-09-26 20:34:47 UTC · Natanael Wildner Fraga

commented on curve #3046

2-isogenous to curve#1347 via the rational 2-torsion point x=24843. 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 independenc…
2026-09-26 20:34:47 UTC · Natanael Wildner Fraga

submitted curve #3046 — rank ≥ 8, torsion ℤ/2ℤ, log |Δ| = 68.07
2026-09-26 20:34:44 UTC · Natanael Wildner Fraga

commented on curve #3045

2-isogenous image of D-z6old678-065, rational kernel x=291804693239683. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadr…
2026-09-26 20:34:43 UTC · Natanael Wildner Fraga

submitted curve #3045 — rank ≥ 8, torsion ℤ/6ℤ, log |Δ| = 201.64
2026-09-26 20:34:40 UTC · Natanael Wildner Fraga

commented on curve #3044

Dujella - Lecacheux - Petricevic (2021). Source: https://dujella.github.io/tors/z5old678.html (curve entry 10). Published independent points; exact point coordinates checked.
2026-09-26 20:34:40 UTC · Natanael Wildner Fraga

submitted curve #3044 — rank ≥ 8, torsion ℤ/5ℤ, log |Δ| = 207.80
2026-09-26 20:34:38 UTC · David Renshaw

commented on curve #3043

Cremona 115430r1 = LMFDB 115430.k3: https://www.lmfdb.org/EllipticCurve/Q/115430/k/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 115430, minimal discriminant 23351489000000, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.
2026-09-26 20:34:38 UTC · David Renshaw

submitted curve #3043 — rank ≥ 2, torsion ℤ/6ℤ, log |Δ| = 30.78