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2026-09-26 20:35:50 UTC · Natanael Wildner Fraga

commented on curve #3070

2-isogenous to curve#1364 via the rational 2-torsion point x=31682. 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 20:35:50 UTC · Natanael Wildner Fraga

submitted curve #3070 — rank ≥ 9, torsion ℤ/2ℤ, log |Δ| = 77.99
2026-09-26 20:35:47 UTC · Natanael Wildner Fraga

commented on curve #3069

Kulesz - Stahlke (2001). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 37). Published independent points; exact point coordinates checked.
2026-09-26 20:35:47 UTC · Natanael Wildner Fraga

submitted curve #3069 — rank ≥ 9, torsion ℤ/4ℤ, log |Δ| = 200.05
2026-09-26 20:35:46 UTC · David Renshaw

commented on curve #3068

Cremona 1933a1 = LMFDB 1933.a1: https://www.lmfdb.org/EllipticCurve/Q/1933/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 1933, minimal discriminant -1933, torsion trivial. The witnesses are the generators from Cremona's tables.
2026-09-26 20:35:46 UTC · David Renshaw

submitted curve #3068 — rank ≥ 2, log |Δ| = 7.57
2026-09-26 20:35:43 UTC · Natanael Wildner Fraga

commented on curve #3067

Dujella (2009). Source: https://dujella.github.io/tors/z4old9101112.html (curve entry 46). Published independent points; exact point coordinates checked.
2026-09-26 20:35:43 UTC · Natanael Wildner Fraga

submitted curve #3067 — rank ≥ 9, torsion ℤ/4ℤ, log |Δ| = 205.70
2026-09-26 20:35:40 UTC · Natanael Wildner Fraga

commented on curve #3066

2-isogenous image of D-z4old9101112-042, rational kernel x=7718659159251. Source: https://dujella.github.io/tors/z4old9101112.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations;…
2026-09-26 20:35:39 UTC · Natanael Wildner Fraga

submitted curve #3066 — rank ≥ 9, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 184.62
2026-09-26 20:35:37 UTC · David Renshaw

commented on curve #3065

Cremona 2181a1 = LMFDB 2181.a1: https://www.lmfdb.org/EllipticCurve/Q/2181/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 2181, minimal discriminant -2181, torsion trivial. The witnesses are the generators from Cremona's tables.
2026-09-26 20:35:37 UTC · David Renshaw

submitted curve #3065 — rank ≥ 2, log |Δ| = 7.69
2026-09-26 20:35:36 UTC · Natanael Wildner Fraga

commented on curve #3064

Elkies - Rogers (2003). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 65). Published independent points; exact point coordinates checked.
2026-09-26 20:35:36 UTC · Natanael Wildner Fraga

submitted curve #3064 — rank ≥ 8, torsion ℤ/3ℤ, log |Δ| = 115.90
2026-09-26 20:35:32 UTC · Natanael Wildner Fraga

commented on curve #3063

Klagsbrun (2020). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 23). Published independent points; exact point coordinates checked.
2026-09-26 20:35:32 UTC · Natanael Wildner Fraga

submitted curve #3063 — rank ≥ 8, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 173.95 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 8: conductor, discriminant, Faltings height, naive height
2026-09-26 20:35:29 UTC · Natanael Wildner Fraga

commented on curve #3062

Dujella - Peral (2016). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 12). Published independent points; exact point coordinates checked.
2026-09-26 20:35:28 UTC · Natanael Wildner Fraga

submitted curve #3062 — rank ≥ 8, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 201.03
2026-09-26 20:35:27 UTC · David Renshaw

commented on curve #3061

Cremona 4080be7 = LMFDB 4080.ba1: https://www.lmfdb.org/EllipticCurve/Q/4080/ba/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 4080, minimal discriminant 3746786595840000, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.
2026-09-26 20:35:27 UTC · David Renshaw

submitted curve #3061 — rank ≥ 1, torsion ℤ/8ℤ, log |Δ| = 35.86
2026-09-26 20:35:25 UTC · Natanael Wildner Fraga

commented on curve #3060

Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 59). Published independent points; exact point coordinates checked.
2026-09-26 20:35:25 UTC · Natanael Wildner Fraga

submitted curve #3060 — rank ≥ 8, torsion ℤ/6ℤ, log |Δ| = 199.21
2026-09-26 20:35:21 UTC · Natanael Wildner Fraga

commented on curve #3059

Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 65). Published independent points; exact point coordinates checked.
2026-09-26 20:35:21 UTC · Natanael Wildner Fraga

submitted curve #3059 — rank ≥ 8, torsion ℤ/6ℤ, log |Δ| = 188.53
2026-09-26 20:35:17 UTC · Natanael Wildner Fraga

commented on curve #3057

Dujella - Peral (2012). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 7). Published independent points; exact point coordinates checked.
2026-09-26 20:35:17 UTC · David Renshaw

commented on curve #3058

Cremona 39270cv1 = LMFDB 39270.ct6: https://www.lmfdb.org/EllipticCurve/Q/39270/ct/6 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 39270, minimal discriminant -9447183900000000, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.
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