curve #2937

y² + xy = x³ − x² − 3492321452228184642204x + 304395796092599346008815791925428

a-invariants: [1, -1, 0, -3492321452228184642204, 304395796092599346008815791925428]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 301672788158929193370
discriminant (Δ): -37301758245181885632846565419139376044852621619348415150495061312500
Faltings height: 11.6487
naive height: 163.1149
primes of bad reduction: 2, 3, 5, 7, 13, 19, 47, 61, 73, 83, 2707, 41227
regulator: 155899.9336216451167649460184613556390350529008851708
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:29:09 UTC
last updated: 2026-09-26 20:29:09 UTC

Witness: 7 independent points log in to add more points →

(244773328996390993/729, -121100558700847029096685168/19683)
(9315580206613/9, -28390031655710197147/27)
(-9563366220467/144, -26959598547870097483/1728)
(14723311170229512/6241, -1785982145887780735795254/493039)
(4261842078115512/11881, -275352099136282551082074/1295029)
(85352208922, -25062150548086096)
(14083899996037272/121, -1671415260911051954693826/1331)

Commentary

2-isogenous to curve#1263 via the rational 2-torsion point x=42142183992. 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 is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:29:09 UTC · history