curve #2904

y² + xy + y = x³ − 15567874057780318695179x + 837427183239068708883156864245306

a-invariants: [1, 0, 1, -15567874057780318695179, 837427183239068708883156864245306]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 21562908872242620554490
discriminant (Δ): -61482187436127611179256998582710011973699216285785466845330039406900
Faltings height: 11.7375
naive height: 165.1389
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 43, 47, 59, 199, 4253, 200171
regulator: 316897.5759408076962191978870332924308876377517854516
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:41 UTC
last updated: 2026-09-26 20:27:41 UTC

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

(-32139533487987374/1476225, 61247190507620849513440156/1793613375)
(45930010734004324/140625, 9223935642228073786865582/52734375)
(43645757670296/25, -287630941043294057946/125)
(-122934054739, -29889293125883808)
(-1196861745765433/26569, -164756524879427584584654/4330747)
(169560533842875589/144, -69821177182803145764946717/1728)
(138308037549137641698/3575881, -1626555577020812997760756378157/6761990971)

Commentary

2-isogenous to curve#1264 via the rational 2-torsion point x=72981399279. 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 20:27:41 UTC · history