curve #6379

y² + xy + y = x³ − x² − 233635452414722627x + 5165975917630103865042179

a-invariants: [1, -1, 1, -233635452414722627, 5165975917630103865042179]
c-invariants: [11214501715906686081, -4463403142367152017816355521]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/6ℤ
conductor (N): 12853086609924990
discriminant (Δ): 804670362986398715117226718531527670828653114657096000
Faltings height: 9.0333
naive height: 131.5912
primes of bad reduction: 2, 3, 5, 11, 13, 67, 79, 277, 751, 907
regulator: 659511.12229662358993083618796122905347913388364986
submitted by: apkorte
submitted at: 2026-11-01 21:02:15 UTC
last updated: 2026-11-01 21:02:15 UTC

Witness: 6 independent points log in to add more points →

(-1718327022627/3481, 94657854415139882/205379)
(295055061/25, -194061253454506/125)
(-6938465817/49, -2041036972024742/343)
(-462735561, -3767331021902)
(16962488431/4, -2194890804639529/8)
(-138098641544661/280900, 163229740544336815277/148877000)

Commentary

2-isogenous to curve#6362 (submitted by The Wren; the images of its points under the isogeny, moved to the minimal model). Found by Claude (Anthropic) in a scan of the isogeny classes of all leaderboard curves.

last edited by apkorte at 2026-11-01 21:02:16 UTC · history