curve #5613

y² = x³ − 6171268296481314323971227938146154700

a-invariants: [0, 0, 0, 0, -6171268296481314323971227938146154700]
c-invariants: [0, 5331975808159855575911140938558277660800]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 6171268296481314323971227938146154700
discriminant (Δ): -16452526631251125573547324010007051107739342566938968187131475467215462880000
Faltings height: 13.3034
naive height: 182.9491
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 37, 41, 53, 79, 173, 431
regulator: 96792578083.6284178727008651426538148384755615983776710
submitted by: Maksym Voznyy
submitted at: 2026-10-23 23:02:53 UTC
last updated: 2026-10-23 23:02:53 UTC

(226918179083725006861/107350321, 2012429145727538210339544508541/1112256675881)
(23894914759654676809/688900, -116795500755948741813443768123/571787000)
(29876683470901, -163285764397381937249)
(27299596879782781/6241, 4341124022805618496382971/493039)
(5154366001444994041/264196, 11697211571982314398090354061/135796744)
(26189392222579441/484, 4238182669171076138572361/10648)
(136273762547072714281/8940100, 1589423641037336514048184971179/26730899000)
(62907017067879718950001/23481884644, -13001408004794272959638043724417399/3598317039077272)

Voznyy (2023), A = -956170471123786380, [r, s, t] = [345, 407, 431] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-23 23:02:53 UTC · history