curve #5718

y² + y = x³ − 33697879483443796376239842240919

a-invariants: [0, 0, 1, 0, -33697879483443796376239842240919]
c-invariants: [0, 29114967873695440069071223696153800]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 134791517933775185504959368963675
discriminant (Δ): -490556339286063411265448376512904044976316632076457296773676651875
Faltings height: 11.2837
naive height: 158.7131
primes of bad reduction: 3, 5, 11, 13, 19, 29, 107, 149, 283, 419
regulator: 8731704072599.44282616134242473814784208379697742879805
submitted by: Maksym Voznyy
submitted at: 2026-10-24 15:58:08 UTC
last updated: 2026-10-24 15:58:08 UTC

(5827427543162184833722782147072430294969/5259067824683822063261893924, -444846261409877901069670037960076305324458304344038035991081/381384604500365578784024579470947345596968)
(380465849995653926810641/224683584064, 234677803583749195432015759595528583/106501816315008512)
(564182917810274844780641809/9884515356810000, 12125878237301230922613705228293705324377/982727412837871329000000)
(8741606179527473045049458423400562014889/10450303147332546034768994884, -817286553186428909335912064661739015232771669791942838317087/1068300257989665938452415967464113143905848)
(119235991883098012181386646206759514649835646884625036026718933209/1771006872203690361494405973372764159559341053686482884, -38833270153809161266819347828322560857572632267235219751219227355623587131983226973024360254079849/2356841461370527305690737541349080193905243983657941120572185329093052317783790152)
(2043192216149349192452088963824643265969/57069503528374941171762602500, 47603704432245566288372780121385011382306706502407136446547/13633461676457748814853676830020863488875000)
(5363058550986464761/109998144, 10459675519906147603158643955/1153660534272)
(647803323579692314602023339748009112969/19902367450356674984123817744, -2489145673214007371341826850658596793317843240065986854917/2807741429809435788949272219252677956398528)

Voznyy (2023), A = -2234340717525345, [r, s, t] = [65, 200, 283] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 15:58:08 UTC · history