curve #741

y² + xy + y = x³ − x² − 24719180212828601579170057492160791112x + 47391702870825156302880358121555810584233426223310576011

a-invariants: [1, -1, 1, -24719180212828601579170057492160791112, 47391702870825156302880358121555810584233426223310576011]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 285127989577366463602132412866032046495440428541331418487010272748599472215982187571742566090
naive height: 269.9192
Faltings height: 20.2896
discriminant (Δ): -3581817381584736626539463005040817283661181362510750827824228493835005777574473248347475247679189446389350400000
primes of bad reduction: 2, 3, 5, 7, 19, 71, 167, 331, 6069359856253097435968757534882932707863997605785760719997398795931953981426425791
regulator: 5526246359474649847727468.47853535152504266359101957419652333514191673253699445774117
submitted by: Valery Asiryan
submitted at: 2026-09-16 18:14:06 UTC
last updated: 2026-09-16 18:14:06 UTC

Witness: 23 independent points log in to add more points →

(-22575665299102729301/4, -21353487918194478103500509003/8)
(-1530719795708822612261/289, -26787410737448509035988635381053/4913)
(-4832733281848505399, -7347306928417846304904593131)
(-4577561193529737779, -8039075901141629108583061351)
(2787058054379729023549/21904, -21564253737022941925286348350825597/3241792)
(1064553192973284061, -4720513804264481972715394711)
(2755570362973209101, -446957774487481156733454631)
(1236649940928174013669/441, -3275773587788014820368488006491/9261)
(2815341335213744461, -337019073743250492215490151)
(2854297658463146845, -299684601584575040329349143)
(2863314574029295195, -296647735793977492589508973)
(3112304753238993781, -777969655096012041637388191)
(3840255605086087969, -3016313050844787695476354351)
(3940012470857440381, -3340866557604030454744700791)
(15155610266640817741, -56159485354659128123567008231)
(26392308830609903221, -133336652277112992703816947871)
(44302531378709882381, -293096367644938946602706154791)
(48873318470260445851, -339967871052194716215454414381)
(53359276904856718381, -388141199433402919404101786791)
(187641881641776082381, -2569471019355850395692985554791)
(237094338194774458361, -3649951039343480925580881020411)
(524310693823647927931, -12005040185089405474501401544141)
(955087478061963815161, -29516091914473020230414210711551)

Commentary

Specialization T=-61/126 of the family identified by wgxli in the commentary to curve #302. The points were obtained by specializing reconstructed generic sections and running minimized quartic searches. The 23 listed points are certified independent by exact quadratic-character certificates.

last edited by Valery Asiryan at 2026-09-16 18:14:06 UTC · history