curve #739

y² = x³ + x² − 17468920404587017778067942713090785x + 962832039495517952887468773316368993353086347426275

a-invariants: [0, 1, 0, -17468920404587017778067942713090785, 962832039495517952887468773316368993353086347426275]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 983631275147347131453459375659466622093811631944182198659688972050478637343069240
naive height: 248.3111
Faltings height: 18.6523
discriminant (Δ): -59307908241598546438865701982056710913996630831929085812610204578814452759852694747757025704437740000000
primes of bad reduction: 2, 3, 5, 11, 17, 37, 53, 89, 157, 211, 20327, 114407, 49217265343, 852073668103103, 77739055503716341272673923084877
regulator: 10702107244251528767200.97852301754228020298401664062209722482669133270779476688721
submitted by: Valery Asiryan
submitted at: 2026-09-16 17:42:40 UTC
last updated: 2026-09-16 17:42:40 UTC

Witness: 22 independent points log in to add more points →

(-147078316185017770, -18722412492129051263827875)
(-156704864824627310155/1156, -1139056768486310154472297960335/39304)
(-124399349263052905, -34797267093289670832579090)
(-123708859458443245, -35080856353985570556827850)
(-25535954732985941395/5476, -13094395625225531805953617450125/405224)
(27011635681505975, -22598150012360131146882030)
(61119219521704655, -11111242447563485342968050)
(711360060829812075509105/10699441, -341634616478075969027554341320116050/34997871511)
(682238096699718355/9, -232586479820857835681278930/27)
(4104520999781999287/49, -3204691722228926977751820642/343)
(96769367784292355, -13362412465338196771730250)
(104115882234869855, -16512671435792596407947250)
(154623454275178223, -44255265996059389191349746)
(205672371786027215, -77911041295717724245178610)
(445644380301676055, -285801321993460832995757550)
(629153264306216795, -488888893310436223238626710)
(1911520121723369855, -2636681920820841174723947250)
(2337185248428664505, -3567472069097739239151628650)
(40160990927514442385/16, -254165719267437506048507684895/64)
(48594219428965341070/9, -338647667009430679255613009125/27)
(10848171928786689230, -35727511464007371210995760375)
(21522522899528216255, -99846213496374004425756740850)

Commentary

Specialization T=-27/47 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 22 listed points are certified independent by exact quadratic-character certificates.

last edited by Valery Asiryan at 2026-09-16 17:42:40 UTC · history