curve #6235

y² + xy + y = x³ + x² − 2317287964796394204437459324377248668263856413x + 42593050888125128567306673953754804140449392074346524680311961340531

a-invariants: [1, 1, 1, -2317287964796394204437459324377248668263856413, 42593050888125128567306673953754804140449392074346524680311961340531]
c-invariants: [111229822310226921812998047570107936076665107825, -36800395967340111082153800519711477479261872237592173133310109586527625]
rank (lower bound): ≥ 19
torsion subgroup: ℤ/2ℤ
conductor (N): 85846100457142021413369807897710852813676285438536199952814698136832974679317780550
discriminant (Δ): 12658784334903009992753570966874662638458697522633265368482625249985234781616339907461801028321987203411202100127584057744411750168000000
Faltings height: 24.9374
naive height: 324.9838
primes of bad reduction: 2, 3, 5, 11, 13, 19, 31, 71, 73, 79, 83, 157, 211, 223, 227, 251, 443, 521, 1627, 3191, 4373, 7109, 8731, 27061, 109829, 118189, 184181, 64459907
regulator: 4329975062715649381539466273.950388170048370431758463113150016255137853334598
submitted by: apkorte
submitted at: 2026-10-31 11:27:21 UTC
last updated: 2026-10-31 11:27:21 UTC

Witness: 19 independent points log in to add more points →

(15877779695157894128980531/225, -51238132361232659204936107488564711116/3375)
(60581244044177041692722461/2025, -18927391744763201478767355848643078644/91125)
(6799336292069072106227071/225, 1361208721935752952804931103536741036/3375)
(2413464911114581005865045/81, 3875217804444300969479149323996508/729)
(23761997077688333533611631/25, -115685119330059075129167890879072550236/125)
(31689913326476541035995, 991469018012676895343798250541852)
(927456386195487768114231/25, 346484976797779130761575067111708364/125)
(30563560719516142541095, 564673766900443723596722891762452)
(40261800747159587456095, -3815724159539529946752474590770548)
(6036742019310153647048545/81, -12281987102374807993362568733548240742/729)
(41999035518773216737249, -4399100752444256227715340299979462)
(1460344403821680758751651/49, 17096523431845434074964520007243284/343)
(3982470222020108884239026259/41209, 224657982444896165220731001873006765413576/8365427)
(58062930381471091733211979/49, 442074363370269766611331451559682228440/343)
(12632686298421254435092367286871/215003569, -32955959336276953188825160166852255046739319764/3152597332247)
(47109201923753152310471540062764321/312683390761, 9755883991063300423273488323375627681696733728598170/174846611129126741)
(25158950587241403982937102425495/533656201, 76123910515097206518549715287903577211223168252/12327991899301)
(213729388527892802076985865043294295/4857743832841, 54391500910921953640683054204931817144841571032461628/10706608282152716389)
(45537458664476506136024822435431299/17697779089, 9715780871901713806326535605407008949768017535946796/2354388645546937)

Commentary

2-isogenous to curve#6088 (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 2026-10-31 11:27:22 UTC · history