curve #4062

y² + xy = x³ − 359397521150188723930245745958585103177358083747585x + 2599846326398766021293165718011731172097311156054900963042955736971957609225

a-invariants: [1, 0, 0, -359397521150188723930245745958585103177358083747585, 2599846326398766021293165718011731172097311156054900963042955736971957609225]
c-invariants: [17251081015209058748651795806012084952513188019884081, -2246267226008533842397295206238757255505664961809128141087241185513553404196521]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 2068433157780159063084093615556099330453046637971536818742205532992224375804129639558855110
discriminant (Δ): 51042675694652573590398883350745381663748312989015566489709777129221067847555968193232855520290363198847397780024990290180328246841278063929973145600000
Faltings height: 27.9287
naive height: 360.8391
primes of bad reduction: 2, 3, 5, 11, 13, 19, 23, 31, 53, 71, 79, 89, 103, 107, 113, 127, 151, 271, 283, 293, 739, 743, 977, 1471, 3191, 3617, 744701, 1489951, 14742361, 28928843, 1705548529
regulator: 8127641834889432391954333.07849854328980187793461046728289192566974769287547666
submitted by: wgxli
submitted at: 2026-10-08 21:47:07 UTC
last updated: 2026-10-08 21:47:07 UTC

Witness: 20 independent points log in to add more points →

(10100759858053392652478310, 437982347020698623128076672411461575)
(11767848399649421208942570, 385974660456980680347676006703747115)
(9121611261237192191273700, 8972987033843719529382551158908209985)
(9371303262773785051456170, 7404284695517165827166446794970931115)
(9966374341466715936560466, 2811099106772951786004791986371256827)
(10073662059919322054201340, 1288003806136875249694917036728373945)
(12343818428079422338273530, 6658407160972954783940569100649690315)
(12455822459965145873190570, 7466223232252669211979930236041062315)
(2978226757575339515996970, 39444839853928711266458909871370527915)
(6325215335866747788522570, 24075735438187980365891550630980730315)
(6671595833476533680514870, 22339322423079590902537997452128416115)
(7876964462627783725712982, 16050652464282401236453503882136537011)
(16142986220726589628648170, 31700075684996371305469169312475971115)
(69215856523125036557390250, 556170453018738877936105498909913382315)
(138301997740740825446598030, 1611911279049219280004967343000123789155)
(5187391966888292767915013754/169, 314466819591720973374997772090002387374279/2197)
(-27326196877575586381349558070/1681, 4438040304317773598542044688752759355940115/68921)
(27173974118326303229095892650/3969, 5363761707566058900369470166857573547142805/250047)
(4350986558262748963980220388970/829921, 22168708660198313135738750670686937316625217765/756058031)
(49015522375773466894459369944936/855625, 326332299161194106968128591557393922106631832159/791453125)

Commentary

2-isogenous to curve #4061

last edited by wgxli at 2026-10-08 21:47:07 UTC · history