curve #4306

y² + xy + y = x³ − x² − 388331913799637255313675867719955x + 2724003900978737437653410772455041736711758308147

a-invariants: [1, -1, 1, -388331913799637255313675867719955, 2724003900978737437653410772455041736711758308147]
c-invariants: [18639931862382588255056441650557825, -2353539370445629062252853526679508912764971750729025]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 25549334250540335834393568462217271122128979965910719772132760809472714123481384650
discriminant (Δ): 542385389385572594401846576551326567143173339867318226037130486353343353060822973517772661268480000
Faltings height: 17.6872
naive height: 236.7318
primes of bad reduction: 2, 5, 7, 13, 29, 61, 151, 2039, 3833, 29191, 46488403859, 9396288357523, 30134180253834802216372839712071391999
regulator: 202819411050871353458710.138648194377587403742073804948125601345746454414877466928712
submitted by: C. R. Hill
submitted at: 2026-10-17 00:18:38 UTC
last updated: 2026-10-17 00:18:38 UTC

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

(1535992624420086331/1089, -53049179438294242248963255550/35937)
(45424164412585190548110379/964413025, -282423563095092024046723507310778046818/29949846491375)
(27129107316102331/4, 5073597223326097429104885/8)
(58855820930091978657955/2476953361, -203115840159080055371240142701749481158/123275491823609)
(148186911904804931/49, -430770452235405407225396050/343)
(2686024131837735789293899/109014481, 3242221885184155006304442338146721170/1138220196121)
(583459606682957074066786099/32681769961, 7190733199732212011997880022189520575530/5908243055319541)
(110017566286565615876131/16184529, -41094552602372949865406310120493370/65110360167)
(-369036362988387204003431/23145721, 245545422886283203650280435415824490/111354063731)
(-498955498151538656735013/46144849, -745668174588091806504478377054007678/313461959257)
(1400420303067663357438815779/101059774201, -1960931473431082893157920325127008311770/32126801158723699)
(-5562744261265122003837349307/4458512487361, 16857975407771631210257561199689174675625764/9414233828800011359)
(-58416259745993234513986389/4013602609, 584986254465307057340551257150975372690/254273766087977)
(-255278607213169203879777341/11729106601, 1182181864172778037251213646263141165930/1270273973994901)
(8178999572148930192038319/202236841, 20970685828258365140983283587384060730/2876010115861)
(4866830541030402827741443/351150121, -424669445512439410917204598546401770/6580202117419)
(993058422937585979, 989412238427064362205669250)
(799732296943672794503/11881, -21730538664945227862308080765190/1295029)
(1471231064532024891/169, 122945842825146391946137130/2197)
(139365753889974301/9, 17576691914235768947938730/27)
(80413794863672002811439/24453025, 147231796472015489442796866193613822/120920208625)
(542600826188268549, -399427331947303199168929060)
(3290171877577979, 1217350411991429027688770)

Commentary

Found with Rank Hunter v0.9.2; family=x1152_3926_padic_minimized_rr_half_lattice; parameter=2645/5314; local status: rigorous rank lower bound >= 23.

last edited by C. R. Hill at 2026-10-17 00:18:38 UTC · history