curve #375

y² + xy + y = x³ − x² − 5294538512342122389440470772x + 147333838524398950267979074374742550207319

a-invariants: [1, -1, 1, -5294538512342122389440470772, 147333838524398950267979074374742550207319]
c-invariants: [254137848592421874693142597041, -127296436485079549411215254361341444237437161]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 3435889424901540260831120722590444607106072049491801762070
discriminant (Δ): 121166701324216502059283397934007212496711811609807379623239561661383591520000000000
Faltings height: 14.7730
naive height: 203.1230
primes of bad reduction: 2, 3, 5, 7, 13, 43, 103, 7331, 830899, 1358365011381977, 880599231416386767013853
regulator: 306780937745709613.22527189812930393933895491920933054684743850952464640598
submitted by: C. R. Hill
submitted at: 2026-08-26 12:59:48 UTC
last updated: 2026-08-26 12:59:48 UTC

Witness: 18 independent points log in to add more points →

(144798075003846677/6241, -94817006724053625482365101/493039)
(217392872366840693/2209, 79028904141656143676610003/103823)
(74446695995566853, -20312713155305102240419827)
(6699980290020317/121, 205928564450366351767191/1331)
(154676576499263/4, -164076549923880547797/8)
(47912291691677, -60392343020871794139)
(127770774295149497253/339889, -1418992470407890843459828211893/198155287)
(3385847468182465013/12769, -6016569298230834033625039683/1442897)
(569805071625821334317/14523721, -77142652149392625304628424609/55349900731)
(10086842753184533/529, -2809273552467822638358213/12167)
(2965827766710985698557/61952641, 29193065936582125222452076707771/487629237311)
(64836307200338933/529, -14082002036477605715845413/12167)
(355957407260777, 6585174646903317305361)
(55674010547477, -158532533478525702339)
(331699470869907, -5906455920049360558089)
(-31246272625358203/961, -15907072977698057376921549/29791)
(2402887164619277, -117734343689406758708139)
(3109793834858767/81, 18631423225472272375499/729)

Commentary

Found with Rank Hunter v0.8.0; family=Mestre/Fermigier sextuple, generic rank >=11; parameter=25386/35; local status: rigorous rank lower bound >= 18.

last edited by C. R. Hill at 2026-08-26 12:59:48 UTC · history