curve #3881

y² + xy + y = x³ − x² − 4720150013688906556121694982513523x + 120762825259136167607219516783358261754508276142931

a-invariants: [1, -1, 1, -4720150013688906556121694982513523, 120762825259136167607219516783358261754508276142931]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 486635770492450191781083594169464299600456273214066750246945613580161648183659630
discriminant (Δ): 430359664174330100725174359882994769246739338140328718630887569042210484569732487831637051383788339200
Faltings height: 18.2708
naive height: 244.2250
primes of bad reduction: 2, 3, 5, 7, 17, 19, 29, 41, 89, 7140044804191667239273701577217, 3165105268447721459104893327932499108691
regulator: 42751901395200529020544.8107556012341341067943325955611736729577239392557042312582832
submitted by: 7fff-zip
submitted at: 2026-10-04 14:01:13 UTC
last updated: 2026-10-04 14:01:13 UTC

(92657902640360891, -21884168665556953112976158)
(33564137549085487, 383124928788217916170226)
(9492294047636400667/289, -5296092476878939879876604990/4913)
(9176148746168724835/361, 28451250383343904899512916278/6859)
(-70955618981012765, -9921882137803944640906078)
(99006145589348703115/529, 926056458274996367074413901774/12167)
(47079356835806275, -1700289600441383655761758)
(5385660642905635, -9772303314752496367805278)
(145278086699623691675/841, -1628810807088820247132305522262/24389)
(3860377256634142435/121, 2164757606957674380862717702/1331)
(413634482523269231555/2809, -7618483345948543449843458454886/148877)
(100250144366635194565/2209, 14403117719049764612447379106/103823)
(631649468932785661495/249001, -1296065123165061171268766768722522/124251499)
(32766113906272332931/121, 182010560807624503373420816422/1331)
(129189586999233445, -40830580063211741748180418)
(1916842946947127245/81, -3443664023743020128628366322/729)
(-3598071329244360598266125/46280809, -1329342166597444509936456333334469066/314848343627)
(-6288438258276677, -12255469156448121519266590)
(57366191309530882027/529, -361784417040559209540588585170/12167)
(16372470709134609829/529, -25293146171634959251225656716/12167)
(2824833715734935329331/14641, 141640764671712357425613926499826/1771561)
(187106357032736275, -76078641616100555104679518)
(57311925759022075, 6204187809338974873286882)

X1008, t=117/7.

last edited by 7fff-zip at 2026-10-04 14:01:13 UTC · history