curve #3918

y² + xy + y = x³ − x² − 1321456503683732842928593176117x + 571279313653043170346472425092554935422440141

a-invariants: [1, -1, 1, -1321456503683732842928593176117, 571279313653043170346472425092554935422440141]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 99891175297986018950652311813618544552656089113357208124952288283107586510
discriminant (Δ): 6698206335870354049112246832335998131424038711868407591588098097115623409932619196416000000
Faltings height: 16.2093
naive height: 219.6825
primes of bad reduction: 2, 5, 7, 11, 23, 23327, 4745667041, 50950964294275977515520499733468205558505500391007037583
regulator: 2065007549398993220019.821238752934742205810104742522464170544246206173260940415851
submitted by: 7fff-zip
submitted at: 2026-10-04 15:33:03 UTC
last updated: 2026-10-04 15:33:03 UTC

(3979822735231, 23791179330956833567824)
(579736307196571, 170300267864793323764)
(27779469066951, 23121232456967152043504)
(441498606513951, 8597410274344035566544)
(771771543889871, 3332879439118143010064)
(824913233198271, 6521566373022224404464)
(828678463664191, 6728810447117888437584)
(345639478456159, 12482954893745035450576)
(750864313314871, -1542723175547185304936)
(759644259074071, -2408802494939583200336)
(785766323327839, -4251821946180057956144)
(789826989799421, -4502493608014957643036)
(1644481025355371, 53341995263876968174564)
(1644528533445371, 53345019644863038604564)
(1724320118991071, 58476931187720482733264)
(3526054008454271, -199377488775818753519536)
(15263685856803359, 1880568026300280736589776)
(1671841489909784989/2209, -224315725811552333523902628/103823)
(17591094891032679359/16129, 42346575899472478643761806512/2048383)
(92490116168457050911/103041, -344260673219055895300968616496/33076161)
(240006259548093755031/175561, -2672262887097515235020681521424/73560059)
(12694811775597373994761/7177041, -1180236113381716570178304955406354/19227292839)

X1092, t=-33/17

last edited by 7fff-zip at 2026-10-04 15:33:03 UTC · history