curve #294

y² = x³ + x² − 4101421576978444120802996800x + 101007831382914631822039670440279140956948

a-invariants: [0, 1, 0, -4101421576978444120802996800, 101007831382914631822039670440279140956948]
c-invariants: [196868235694965317798543846416, -87270766314839423103656445052307969049881536]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 217873563048441677123261565462786245922350374836628933506836707920
discriminant (Δ): 8018334857353013653045886055527983056792394599283510532177835012644680732588800000
Faltings height: 14.6330
naive height: 202.3570
primes of bad reduction: 2, 3, 5, 7, 19, 29, 53, 6697380388286085792690029, 663075252818104711935615376946987
regulator: 1208600411369034296.838590940854719100031597630103032049038447727539628989960
submitted by: 7fff-zip
submitted at: 2026-08-23 15:36:41 UTC
last updated: 2026-08-23 15:36:41 UTC

(9816391006916, 248379942787582562550)
(199235268409642457669/5244100, 58876056378278483695246370097/12008989000)
(70632107919797399/2809, -17473996980885203219463870/148877)
(227259561549075429596/5997601, -21710087519974991359992766710/14688124849)
(61091091470874926/361, 14145603704864145137372700/6859)
(1300323243322529283926/36060025, -107253595989911519649851234724/216540450125)
(27981050123877884/1849, -16372718461863549955019550/79507)
(374646003569732025101/7873636, -2574880931727838137792294668475/22093422616)
(8819088695929396/121, 579034674774856394174430/1331)
(364217264598474428291/10118761, -119936796277822964255804622480/32187778741)
(-133894700932903186/1849, -10748720416912863550886820/79507)
(10384410867215787570563/256608361, 148451449718529412416693329365488/4110609334859)
(2606017312369541843174/8334769, -130438849576756584559213835494380/24062478103)
(2205397017283454/49, -29872247874729744424620/343)
(2309513023715430585734/37295449, -66204304299660851668530083387700/227763307043)
(4380692914628661494/18769, -8854719165686019976234593660/2571353)
(1296010927097206, 46600675071259694041020)
(10568924254673382902/2809, -34354502941053436485891837444/148877)
(51864925460388134/289, -11143905141681513619690860/4913)

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