curve #1114

y² + xy + y = x³ + x² − 3303894515586689289541165506478574062530571840x + 73094841061617585831898118162636503049865840051589473263026790881505

a-invariants: [1, 1, 1, -3303894515586689289541165506478574062530571840, 73094841061617585831898118162636503049865840051589473263026790881505]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 229584468983534025788078945027068319227598545134330
discriminant (Δ): 6877297372884722943214333449468141466925635132063519816482741007547913556042205544982852575213180126683749431572144726689910807040000
Faltings height: 24.7494
naive height: 326.0479
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 37, 61, 71, 199, 239, 313, 353, 383, 503, 569, 787, 1609, 8263, 159911, 210361
regulator: 4392947078650.8550450300358407082134528592909204943264779601183
submitted by: dujella
submitted at: 2026-09-23 20:47:33 UTC
last updated: 2026-09-23 20:47:33 UTC

(10964158046678425550933, 6179680504792198696394524466665173)
(33106810035885536256585, 22627223537078412857384144067409)
(-24822770633695769418097, -11824196026778126896329141995533857)
(-14044424885259044094617, -10803977721389302939133739550788857)
(74232009144658178109029, 15391150761185424682638070662574725)
(33572549493331599248623, 121816581295680995324783410946193)
(31510749310311982725029, 523959123598909555301109331041045)
(33222091076171388326533, 4709487224076442373866152631573)
(30092098610217933296363, 960807953463745240613272147906593)
(62902156519285575854053, 10684406264237425296602564682658053)
(-260497096364741168846953/4, -27776692903862857085922317803170321/8)
(4922128977127785626713, 7546648016739846598291203921457893)

found by Dujella - Peral (2014)

last edited by dujella at 2026-09-23 20:47:33 UTC · history