curve #4626

y² + xy + y = x³ − 3628643910628541291135012760525931028x + 2643788816928815650421414912770133685520912592159899598

a-invariants: [1, 0, 1, -3628643910628541291135012760525931028, 2643788816928815650421414912770133685520912592159899598]
c-invariants: [174174907710169981974480612505244689321, -2284233537826496722225364846198650477251789398384020286869]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 2284850412066332199034027332367937146859263362365044317615667290
discriminant (Δ): 38312289879606584902366334518500913942344726413787235744648840837750476672696332971012142827644274507607812500
Faltings height: 19.8586
naive height: 264.1594
primes of bad reduction: 2, 3, 5, 7, 11, 19, 37, 47, 53, 79, 103, 191, 263, 461, 1759, 9613, 70881409, 370175059, 2410702669, 2802557011
regulator: 444019867443930142.512525170429784065084250558534482719480905600127354598
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:31:19 UTC
last updated: 2026-10-19 03:31:19 UTC

(-2150737972821624051, 706709781794964885754024525)
(-2010862924975675251, 1345150522080669672298785325)
(-179363967208668261, 1813523197768989172352396365)
(-62836314413233842, 1694565231450832339368563803)
(112154618743713549, 1496071655054255598740220325)
(228036956088729483, 1352102814441647650617729943)
(692806003979999814, 679982106323178266727271315)
(796866083337893319, 508184982366998593176544495)
(829495375212976299, 452316482438626716263303575)
(962923420650946799, 206218141739073307931842575)
(1997151174451916604, 1833766923747786580630648930)
(6136416286231248999, 14541230550847775032378440175)
(19430812794250280791/9, 59602381641188294693821179925/27)
(80084096616553035561/64, 128006914405096890634822511225/512)
(1196370805098921783984/841, 14646011068030033660425183131225/24389)
(5085573197656938592299/6241, 235427084108603661173070274201555/493039)
(6217002282630054392181/26569, 5822427679091771387481962240617975/4330747)

X400, T=-4766/1315

last edited by Andrii Prokhorenkov at 2026-10-19 03:31:19 UTC · history