curve #4631

y² = x³ + x² − 1034997150009566805873332641329938690614840x + 398059471050232629080486202812792923031588390926177137302193188

a-invariants: [0, 1, 0, -1034997150009566805873332641329938690614840, 398059471050232629080486202812792923031588390926177137302193188]
c-invariants: [49679863200459206681919966783837057149512336, -343923382987400991525838158409455840739383889560920068971991988416]
rank (lower bound): ≥ 18
torsion subgroup: ℤ/2ℤ
conductor (N): 39074194855695436031173540064661548058671150699483415904066923420321417840
discriminant (Δ): 2506377872376038552747999781582106205411995244457728162675627585643119804025183564938047273816206010964207790368950977744000000
Faltings height: 23.0444
naive height: 301.8425
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 29, 43, 61, 83, 181, 277, 331, 359, 389, 601, 647, 829, 1373, 1451, 3847, 13691, 30089, 76679, 106291, 11507869
regulator: 7162197377061253262.6514704273789477841895610786821800169233847335229876663
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:32:15 UTC
last updated: 2026-10-19 03:32:15 UTC

(-713721330052074579904, 27806306797378906968754019823750)
(192548163810180840266, 14349611633854839273552762381240)
(313829983186152565646, 10205646239016473776569570905100)
(432877465892761459616, 5580892639918830832980135498810)
(488556783114010315166, 3002849081554348752787002401460)
(501858619279360507496, 2244188710169774056470984889050)
(650275853256835347146, 24670198342804788980997390600)
(936661381638222006371, 15823495079608658913204767233200)
(997624557348537851246, 18931758614559524388932804954700)
(-8850775631161817036816/9, 582109695118811390481116779271230/27)
(11120054452250600257784/25, 633617350433860243258176971176302/125)
(142949484276894304962194/289, 13121443137361540683584000375314200/4913)
(147548908608651797871074/169, 27784343666782851423028984097544600/2197)
(239802680069679762951866/121, 104217529510048911983200761415101000/1331)
(4645962619151859773705234/16129, 22794062773527524724682789565815001400/2048383)
(13650436876617320786313296/1681, 50055113064260425130928694119364110090/68921)
(22233182240493326738913074/18769, 74268343972721749010079333352838445000/2571353)
(180147016856571496675598579/552049, 3999216896215723369038956947937150355000/410172407)

X660, T=3862/585

last edited by Andrii Prokhorenkov at 2026-10-19 03:32:15 UTC · history