curve #4623

y² + xy = x³ − 128037272356574941639797558244758775988x + 553680513865692758622528988661839730052294078653904872592

a-invariants: [1, 0, 0, -128037272356574941639797558244758775988, 553680513865692758622528988661839730052294078653904872592]
c-invariants: [6145789073115597198710282795748421247425, -478379963979958543459083729813502922563247508150596441790625]
rank (lower bound): ≥ 17
torsion subgroup: ℤ/2ℤ
conductor (N): 48132758481351491535523418003114261028745289222225156169871950
discriminant (Δ): 1900178700961372101467123528822031507349993292235384539488931512638033793555343127759494245490734419745849344000000
Faltings height: 20.7546
naive height: 274.8498
primes of bad reduction: 2, 3, 5, 7, 11, 13, 37, 43, 47, 53, 67, 131, 181, 547, 673, 733, 839, 21569, 109717, 2534401, 13727437, 248323087
regulator: 399298495774310690.942980484040515130697991384182233581164659969549698348
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:30:50 UTC
last updated: 2026-10-19 03:30:50 UTC

(-9842948195657115188, 29331283811382884828987194744)
(-1025361171537319208, 26151231941971364973262417804)
(3987472836122308312, 10321625144205834494300098444)
(4679336867853260392, 7550539745607352350759496204)
(4987074187522623976, 6259569144774707291686125580)
(5366055718251699712, 4597668686988273621316579444)
(5666224417445714902, 3180087706949911129355597224)
(7131286738465262152, 1809249918779057881134522124)
(7853231685260494312, 5701618561060165182444639244)
(8963177091879022792, 11231578726364552267135617804)
(22053244486360700392, 91954018371714928440153736204)
(46233375279392797548, 305710778770007176855160211132)
(-835636891590291085649432/124609, 1465978595387587067869902903155467148/43986977)
(-158554483615238198178392/196249, 2227721242780850544087585680609845028/86938307)
(-3043046018228478489032/289, 133143649302982833291152476027772/4913)
(2764969126035449088808/729, 217956984809778780314136550355492/19683)
(18664942793288341713915232/863041, 71262830838161773041460712310736646036/801765089)

X400, T=-5245/1466

last edited by Andrii Prokhorenkov at 2026-10-19 03:30:50 UTC · history