curve #583

y² + xy = x³ − 21931430647545290962975112445891024051790x + 1143485922983816588968442719896673870007162534674064734751492

a-invariants: [1, 0, 0, -21931430647545290962975112445891024051790, 1143485922983816588968442719896673870007162534674064734751492]
c-invariants: [1052708671082173966222805397402769154485921, -987971837458017532870313572997349484635522638054496084557017969]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 408151225931333636120101726342826073778668448086028074168154441438757841614211839980345370430
discriminant (Δ): 110253882580621611049080760317936376921573127670772185363721484560221377925783427364876272154621816087245038474950400000000
Faltings height: 22.1558
naive height: 290.2798
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 23, 37, 347, 5325577263031, 1282497921465413, 3947091299768911220094720296669177876224660861450987
regulator: 12739255083367364094549997.914991917461565973396740198069693185741293551712307818336021
submitted by: FNacc
submitted at: 2026-09-04 22:33:49 UTC
last updated: 2026-09-04 22:33:49 UTC

(174676152917169008174, 1625504403226161947314238700038)
(8666603840379940304, 976762944990501782510269247918)
(3788004935097009465316/9, 220132750353654702461867665938526/27)
(64206263523978338924, 6119713920068774410321477538)
(121903151465897222204, 530567961831616231114958718818)
(-168719751676699488196, 202274999807545092267957784418)
(-133194199109209895926, 1304479836762492293667251008688)
(183462054512881018372, -1815193140168223374902848526270)
(15587762077076525736824, -1946059512470458812276147717873562)
(298018044904806304004, -4590852155220567267583000296382)
(-83200918678799230666, -1546690549048264531190919599452)
(557493668216962808114, 12735204464937577409515790874278)
(3361797620156551967174, -194734142541785801561478612167962)
(807347717303703393458, 22575978003884722933462636149926)
(147505961183914041404, -1057310330547570316754497869982)
(-102248274266274434996, 1522156642880349241063174249618)
(284440404914867842424, -4233005332293655939527053975962)
(63939011224839771674, 51060909739519942355101308038)
(501025975076474437151/4, 4810685771344606134052555139809/8)
(37500314079828947924, 611380475230711754694473146538)
(2043374600000789232709/16, 41751244617885965738343522117157/64)
(291088825010618060924, 4407293364917495585444794669538)
(-51955046611520439076, -1463793281577212241007978630462)
(176240653403153771644, -1659049814772383940865574938142)

Specialization t=-27/79 of the Elkies fibration

last edited by FNacc at 2026-09-04 22:33:49 UTC · history