curve #3889

y² + xy + y = x³ − x² − 20546916546148434498519724333155x + 36397308322812757116926507085542461511354173347

a-invariants: [1, -1, 1, -20546916546148434498519724333155, 36397308322812757116926507085542461511354173347]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 716520075053637095452647345185168259531108219886775881468558993450
discriminant (Δ): -17135798299239180017104886748365234644524381456575344739612019429060646684177870204676096000000
Faltings height: 16.8785
naive height: 227.9448
primes of bad reduction: 2, 5, 11, 17, 19, 31, 43, 47, 67, 79, 181, 3952808304595066983647047046854004158594833665543
regulator: 1196790624089474052.07032670643495516601795997008316922745084245309438253408418
submitted by: 7fff-zip
submitted at: 2026-10-04 14:08:53 UTC
last updated: 2026-10-04 14:08:53 UTC

(19805071525466611/9, -1157761110422202444119930/27)
(766524465366009, -145251413561235711744280)
(62720794501601791/25, -3161617318995456770523654/125)
(3323900973210258899/361, 5434654075856120279491217830/6859)
(-5113804178250597, -87972480928902927249550)
(-2640974132769614493/529, 1467394150820002596610827190/12167)
(3135813433143963, -52929075035839344307854)
(2871265797189979, 32754313365604733215410)
(94020361283685085387/7569, -858040030158169195655892113762/658503)
(329119393701250739/121, -33496146205702818354121930/1331)
(206235213702901651099/25281, -2579067367529248142724313525810/4019679)
(2264858775925869111/2209, 13299324643809107304762089530/103823)
(726308324491636665259/249001, 4448533635870931978812420587230/124251499)
(154182299788501659/121, 147523015624201794955310710/1331)
(423869508971143771/49, -243979423733907015412676370/343)
(-281994197709204809/729, -4142205553631004034044093370/19683)
(99729441649957753041227/39853969, 6418451914989680801808586910420962/251598106297)
(16537178068396337063/841, -65603986528458095750471490806/24389)
(82858877166916971/49, -27627760981336349843058370/343)
(4875328037379748555/529, -9655900767789524647003288674/12167)

X1008, t=-69/53

last edited by 7fff-zip at 2026-10-04 14:08:53 UTC · history