curve #98

y² + xy + y = x³ − x² − 81178834234583541704958093x + 308750682382680533525277345167136070581

a-invariants: [1, -1, 1, -81178834234583541704958093, 308750682382680533525277345167136070581]
c-invariants: [3896584043260010001837988449, -266760589578618446337644956179397294034193]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 78703766491526567026991736810838956441659641637530859417300830
discriminant (Δ): -6943255656099873846088189823650058376374717862862923480133566806025633174732800
Faltings height: 13.8642
naive height: 190.7743
primes of bad reduction: 2, 5, 11, 13, 37, 89, 257, 179407, 378296549, 3677123397354060259, 260588146825380416113
regulator: 73374077163928442.491606296355008103610686750381720681630217331306538695310
submitted by: David Renshaw
submitted at: 2026-06-23 17:40:14 UTC
last updated: 2026-07-01 22:32:41 UTC

(3690651960015, 7708299126156239672)
(8639928534543, -15884836569860852104)
(1889154717743, 12733165176223454296)
(5622697901945, 5483308873225802732)
(3578858431597, -8003873391211964634)
(3208977934715, 9016326430132245272)
(1031355338891, -15037404035089789864)
(-10461566649345, 3612321023566239032)
(4283688150047, 6293763175233626296)
(-9991696653105, -11061364945580666568)
(6202108581793, 6621324732236625810)
(6544346735947, 7600827529120240476)
(-10329673278905, 6715894460094173272)
(-3048636399034585/361, -135806158318089918059992/6859)
(9517072918655, 19954232950098826312)
(-76643965808353/49, -7128301363421291146360/343)
(155240191243351/25, -830094926073353765064/125)
(232411898324105/64, 4026412141608081380239/512)

Generated by generalized Mestre quartic-family search over (u,v) in [-50,50]^2, denominator <= 40; certified rank >= 18.

last edited by David Renshaw at 2026-06-23 17:40:14 UTC · history