curve #5759

y² = x³ − 782280190450022894153201079675

a-invariants: [0, 0, 0, 0, -782280190450022894153201079675]
c-invariants: [0, 675890084548819780548365732839200]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 3129120761800091576612804318700
discriminant (Δ): -264367712032066407090622751148132647568866907236269021581630000
Faltings height: 10.6566
naive height: 151.1872
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 29, 53, 67, 163
regulator: 3443898008127.51716234633833658035009463271972167117838
submitted by: Maksym Voznyy
submitted at: 2026-10-24 19:47:00 UTC
last updated: 2026-10-24 19:47:00 UTC

(449134629824542238241943077979/47826095710599587161, -70875143170302216296921891689341023251693508/330748126587889105292127909341)
(303524087312354438570350102785882671798433481/281493942991806389967179402049936, 5287977606225193299834488779975524018594368873798920890629824569221/4722843793003284700526336556844596084600808746816)
(693154626771669065696476470913591/47738107307584366962601, 15745787598282001140324692355072075950217808881086/10430323887015264808842710327427349)
(5440528023119067156742006729/322889058226625284, -367017348616152924442934767170634116925733/183476307986448152005000952)
(1509263204908551656512385161/22852269127908900, -58554058659246462390196430000977765939909/3454569982817176203063000)
(4174451824798708979827177681639/59123899906001091225, 8519537534232302560322065039235011471258703162/454615888174211459444597575875)
(119603781270628758800288285677730834161/12290645203804342002700961344, 508467640459023763871491588086251483458699202253611511241/1362580040596748032716874703333143837276672)
(2928986063334859363668647137834891/235295120901916003345209, -122217105557235052161041835680537366945142426702664/114135141757713445261901118766433427)

Voznyy (2023), A^2 = 340431140685090^2, [r, s, t] = [90, 163, 276] or [326, 335, 371] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 19:47:00 UTC · history