curve #3859

y² + xy = x³ − 71140576654009499718317864530x + 7620520695817668367216316859628694693563652

a-invariants: [1, 0, 0, -71140576654009499718317864530, 7620520695817668367216316859628694693563652]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 1895504685727218625360763694050688870
discriminant (Δ): -2044615233903699504860727187597903138012286706360358808794527752024812573903982784000000
Faltings height: 15.5135
naive height: 211.0020
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 29, 43, 67, 71, 79, 103, 181, 112207, 164676006259
regulator: 121662639553.5107324411945262815288653693485572631071007734
submitted by: Maksym Voznyy
submitted at: 2026-10-04 03:21:59 UTC
last updated: 2026-10-04 03:21:59 UTC

(26613946614325799876/9025, 136755636542704776191905852066/857375)
(281998188234566407184/2493241, -3978118341822007597529058300298/3936827539)
(605540309991340820042324/2842062721, 221401881606618346027766355601403618/151513205719231)
(-140620746981807589/1444, -202542857233459574408869859/54872)
(7877230344970289446811864/51869607001, -6674375256095629958061197513859650398/11813251124870749)
(8845177629878177/64, 335086775744512484709667/512)
(268363519308404842469/16, 4396278712327841816368067517047/64)
(177426716580344, -764014055613868939222)
(-446274495566812444/4489, 1113652498729924571035786154/300763)
(-3409885556274143405872/29019769, 592349946873360041883335307618934/156329495603)

Eroshkin - Voznyy (2026)

last edited by Maksym Voznyy at 2026-10-04 03:21:59 UTC · history