curve #3924

y² + xy = x³ − 2357071242718812043393251435x + 43747288136281047881665586467479641531697

a-invariants: [1, 0, 0, -2357071242718812043393251435, 43747288136281047881665586467479641531697]
c-invariants: [113139419650502978082876068881, -37797656949746995078888542462369534597489529]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 529736819274567957038632776825402623370
discriminant (Δ): 11331869096342475742781762252783714812272494959669482358723384353532286872632000000
Faltings height: 14.5732
naive height: 200.6953
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 31, 37, 43, 59, 191, 211, 394050542917689662929
regulator: 122042506220.0720457886101374797096871497490265871356098616
submitted by: Maksym Voznyy
submitted at: 2026-10-05 00:12:25 UTC
last updated: 2026-10-05 00:12:25 UTC

(2603822178077256516/87025, -74499340294649315057375721/25672375)
(29181699112751860372041696/259878707089, 144819587691364708715189705877469609551/132481746935951687)
(620227849976059006866306083585918694/9942223000702961503441, 370238464124134379574137159921497363174462714591646313/991345980367198964135551448228761)
(112460913425545799286/3003289, 465264465954773070837137804301/5204699837)
(41151122868677032446/1138489, 92303008298710897953275547699/1214767763)
(87736167136662, -715756905267301012935)
(115424603017616101/144, 39144251885304115013563379/1728)
(748708468528779319744661/24103183504, 83874689956964264748393210944462839/3742067445363008)
(293296333392969036/5329, 110536562423538085176234411/389017)
(115438312792852514754/2247001, -812916092981539482214374553893/3368254499)

Eroshkin - Voznyy (2026)

last edited by Maksym Voznyy at 2026-10-05 00:12:25 UTC · history