curve #4396

y² + xy = x³ − x² − 1705142089864x + 1478421014988866524

a-invariants: [1, -1, 0, -1705142089864, 1478421014988866524]
c-invariants: [81846820313481, -1277355388639689266085]
rank (lower bound): ≥ 15
torsion subgroup: trivial
conductor (N): 313470185465711365174722663519489654214
discriminant (Δ): -626940370931422730349445327038979308428
Faltings height: 6.1388
naive height: 97.1982
primes of bad reduction: 2, 283, 23982037, 29853097, 773578425106945399661
regulator: 1021314364254.7002569279828457287649797491938133494194721441619476451
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:21:40 UTC
last updated: 2026-10-17 10:21:40 UTC

(-328619, -1415206776)
(-1325583, 1187866228)
(6565876, 16529784810)
(8001964, 22361397918)
(1101510, 967270442)
(597371, 820061854)
(701164, -792531322)
(-1601612, -317008078)
(596682, -820925842)
(-740044, -1527702126)
(992903, -874704278)
(315700, 985525818)
(-1205964, 1335094330)
(2830914, -4398966922)
(397164, -929632922)

BASE records/rank_15.md#18 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:21:40 UTC · history