curve #4403

y² + xy = x³ − x² − 2049670219x + 48898999201369

a-invariants: [1, -1, 0, -2049670219, 48898999201369]
c-invariants: [98384170521, -42248292581215485]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 240918419474403489984588164194
discriminant (Δ): -481836838948806979969176328388
Faltings height: 4.4005
naive height: 76.5647
primes of bad reduction: 2, 53527, 2250438278573462831697911
regulator: 333773678945.3826137934771093831190928784926395371763217232438749
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:13 UTC
last updated: 2026-10-17 10:22:13 UTC

(-47765, 6174018)
(-41117, 7999362)
(-40722, 8072435)
(-508, 7067085)
(33789, 4251433)
(40830, 5748203)
(77964, 19013293)
(82167, 20820898)
(531863/4, 368438139/8)
(208745, 93260298)
(381728, 234096037)
(12475639, 44058514338)
(-868995/16, 7471163/64)

BASE records/rank_13.md#16 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:13 UTC · history