curve #4401

y² + y = x³ − 2217077947x + 28425800438316

a-invariants: [0, 0, 1, -2217077947, 28425800438316]
c-invariants: [106419741456, -24559891578705240]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 348398420573690733009119729797
discriminant (Δ): 348398420573690733009119729797
Faltings height: 4.3749
naive height: 76.1720
primes of bad reduction: 48647, 17551319, 83547923, 4883989223
regulator: 444536073053.4218294789531854558804749839741950126595524221575207
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:08 UTC
last updated: 2026-10-17 10:22:08 UTC

(-1992, 5730123)
(607, 5203869)
(10905, 2354862)
(38511, 399330)
(43592, 3822980)
(47123, 5347026)
(76053, 17312001)
(102842, 29801394)
(448418, 298666298)
(-13012501/289, 29872122205/4913)
(-34298519/1296, 386329606955/46656)
(1493376/25, 1305873751/125)
(3154275529/3364, 176932931836535/195112)

BASE records/rank_13.md#14 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:08 UTC · history