curve #4406

y² + xy = x³ − x² − 326831689x + 2215060677769

a-invariants: [1, -1, 0, -326831689, 2215060677769]
c-invariants: [15687921081, -1913741829947565]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 57453726914665426475770586
discriminant (Δ): 114907453829330852951541172
Faltings height: 3.7774
naive height: 70.4285
primes of bad reduction: 2, 2957, 1152623, 14947259, 563881757
regulator: 86308690.090345669594142471028124265154491560614375261451967759
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:32 UTC
last updated: 2026-10-17 10:22:32 UTC

(8967, -77360)
(2336, 1208925)
(16899, -1240387)
(8824, -138957)
(13556, -531671)
(-18204, -1451005)
(13349, 473728)
(15583, -959568)
(106597/9, 1833664/27)
(7840, -370723)
(8511, -227536)
(5822, 710925)

BASE records/rank_12.md#26 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:32 UTC · history