curve #4464

y² + xy = x³ − x² − 2834795014x + 46808291571064

a-invariants: [1, -1, 0, -2834795014, 46808291571064]
c-invariants: [136070160681, -40441751601676245]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 255733741895151889311142284086
discriminant (Δ): 511467483790303778622284568172
Faltings height: 4.4163
naive height: 76.9093
primes of bad reduction: 2, 133276381583, 959411333267213621
regulator: 34539214097.44949136428035727903348635166244441929504021797164727
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:07 UTC
last updated: 2026-10-17 10:30:07 UTC

(-50050, 7981942)
(-2388, 7319948)
(-1316, 7109568)
(2684, 6261168)
(13418, 3337942)
(15173, 2692210)
(41660, 985488)
(41710, 1042902)
(42013, 1344842)
(44988, 3191092)
(46886, 4095270)
(99585, 27374638)
(-3174287/121, 13533550930/1331)

BASE records/rank_13.md#19 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:07 UTC · history