curve #4412

y² + y = x³ − 234270673x + 1016774489478

a-invariants: [0, 0, 1, -234270673, 1016774489478]
c-invariants: [11244992304, -878493158909208]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 75252011735942348487679505
discriminant (Δ): 376260058679711742438397525
Faltings height: 3.8079
naive height: 69.4296
primes of bad reduction: 5, 1447, 1901, 205499401, 26624833583
regulator: 98653621.322176908447866017749366956539488270124940209845984113
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:48 UTC
last updated: 2026-10-17 10:22:48 UTC

(-13249, 1339757)
(-2424, 1253157)
(-1524, 1170582)
(86, 998312)
(2041, 739682)
(2641, 645357)
(3639, 460925)
(4711, 132962)
(4816, 15117)
(12456, 176837)
(12472, 187029)
(16291, 1234442)

BASE records/rank_12.md#18 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:48 UTC · history