curve #476

y² + y = x³ − 332557057x + 2359264710636

a-invariants: [0, 0, 1, -332557057, 2359264710636]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 50719803766045246971171323
discriminant (Δ): -50719803766045246971171323 ★ record for rank ≥ 12
Faltings height: 3.7427
naive height: 70.5019
primes of bad reduction: 50719803766045246971171323
regulator: 103519732.35931705653142120237077856759087784763975371707390203
submitted by: NDElkies
submitted at: 2026-09-01 03:18:45 UTC
last updated: 2026-09-01 03:18:45 UTC

Witness: 12 independent points log in to add more points →

(10452, 158744)
(10433, 159068)
(10565, 158292)
(10624, 159068)
(10286, 163890)
(10254, 165458)
(10774, 164106)
(10172, 170255)
(10832, 167180)
(10109, 174651)
(10939, 174363)
(9538, 234606)

Commentary

Prime conductor. Found in the output of the searches from earlier this year that found Curves 157, 158, 244 of ranks 12, 13, 14 and smallest conductor known.

last edited by NDElkies at 2026-09-01 03:18:45 UTC · history