curve #475

y² + y = x³ − 113679727x + 682491235476

a-invariants: [0, 0, 1, -113679727, 682491235476]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 107201228152577318687714363
discriminant (Δ): -107201228152577318687714363
Faltings height: 3.6956
naive height: 68.0212 ★ record for rank ≥ 12
primes of bad reduction: 7499, 26317, 530393, 1024146872477
regulator: 134979922.92325185433800770837655815890241380891706831331379159
submitted by: NDElkies
submitted at: 2026-09-01 03:00:19 UTC
last updated: 2026-09-01 03:00:19 UTC

(5559, 471521)
(5498, 472941)
(5335, 477342)
(6129, 464738)
(4947, 491105)
(4666, 503634)
(4622, 505769)
(6494, 467033)
(6576, 468299)
(6709, 470946)
(4096, 534395)
(3806, 552230)

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 03:00:19 UTC · history