curve #556

y² + y = x³ − 160923919x + 872942963892

a-invariants: [0, 0, 1, -160923919, 872942963892]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 62485188121355020192595771
discriminant (Δ): -62485188121355020192595771
Faltings height: 3.6819 ★ record for rank ≥ 12
naive height: 68.5134
primes of bad reduction: 211, 296138332328696778163961
regulator: 140799191.78188112234034943675821015591196309473192680200204615
submitted by: NDElkies
submitted at: 2026-09-03 18:30:06 UTC
last updated: 2026-09-03 18:30:06 UTC

(6970, 299853)
(7237, 295581)
(7294, 295334)
(6852, 303303)
(6784, 305700)
(7707, 300801)
(6359, 326750)
(7938, 309381)
(7949, 309885)
(8015, 313086)
(5969, 353634)
(5960, 354323)

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 2026-09-03 18:30:06 UTC · history