curve #685

y² + xy = x³ − x² − 17511333709x + 745147974695329

a-invariants: [1, -1, 0, -17511333709, 745147974695329]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 51901807229711945130373780604666
discriminant (Δ): 103803614459423890260747561209332 ★ record for rank ≥ 14
Faltings height: 4.8632 ★ record for rank ≥ 14
naive height: 82.3719 ★ record for rank ≥ 14
primes of bad reduction: 2, 26640112403, 974128908402563115311
regulator: 1965047475033.57742796431515409297424241395231633244235334564296383
submitted by: Michael Rubinstein
submitted at: 2026-09-09 03:39:26 UTC
last updated: 2026-09-09 03:39:26 UTC

(-85915, 40235703)
(-1619, 27812580)
(564, 27115613)
(708, 27069007)
(2064, 26626273)
(33852, 13808645)
(102032, 4491105)
(116870, 17113297)
(124358, 22088385)
(183630, 60912413)
(26171988, 133877339005)
(-8046479/64, 15891006891/512)
(1383280/9, 1106070619/27)
(6295744/9, 15519675125/27)

From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-11 02:00:23 UTC · history