curve #785

y² + xy = x³ − x² − 266451964x + 1712164041364

a-invariants: [1, -1, 0, -266451964, 1712164041364]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 27805670188643664300931114
discriminant (Δ): -55611340377287328601862228
Faltings height: 3.7223
naive height: 69.8606
primes of bad reduction: 2, 2311, 12333707, 487764062196841
regulator: 78281639.467582174909688157867626234865692541798465645454081475
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:39:43 UTC
last updated: 2026-09-18 12:39:43 UTC

(11400, -400742)
(6971, 436339)
(7345, 385287)
(8486, -253430)
(-3890, -1638112)
(1178, 1182592)
(50106, 10659334)
(1784, 1113778)
(3131, -954765)
(20934, -2314352)
(7672, 341810)
(9006, 202610)

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

last edited by Michael Rubinstein at 2026-09-18 12:39:43 UTC · history