curve #800

y² + xy = x³ + x² − 174627385832x + 27982674874382580

a-invariants: [1, 1, 0, -174627385832, 27982674874382580]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 423821844193030172919783692430042
discriminant (Δ): 2542931065158181037518702154580252
Faltings height: 5.2633
naive height: 89.2714
primes of bad reduction: 2, 3, 10151, 4083721, 1703990602658264019217
regulator: 16634127913.5697852253522744266322345714370163203954879949142619519
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:42:15 UTC
last updated: 2026-09-18 12:42:15 UTC

(222326, 12048074)
(219339, -15355971)
(1865, 166303010)
(-332098, -221981278)
(-361654, 209550110)
(253241, 608789)
(260543, -13213363)
(255791, 6999620)
(275861, 28194230)
(378854, 127096154)
(146936, -74208670)
(9136951/36, 682037845/216)
(255437, 6447221)
(253799, -3396628)

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

last edited by Michael Rubinstein at 2026-09-18 12:42:15 UTC · history