curve #714

y² + y = x³ − 21939919267x + 649337940785766

a-invariants: [0, 0, 1, -21939919267, 649337940785766]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 493755674212808044114451600614357
discriminant (Δ): 493755674212808044114451600614357
Faltings height: 4.9701
naive height: 83.0483
primes of bad reduction: 4157, 455683, 260656913414353491310547
regulator: 144271421772647.139609736538521631190293467835698343613634502335904
submitted by: Michael Rubinstein
submitted at: 2026-09-11 02:03:46 UTC
last updated: 2026-09-11 02:03:46 UTC

(-127138, 37197684)
(-1620, 26170142)
(-120, 25533717)
(1021005, 1021076132)
(-562064484938/3508129, 47271451162511756/6570725617)
(-189408467/1369, 1630693958927/50653)
(-477486407/4096, 10560152015789/262144)
(-20211714/169, 86848491956/2197)
(-1871/36, 5508966331/216)
(1358194/9, 751746968/27)
(7972092/49, 12771156999/343)
(102341593/729, 360822194945/19683)
(393676606/12769, 2150516645467/1442897)
(462062546/49, 9931108679528/343)

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

last edited by Michael Rubinstein at 2026-09-11 02:03:47 UTC · history