curve #2109

y² = x³ + x² − 16824951736143567031119198400x + 2229711729929969707866416499172006945042448

a-invariants: [0, 1, 0, -16824951736143567031119198400, 2229711729929969707866416499172006945042448]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/4ℤ
conductor (N): 1128310354841987032068083640
discriminant (Δ): -1842918826394226368055731166624954123981130379579930000290272035202111592968430358246400
Faltings height: 15.4307
naive height: 208.5440
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 23, 31, 41, 53, 61, 67, 109, 257, 263, 6857
regulator: 233557909.634031665003976922249867242089139925297950721
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:58:12 UTC
last updated: 2026-09-26 06:58:12 UTC

Witness: 8 independent points log in to add more points →

(-165288063267904/25, 191240247832121108883444/125)
(97456826846789/4, 10834753198037905525935/8)
(221261040094736, 3056003923907204427300)
(-20608229963264, 1602401918009707460100)
(1651693171244096, 66935851571739081130500)
(414246644582014624/289, 265624822726722257019281340/4913)
(1309319642593070336/7921, 1403763255186224717247792420/704969)
(-358698438158106688/5329, 680195329801737863690034276/389017)

Commentary

2-isogenous partner of curve#1108 (Eroshkin (2008)); 4-isogenous partner of curve#1147, curve#1166 (David Renshaw); 8-isogenous partner of curve#1136 (David Renshaw).

last edited by Steps Unbounded at 2026-09-26 21:47:22 UTC · history