curve #34

y² = x³ + x² − 115306530165769495485x + 304950013864929098742150007444

a-invariants: [0, 1, 0, -115306530165769495485, 304950013864929098742150007444]
rank (lower bound): ≥ 11
conductor (N): 159117919909446340006437537659166966132164
naive height: 150.1960
Faltings height: 10.5532
discriminant (Δ): 57942789150218118922071208483979411230699716000862987088178512
primes of bad reduction: 2, 19, 23, 29, 31, 37, 47, 53, 59, 61, 67, 79, 83, 97, 7163230956091032353
regulator: 251615995233.483808978493583609207799224828706024666003168936
submitted by: David Renshaw
last updated: 2026-07-01 22:49:32

(16720669911, 1746918971478919)
(-27494384469/25, 82009061233472771/125)
(24003278596/9, 3457124546861636/27)
(-473203304125/49, 246826926055649591/343)
(143049082761/64, 123719807142058949/512)
(-5963359769, 883457619817881)
(6678087633629/676, 6335744808950599147/17576)
(10500034749/4, 1141436027393173/8)
(9063959795, 66852115553887)
(70954716481/25, 2933723417746929/125)
(13823082740, 1162901547372488)

Found by Schneiders - Zimmer (1991). A curve of rank exactly 11, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:32:06 · history