curve #32

y² + xy = x³ − 3414948705808928485x + 1462640470912335058581199361

a-invariants: [1, 0, 0, -3414948705808928485, 1462640470912335058581199361]
rank (lower bound): ≥ 10
conductor (N): 929053397624034727388941088597323782
naive height: 139.6377
Faltings height: 9.6778
discriminant (Δ): 1624596034552120480493303406632087249542571198120190723072
primes of bad reduction: 2, 3, 17, 19, 23, 29, 31, 37, 43, 47, 53, 59, 281, 74177, 4756942171609
regulator: 347100868.2553289242017767590904381615260046941546101545684
submitted by: David Renshaw
last updated: 2026-07-01 22:51:30

(1651118138, 18038584222223)
(1588614902, 6839177749439)
(-1189653814, -61979712512809)
(-700495294, -59253910115977)
(-147325510, -44300624514889)
(11898974402, 1282784596947959)
(448355771899346/126025, 8290865418217263800429/44738875)
(-621829360, -57841818977839)
(1692223027970/841, 1276149459553975651/24389)
(-380499314, -52028047503377)

Found by Kretschmer (1986). A curve of rank exactly 10, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:32:04 · history