curve #84

y² + y = x³ − 2438527x + 1545098346

a-invariants: [0, 0, 1, -2438527, 1545098346]
rank (lower bound): ≥ 10
conductor (N): 103294665688000244363
naive height: 55.8399
Faltings height: 2.5934
discriminant (Δ): -103294665688000244363
primes of bad reduction: 568841213, 181587872551
regulator: 883114.6071087112093983008109847701591149707946289746317701
submitted by: David Renshaw
last updated: 2026-07-01 22:50:31

Witness: 10 independent points

(-17, 39831)
(20, 38682)
(57, 37500)
(67, 37175)
(-127, 43043)
(169, 33731)
(281, 29699)
(-324, 47970)
(-353, 48599)
(354, 26948)

Commentary

Provenance: Elkies-Watkins, Elliptic curves of large rank and small conductor (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=10: [0,0,1,-2438527,1545098346], |Delta|=103294665688000244363, I=173. The submitted integral points give the rank >= 10 witness checked by the site.

last edited by David Renshaw at 2026-06-02 18:44:35 · history