curve #79

y² + y = x³ − 514507x + 140806716

a-invariants: [0, 0, 1, -514507, 140806716]
rank (lower bound): ≥ 9
conductor (N): 151673348057775877
naive height: 51.0665
Faltings height: 2.1149
discriminant (Δ): 151673348057775877
primes of bad reduction: 409, 6129953, 60496301
regulator: 82462.036760633052867653702337648351572050396724991183500
submitted by: David Renshaw
last updated: 2026-07-01 22:51:31

Witness: 9 independent points

(8, 11691)
(-22, 12333)
(-48, 12860)
(83, 9933)
(-114, 14070)
(159, 7938)
(184, 7236)
(198, 6833)
(-207, 15441)

Commentary

Provenance: Elkies-Watkins, Elliptic curves of large rank and small conductor (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=9: [0,0,1,-514507,140806716], |Delta|=151673348057775877, I=126. The submitted integral points give the rank >= 9 witness checked by the site.

last edited by David Renshaw at 2026-06-02 18:44:32 · history