curve #82

y² + y = x³ − 1788817x + 843180666

a-invariants: [0, 0, 1, -1788817, 843180666]
rank (lower bound): ≥ 10
conductor (N): 59202439687694448757
naive height: 54.8048
Faltings height: 2.5324
discriminant (Δ): 59202439687694448757
primes of bad reduction: 59202439687694448757
regulator: 774709.5755443039950812393750908533891851784680859970994988
submitted by: David Renshaw
last updated: 2026-07-01 22:50:30

Witness: 10 independent points

(-32, 30006)
(38, 27843)
(-84, 31509)
(-87, 31593)
(105, 25622)
(214, 21683)
(-234, 35340)
(-291, 36593)
(313, 17718)
(355, 15902)

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,-1788817,843180666], |Delta|=59202439687694448757, I=176. The submitted integral points give the rank >= 10 witness checked by the site.

last edited by David Renshaw at 2026-06-02 18:44:34 · history