curve #83

y² + y = x³ + x² − 1856500x + 1072474760

a-invariants: [0, 1, 1, -1856500, 1072474760]
rank (lower bound): ≥ 10
conductor (N): 87950374485438204043
naive height: 55.1108
Faltings height: 2.5614
discriminant (Δ): -87950374485438204043
primes of bad reduction: 1651819847, 53244531869
regulator: 995214.3440764446000421615341619391028494443800016433750965
submitted by: David Renshaw
last updated: 2026-07-01 22:50:31

Witness: 10 independent points

(26, 32003)
(-80, 34935)
(91, 30071)
(116, 29303)
(211, 26271)
(-244, 38871)
(248, 25047)
(349, 21614)
(-433, 42371)
(-463, 42813)

Commentary

Provenance: Elkies-Watkins, Elliptic curves of large rank and small conductor (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=10: [0,1,1,-1856500,1072474760], |Delta|=87950374485438204043, I=154. 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