curve #78

y² + xy = x³ − x² − 201814x + 34925104

a-invariants: [1, -1, 0, -201814, 34925104]
rank (lower bound): ≥ 8
conductor (N): 321754587851786
naive height: 48.2589
Faltings height: 1.7774
discriminant (Δ): 643509175703572
primes of bad reduction: 2, 2710699, 59349007
regulator: 6527.55172023458019453817713717187218224406628323898374
submitted by: David Renshaw
last updated: 2026-07-01 22:55:24

Witness: 8 independent points

(-5, -5992)
(-18, -6200)
(40, 5168)
(62, 4728)
(-69, -6931)
(79, 4373)
(113, 3625)
(154, 2658)

Commentary

Provenance: Elkies-Watkins, Elliptic curves of large rank and small conductor (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=8: [1,-1,0,-201814,34925104], |Delta|=643509175703572, I=109. The submitted integral points give the rank >= 8 witness checked by the site.

last edited by David Renshaw at 2026-06-02 18:44:31 · history