curve #76

y² + y = x³ − 23737x + 960366

a-invariants: [0, 0, 1, -23737, 960366]
c-invariants: [1139376, -829756440]
rank (lower bound): ≥ 8
torsion subgroup: trivial
conductor (N): 457532830151317
discriminant (Δ): 457532830151317
Faltings height: 1.5176
naive height: 41.8380
primes of bad reduction: 457532830151317
regulator: 10423.4798881981483561708641513672204334594588544763000
submitted by: David Renshaw
submitted at: 2026-06-01 15:47:39 UTC
last updated: 2026-07-01 22:54:25 UTC

Witness: 8 independent points log in to add more points →

(5, 917)
(-13, 1125)
(17, 749)
(-18, 1175)
(-29, 1274)
(33, 461)
(36, 390)
(38, 336)

Commentary

Provenance: Elkies-Watkins, "Elliptic curves of large rank and small conductor" (ANTS VI / arXiv:math/0403374), Table 4 low absolute-discriminant list for r=8: [0,0,1,-23737,960366], |Delta|=457532830151317; their I-column records 96 integral x-coordinates. The submitted integral points certify rank >= 8 here.

last edited by David Renshaw at 2026-06-01 15:47:39 UTC · history