curve #44

y² = x³ − 10012x + 346900

a-invariants: [0, 0, 0, -10012, 346900]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 382623908456 ★ record for rank ≥ 7
naive height: 39.2482
Faltings height: 1.2447
discriminant (Δ): 12243965070592
primes of bad reduction: 2, 47827988557
regulator: 4318.994211976314485322288857542918022772937787830133
submitted by: David Renshaw
submitted at: 2026-05-28 05:01:41 UTC
last updated: 2026-07-01 22:56:23 UTC

Witness: 7 independent points

(-114, 82)
(-111, 301)
(-106, 466)
(-102, 554)
(-100, 590)
(-98, 622)
(-79, 803)

Commentary

Lowest-conductor rank 7 curve in the Sage/Watkins elliptic-curves database: [0, 0, 0, -10012, 346900], conductor 382623908456. The submitted integral points were found by an exact search and certified independent by the site verifier.

last edited by David Renshaw at 2026-05-28 05:02:16 UTC · history