curve #70

y² + xy + y = x³ − x² − 6x

a-invariants: [1, -1, 1, -6, 0]
rank (lower bound): ≥ 3
conductor (N): 11197
naive height: 16.8284 ★ record for rank ≥ 3
Faltings height: -0.5324
discriminant (Δ): 11197
primes of bad reduction: 11197
regulator: 0.86842195369372664900484860186367158964425101
submitted by: David Renshaw
last updated: 2026-07-01 23:04:07

Witness: 3 independent points

(0, 0)
(-1, 2)
(-2, 1)

Commentary

Provenance: found by a local bounded-height search over reduced integral Weierstrass models. Invariants are c4=273, c6=999, Delta=11197. The submitted points (0,0), (-1,2), (-2,1) were checked exactly on the curve, with an additional finite-field independence sanity check; the site Neron-Tate verifier gives the definitive certificate.

last edited by David Renshaw at 2026-05-29 13:46:08 · history