curve #3341

y² + xy = x³ + 11156415x + 90281340297

a-invariants: [1, 0, 0, 11156415, 90281340297]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/6ℤ
conductor (N): 45225870
discriminant (Δ): -3609908445284280868032000
Faltings height: 3.3924
naive height: 63.9755
primes of bad reduction: 2, 3, 5, 41, 83, 443
regulator: 131.14777551291934873929853554304780385909927
submitted by: David Renshaw
submitted at: 2026-09-26 21:03:40 UTC
last updated: 2026-09-26 21:03:40 UTC

Witness: 3 independent points log in to add more points →

(28194, 4762563)
(17502, 2367555)
(-2478, 219003)

Commentary

Rationally isogenous to curve#1799 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 3 carries over. Torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-26 21:03:40 UTC · history