curve #3342

y² = x³ + x² + 11141842980x + 36412912304100

a-invariants: [0, 1, 0, 11141842980, 36412912304100]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/6ℤ
conductor (N): 39777459540
discriminant (Δ): -89094643026019812274042404000000
Faltings height: 4.8200
naive height: 81.0155
primes of bad reduction: 2, 3, 5, 7, 13, 41, 137, 1297
regulator: 1578.938956291323522017631558179115132242474747
submitted by: David Renshaw
submitted at: 2026-09-26 21:03:50 UTC
last updated: 2026-09-26 21:03:50 UTC

Witness: 4 independent points log in to add more points →

(-565360/289, 18778366950/4913)
(615240/1369, 325995405450/50653)
(5836049/256, 71211824775/4096)
(30960, 20274150)

Commentary

Rationally isogenous to curve#822 (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 4 carries over. Torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-26 21:03:50 UTC · history