curve #3348

y² + xy = x³ − 378450x + 143224402500

a-invariants: [1, 0, 0, -378450, 143224402500]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/6ℤ
conductor (N): 41061390
discriminant (Δ): -8861715565306427709000000
Faltings height: 3.4659
naive height: 64.8985
primes of bad reduction: 2, 3, 5, 29, 109, 433
regulator: 113.40389713295223180429669355727218915125454
submitted by: David Renshaw
submitted at: 2026-09-26 21:08:44 UTC
last updated: 2026-09-26 21:08:44 UTC

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

(37800, 7339050)
(9750, 1027800)
(-2394, 362322)

Commentary

Rationally isogenous to curve#1800 (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 21:08:45 UTC · history