curve #2652

y² + xy = x³ − 691776600200x − 221460364623960000

a-invariants: [1, 0, 0, -691776600200, -221460364623960000]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1008210
discriminant (Δ): 99274350343824748984449600000000
Faltings height: 5.3735
naive height: 93.4012
primes of bad reduction: 2, 3, 5, 7, 4801
regulator: 37.0072522647781926223820780053900169426110
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:15:38 UTC
last updated: 2026-09-26 20:15:38 UTC

Witness: 2 independent points log in to add more points →

(-254313920/529, -760156600/12167)
(-81234650/169, -428007650/2197)

Commentary

2-isogenous to curve#1466 via the rational 2-torsion point x=240400. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny.

last edited by Natanael Wildner Fraga at 2026-09-26 20:15:38 UTC · history