curve #2570

y² = x³ − x² − 680x − 5700

a-invariants: [0, -1, 0, -680, -5700]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 840
discriminant (Δ): 4978713600
Faltings height: 0.5863
naive height: 31.1814
primes of bad reduction: 2, 3, 5, 7
regulator: 2.196597963753069286457897954426581558085
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:09:56 UTC
last updated: 2026-09-26 20:09:56 UTC

Witness: 1 independent point log in to add more points →

(-15, -30)

Commentary

2-isogenous to curve#1167 via the rational 2-torsion point x=10. 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 20:09:56 UTC · history