curve #2573

y² + xy = x³ − 25200620x + 48690669456

a-invariants: [1, 0, 0, -25200620, 48690669456]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/10ℤ
conductor (N): 32718
discriminant (Δ): 2244956575342666752
Faltings height: 2.7996
naive height: 62.7407
primes of bad reduction: 2, 3, 7, 19, 41
regulator: 3.519231878892935649110769594843047170222
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:10:10 UTC
last updated: 2026-09-26 20:10:10 UTC

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

(9376, -802604)

Commentary

2-isogenous to curve#1729 via the rational 2-torsion point x=-1448. 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 20:10:10 UTC · history