curve #2578

y² + xy = x³ + 1051010430x − 31142219309100

a-invariants: [1, 0, 0, 1051010430, -31142219309100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 249690
discriminant (Δ): -493274390082338961058364010000
Faltings height: 4.3803
naive height: 75.6623
primes of bad reduction: 2, 3, 5, 7, 29, 41
regulator: 9.491229236603796558080511727766080126232
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:10:29 UTC
last updated: 2026-09-26 20:10:29 UTC

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

(1035780/49, 243669390/343)

Commentary

2-isogenous to curve#1079 via the rational 2-torsion point x=-10460. 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 20:10:29 UTC · history