curve #2784

y² + xy = x³ − 2494386716254257179900313435657471298255x + 47950428811853578302303100075736441050437846119869139884025

a-invariants: [1, 0, 0, -2494386716254257179900313435657471298255, 47950428811853578302303100075736441050437846119869139884025]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 17569174278352986897510210
discriminant (Δ): 5927243673102551071320762927517904179868335548961534601463645581140722578038457773804898582224376194417710000000000
Faltings height: 21.2428
naive height: 283.7582
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 61, 79, 149, 181, 709, 10711, 19709
regulator: 179087.4451211278996846883999466263160349637546
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:22:17 UTC
last updated: 2026-09-26 20:22:17 UTC

(28509015942778302410, 3003281534671521511510019045)
(-4710087341394312480646/289, 1426248104611211485908211687075441/4913)
(651746601062048885608610/27889, 229159071225334021088598309104574895/4657463)
(2474363018938566848121587468060/27532433041, 3386940458446040733191786369680733084310244255/4568429082060089)

Elkies (2006). Source: https://dujella.github.io/tors/z10.html (curve entry 3). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:22:17 UTC · history