curve #2826

y² + xy + y = x³ − x² − 1288486888765840006660359584402x + 551370471381336433474899429016996626668795729

a-invariants: [1, -1, 1, -1288486888765840006660359584402, 551370471381336433474899429016996626668795729]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 11969747194951591955910
discriminant (Δ): 5573153530048446876229720872345034888572418885737489037410291033153383152571809967361000000
Faltings height: 16.1980
naive height: 219.6067
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 37, 97, 137, 283, 373, 6547
regulator: 69164.5306449847764606397236196323316995086407442
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:11 UTC
last updated: 2026-09-26 20:24:11 UTC

(275840694411987, 14728935480961756884631)
(568996051166427, 1562911512615410438941)
(532841297240187, 4011940191599356415431)
(6247507242483057, 486158572625421684880231)
(65379001260055649067/6241, 525651766712267023133539893859/493039)

Voznyy (2021). Source: https://dujella.github.io/tors/z2z6old5.html (curve entry 27). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:11 UTC · history