curve #3049

y² + xy = x³ − 55770783304388775819212152590x + 41845524204552863364522334541356125554692

a-invariants: [1, 0, 0, -55770783304388775819212152590, 41845524204552863364522334541356125554692]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 40671677445041477433310596010
discriminant (Δ): 11101217566758100654949756159762288423826424014600317105422493292781497158753450983424000
Faltings height: 15.5838
naive height: 210.1867
primes of bad reduction: 2, 5, 7, 19, 23, 29, 37, 53, 107, 131, 239, 263, 3329, 7971031
regulator: 22698361.3937660874445369616515514824338013522908709259
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:34:55 UTC
last updated: 2026-09-26 20:34:55 UTC

Witness: 8 independent points log in to add more points →

(306541429369044, 3427939023665242824898)
(527877698364, 111380063363099860258)
(244334067358908, 1000837542844271276066)
(258256536657212, 1692178187168780721570)
(-231496040870596, -739318290282078949982)
(-232703773019716, -647120051349991086302)
(-129154370822916, -2256209383051094209502)
(-141999532315716, -2257877463627263982302)

Commentary

Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 66). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:34:55 UTC · history