curve #3060

y² = x³ + x² − 14056407680017271277544631905x + 1082872295776815338920297488812717727150600

a-invariants: [0, 1, 0, -14056407680017271277544631905, 1082872295776815338920297488812717727150600]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 28662861085935403583774269180
discriminant (Δ): -328821262620771793088860257067339220144043090605989193354654489213312501742573604750000
Faltings height: 15.2960
naive height: 207.0995
primes of bad reduction: 2, 5, 11, 13, 17, 19, 31, 61, 71, 79, 163, 241, 661, 1129, 99787
regulator: 16531353.2605234007791993764344309609858582214625929165
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:35:25 UTC
last updated: 2026-09-26 20:35:25 UTC

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

(59634286205865, 675797879291569588125)
(-72491520392635, 1311830107876079631125)
(-145856174368105, 173604289809758688595)
(55369108120840, 688715271624167187400)
(51366212060820, 704540274874545565170)
(-32985584476331, 1229081443064564094005)
(-7360495312085, 1089006726267725332925)
(-142604450061560, 432862940841014483800)

Commentary

Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 59). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:35:25 UTC · history