curve #2843

y² + xy = x³ − 14308480358642264809261681298200x + 20832355619626831304182830954139201872779240000

a-invariants: [1, 0, 0, -14308480358642264809261681298200, 20832355619626831304182830954139201872779240000]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/8ℤ
conductor (N): 344341391147749705710
discriminant (Δ): 446126168951856068263041717922777514876517999410934122561810051704892034179097600000000
Faltings height: 16.3298
naive height: 226.8288
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 41, 71, 191, 271, 311, 10639
regulator: 53285.3925724629411689783202722754305883064597569
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:56 UTC
last updated: 2026-09-26 20:24:56 UTC

Witness: 5 independent points log in to add more points →

(1211191369036400, 72655671639587522661800)
(2184005996951920, 5205662428129388200)
(1791360394830560, 30808050954630647143400)
(2718620200653680, 45011891361086352564200)
(1332000953825150, 64317318766862744365550)

Commentary

Dujella - MacLeod - Peral (2013). Source: https://dujella.github.io/tors/z8old5.html (curve entry 12). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:56 UTC · history