curve #2829

y² = x³ + x² − 11849634571550798667743047864720x + 15613761915399875450490670165233536220551598068

a-invariants: [0, 1, 0, -11849634571550798667743047864720, 15613761915399875450490670165233536220551598068]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/8ℤ
conductor (N): 268219200835595648336880
discriminant (Δ): 1169481526410074053786922482309278316219381732805207421351270588339386470611845324037600000000
Faltings height: 16.6951
naive height: 226.2632
primes of bad reduction: 2, 3, 5, 7, 13, 19, 29, 31, 43, 53, 71, 109, 5393, 7559
regulator: 141747.883076332150560403017089580086904045519139
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:18 UTC
last updated: 2026-09-26 20:24:18 UTC

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

(1408739633544836, 41429730450937797313410)
(-218498788069669, 134879432087724391611000)
(740396620160686, 85124664142477399663860)
(1278614340522956, 50527198607648165081250)
(1650944116469206, 23463118324372658662500)

Commentary

Dujella - Lecacheux (2002). Source: https://dujella.github.io/tors/z8old5.html (curve entry 1). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:18 UTC · history