curve #2794

y² + xy = x³ − 103489768893628312781079515942046035045283420x + 426821159313037167421541292563415138855201471354579842159144432400

a-invariants: [1, 0, 0, -103489768893628312781079515942046035045283420, 426821159313037167421541292563415138855201471354579842159144432400]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/9ℤ
conductor (N): 130072996979244993654288816690
discriminant (Δ): -7763259248572861510949432934022353005457556927635912944415747374752566852847219473763437205111589313874795675798686863720448000000000
Faltings height: 24.2528
naive height: 315.7616
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 43, 61, 73, 97, 113, 151, 1259, 369698741
regulator: 431223.3370991926849619775429309323680636326802
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:22:45 UTC
last updated: 2026-09-26 20:22:45 UTC

(1563683920360890813240, 518477817173214637679530413217380)
(5716354371461648217240, 148420366242656390066279644033380)
(-9905539577978170473198600/841, -2646465614513059707012797361777715980/24389)
(1219178860627460026852681950815908753765324224383160/245788008683078423834063276809, 22967960388834830874332165756264979800484360179891154079943260243716421393740/121854349765708325351503977114537620910068123)

Voznyy (2026). Source: https://dujella.github.io/tors/z9.html (curve entry 7). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:22:45 UTC · history