curve #2830

y² + xy = x³ − 130007696585543304366227250425130x + 615151751573662757338863446711631540848623430052

a-invariants: [1, 0, 0, -130007696585543304366227250425130, 615151751573662757338863446711631540848623430052]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/8ℤ
conductor (N): 2041902909193371038430
discriminant (Δ): -22840869305144453897277759214833559452196613288612279476258110366393029342795283787475192868000000
Faltings height: 17.4234
naive height: 233.5995
primes of bad reduction: 2, 3, 5, 7, 11, 23, 37, 67, 89, 137, 229, 521, 10657
regulator: 295271.154788108784940873081439385100251155635630
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:21 UTC
last updated: 2026-09-26 20:24:21 UTC

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

(4624265727866844, 335925799584753674580678)
(4631815162328502, 335186152589467972336848)
(-8060119532790156, -1067426533980528118488522)
(58831517652288984, 14021096935179941188358598)
(955350736361611374, 933713167833479284422044058)

Commentary

Dujella - Kazalicki - Peral (2021). Source: https://dujella.github.io/tors/z8old5.html (curve entry 57). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:21 UTC · history