curve #3062

y² = x³ − x² − 155620906905035367584300588900x + 23529944481555251676876571790285671801162500

a-invariants: [0, -1, 0, -155620906905035367584300588900, 23529944481555251676876571790285671801162500]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 115810393716612793243662456840
discriminant (Δ): 2023227811230088546497226503132287116098132934258520579328121679814596936318563961760000
Faltings height: 15.6008
naive height: 213.2653
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 31, 41, 71, 79, 151, 197, 241, 569, 1039, 1877
regulator: 8027412.25470054319680923294949961742219443851442410036
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:35:28 UTC
last updated: 2026-09-26 20:35:28 UTC

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

(-119848234211200, 6360769086691746325950)
(3704327230850, 4790983672414742751000)
(402823572798126, 5119285037015739604560)
(59875247652245, 3798257444515667223090)
(202535726445532, 565077405802465062962)
(-321267781161640, 6353496718852216718070)
(117373386467505, 2623201761704752568340)
(110898103490818270, 36930350949386712434893640)

Commentary

Dujella - Peral (2016). Source: https://dujella.github.io/tors/z2z4old678.html (curve entry 12). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:35:29 UTC · history