curve #3035

y² + xy = x³ − 724016704581073411076105781935x − 220753490559318324998944201709786454755631303

a-invariants: [1, 0, 0, -724016704581073411076105781935, -220753490559318324998944201709786454755631303]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 11357092358577020158149155010
discriminant (Δ): 3237631601102205186043641271090357682445986706978419682843007813332700118176619298816000000
Faltings height: 16.1118
naive height: 217.8774
primes of bad reduction: 2, 3, 5, 11, 37, 43, 47, 101, 149, 223, 283, 359, 379, 3561661
regulator: 91358222.9944397643111920916191657495565926732105942749
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:34:18 UTC
last updated: 2026-09-26 20:34:18 UTC

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

(-394226023171526, -1845109664794335908447)
(-405292302390506, -2472011746215283313507)
(983835558752934, 4383998879741211236733)
(-496375109089826, -4040963278237561638827)
(1058161029785734, 14069405815261419929533)
(696116936708208076/9, 580760291708194905583202621/27)
(26824447802498614, 4391117855252108880847213)
(14301405513797491/4, 1656885557501400892736399/8)

Commentary

Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 52). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:34:18 UTC · history