curve #3064

y² = x³ + 708291392738196762720225

a-invariants: [0, 0, 0, 0, 708291392738196762720225]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 76495470415725250373784300
discriminant (Δ): -216724333115670259601781304169912713587581589870000
Faltings height: 8.3374
naive height: 123.3574
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 29, 41, 47, 59
regulator: 327055.732652397001629942270651692262565342990579299244
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:35:36 UTC
last updated: 2026-09-26 20:35:36 UTC

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

(-88860785, 81396479060)
(-87348261, 204569627262)
(-63256830, 674665720365)
(-40588401, 800890328532)
(126513660, 1653248880465)
(101707060, 1326794024465)
(-29810690, 825711396965)
(-44793980, 786391914385)

Commentary

Elkies - Rogers (2003). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 65). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:35:36 UTC · history