curve #2696

y² + xy = x³ − 1950873533612743056660x + 33177096191505561806432962227600

a-invariants: [1, 0, 0, -1950873533612743056660, 33177096191505561806432962227600]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/9ℤ
conductor (N): 540153536494110
discriminant (Δ): -320880306559112473346277208611638785822589986125270171000000000
Faltings height: 10.9587
naive height: 158.6820
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 853, 848699
regulator: 539.91038209645652064928669329889661585592381
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:11 UTC
last updated: 2026-09-26 20:18:11 UTC

van Beek (2015). Source: https://dujella.github.io/tors/z9old3.html (curve entry 14). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:18:11 UTC · history