curve #2861

y² + xy = x³ − 240169668868104529524321303756x + 29668756031923445007028869559325820330802320

a-invariants: [1, 0, 0, -240169668868104529524321303756, 29668756031923445007028869559325820330802320]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 162918088827470615730
discriminant (Δ): 506352172291747331693164028212312239117978176319758468238782971060210789436136609546240000
Faltings height: 15.9155
naive height: 214.5670
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 41, 53, 197, 337, 353, 2377
regulator: 58164.5742624269195951470838744660001282889941218
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:25:45 UTC
last updated: 2026-09-26 20:25:45 UTC

(-86377451671656, -7054752418018569558540)
(-8889727242996, -5639423401321035640560)
(-370202468947632, -8236744372377746818884)
(50272235005464, 4209743779052349577716)
(-195003322326090480/361, -9163909818068780772090540/6859)

Voznyy (2021). Source: https://dujella.github.io/tors/z2z6old5.html (curve entry 26). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:25:45 UTC · history