curve #2908

y² + xy = x³ − x² − 45123702275641081919424x − 1963535841750202515136116268762932

a-invariants: [1, -1, 0, -45123702275641081919424, -1963535841750202515136116268762932]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 407739781740207625175610
discriminant (Δ): 4214663440569253095228975629561450754700660667382890675014820877562500
Faltings height: 12.0570
naive height: 168.1047
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 29, 41, 67, 101, 997, 2141, 5711
regulator: 477043.0331294476419166005689599831646627442411355343
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:52 UTC
last updated: 2026-09-26 20:27:52 UTC

Witness: 7 independent points log in to add more points →

(-46184748668, -4687994158267666)
(-60161183646, -23095727833899384)
(-48542581178, -10606589957382016)
(-55854944093, -19559910217201666)
(-185253203193, -6173748038545641)
(-64106657393, -25801849446340566)
(-45896523588, -3287014604709246)

Commentary

Dujella (2001). Source: https://dujella.github.io/tors/z6old678.html (curve entry 122). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:27:52 UTC · history