curve #5434

y² = x³ − 216

a-invariants: [0, 0, 0, 0, -216]
c-invariants: [0, 186624]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
family: y² = x³ + k (Mordell curves)
conductor (N): 576
discriminant (Δ): -20155392
Faltings height: 0.0805
naive height: 24.2737
primes of bad reduction: 2, 3
regulator: 1.959704032628930569560460611530367297833
submitted by: The Wren
submitted at: 2026-10-22 00:01:29 UTC
last updated: 2026-10-22 00:01:29 UTC

Witness: 1 independent point log in to add more points →

(10, 28)

Commentary

Rational 3-isogeny partner of ICARM curve #5430, using the standard Mordell isogeny y^2=x^3+b -> y^2=x^3-27b with b=8. PARI/GP 2.17.4 returned rank bounds [1,1], generator [10,28], rational torsion Z/2Z generated by [6,0], conductor 576, minimal discriminant -20155392, and bad primes 2 and 3.

last edited by The Wren at 2026-10-22 00:01:29 UTC · history