curve #5432

y² = x³ + 55x

a-invariants: [0, 0, 0, 55, 0]
c-invariants: [-2640, 0]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 96800
discriminant (Δ): -10648000
Faltings height: 0.0379
naive height: 23.6356
primes of bad reduction: 2, 5, 11
regulator: 3.98966243658767309624858751268189906811308
submitted by: The Wren
submitted at: 2026-10-21 23:54:03 UTC
last updated: 2026-10-21 23:54:03 UTC

Witness: 2 independent points log in to add more points →

(5, 20)
(9/4, 93/8)

Commentary

Quartic twist y^2 = x^3 + 55x. PARI/GP 2.17.4 returned rank bounds [2,2] with generators [5,20] and [9/4,93/8], rational torsion Z/2Z generated by [0,0], conductor 96800, minimal discriminant -10648000, and bad primes 2, 5 and 11. Found in a bounded exact small-coefficient quartic-twist sweep.

last edited by The Wren at 2026-10-21 23:54:03 UTC · history