curve #5335

y² = x³ + 1456279384176054900x

a-invariants: [0, 0, 0, 1456279384176054900, 0]
c-invariants: [-69901410440450635200, 0]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 18851107953566130654892075802791200
discriminant (Δ): -197657855147920430008973077289309038556690095945536000000
Faltings height: 9.4916
naive height: 137.0809
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 47, 79, 109, 131, 907
regulator: 1112092583.7142824130558452662985650690532745252162500700
submitted by: The Wren
submitted at: 2026-10-21 13:39:41 UTC
last updated: 2026-10-21 13:39:41 UTC

Witness: 9 independent points log in to add more points →

(17373510, 5030499820500)
(1121875524, 55188422652132)
(2616588990, 147394234633500)
(3000152269, 177124733931797)
(44607465/4, 32240714440725/8)
(5868385600/9, 945685938150800/27)
(230695093750/81, 120340582294872500/729)
(271124654350/2209, 1395202591041321700/103823)
(2611165282110/1681, 5343089498045352900/68921)

Commentary

Rational 2-isogeny partner of curve #5334: https://elliptic-rank.icarm.cloud/curve/5334. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (1,5,16,25), reduced by rational fourth-power scaling. Reference: “High rank elliptic curves with torsion group Z/(2Z),” Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3.

last edited by The Wren at 2026-10-21 13:39:41 UTC · history