curve #5333

y² = x³ + 15937916148x

a-invariants: [0, 0, 0, 15937916148, 0]
c-invariants: [-765019975104, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 56448260253484257312
discriminant (Δ): -259104279922707835548493019762688
Faltings height: 4.9090
naive height: 82.0895
primes of bad reduction: 2, 3, 7, 11, 19, 23, 59, 223
regulator: 771047.8864977837996198933402942975933722314083810113
submitted by: The Wren
submitted at: 2026-10-21 13:32:10 UTC
last updated: 2026-10-21 13:32:10 UTC

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

(253, 2008061)
(669, 3265389)
(966, 3923892)
(2622, 6465852)
(3594486, 6819034572)
(7659381, 21200665527)
(93214/25, 964019188/125)

Commentary

Rational 2-isogeny partner of curve #5332: https://elliptic-rank.icarm.cloud/curve/5332. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (1,8,23,25), 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 13:32:10 UTC · history