curve #5308

y² = x³ + 3025774875123x

a-invariants: [0, 0, 0, 3025774875123, 0]
c-invariants: [-145237194005904, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 32552226115291044424053792
discriminant (Δ): -1772922742361467548173848943032223095488
Faltings height: 6.2206
naive height: 97.8282
primes of bad reduction: 2, 3, 7, 11, 13, 19, 31, 43, 89, 149
regulator: 9648445.49851155856317759432089342901982160532901237500
submitted by: The Wren
submitted at: 2026-10-21 12:53:24 UTC
last updated: 2026-10-21 12:53:24 UTC

Witness: 8 independent points log in to add more points →

(9387, 168534198)
(75867, 479575998)
(4626843, 10632485214)
(5904171, 14955921162)
(654417/4, 5653508463/8)
(23958753/4, 122117764041/8)
(23958753/121, 1036886912334/1331)
(14264307057/29584, 6377857778739447/5088448)

Commentary

Rational 2-isogeny partner of curve #5307: https://elliptic-rank.icarm.cloud/curve/5307. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (12,16,18,19), 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 12:53:24 UTC · history