curve #5282

y² = x³ + 629940049284x

a-invariants: [0, 0, 0, 629940049284, 0]
c-invariants: [-30237122365632, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 793648931383856697825312
discriminant (Δ): -15998439902404499921602257180885651456
Faltings height: 5.8283
naive height: 93.1203
primes of bad reduction: 2, 3, 7, 13, 19, 43, 47, 83, 181
regulator: 9087665.36374725806404936290498361877970250268141935142
submitted by: The Wren
submitted at: 2026-10-21 12:02:56 UTC
last updated: 2026-10-21 12:02:56 UTC

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

(498, 17711868)
(6708, 65007228)
(263442, 429227196)
(307098, 471609468)
(386058, 548390172)
(418818, 580770588)
(6820313682, 563256908184516)
(6541977/4, 18598840611/8)

Commentary

Rational 2-isogeny partner of curve #5281: https://elliptic-rank.icarm.cloud/curve/5281. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (3,6,9,17), 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 12:02:56 UTC · history