curve #5277

y² = x³ + 61523562408x

a-invariants: [0, 0, 0, 61523562408, 0]
c-invariants: [-2953130995584, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 15140594925484283033856
discriminant (Δ): -14904053388676486349705203086163968
Faltings height: 5.2467
naive height: 86.1417
primes of bad reduction: 2, 3, 7, 11, 19, 23, 29, 37, 71
regulator: 186305.0328769135055725118876131057965742856748496633
submitted by: The Wren
submitted at: 2026-10-21 11:52:22 UTC
last updated: 2026-10-21 11:52:22 UTC

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

(47656, 55137992)
(61161, 63179313)
(82593, 75132099)
(151848, 113329224)
(762496, 700161952)
(2129064, 3127595016)
(172753/9, 930620411/27)

Commentary

Rational 2-isogeny partner of curve #5276: https://elliptic-rank.icarm.cloud/curve/5276. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (3,4,6,10), 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 11:52:22 UTC · history