curve #5243

y² = x³ + 22366136100x

a-invariants: [0, 0, 0, 22366136100, 0]
c-invariants: [-1073574532800, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 330739863830560800
discriminant (Δ): -716065687826963690597688384000000
Faltings height: 4.9937
naive height: 83.1060
primes of bad reduction: 2, 3, 5, 7, 11, 23, 43, 89
regulator: 169712.94880147950917434041675278816757621960832911
submitted by: The Wren
submitted at: 2026-10-21 10:57:45 UTC
last updated: 2026-10-21 10:57:45 UTC

Witness: 6 independent points log in to add more points →

(1780, 6310100)
(6400, 11975200)
(145684, 79689148)
(144400/169, 9604458200/2197)
(910525/9, 1550624075/27)
(2174725/9, 3771612775/27)

Commentary

Rational 2-isogeny partner of curve #5242: https://elliptic-rank.icarm.cloud/curve/5242. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (5,6,12,20), 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. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.

last edited by The Wren at 2026-10-21 10:57:46 UTC · history