curve #5236

y² = x³ + 752466804x

a-invariants: [0, 0, 0, 752466804, 0]
c-invariants: [-36118406592, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 1132412582243948832
discriminant (Δ): -27267292050255722430546333696
Faltings height: 4.1458
naive height: 72.9302
primes of bad reduction: 2, 3, 19, 23, 43, 47, 71
regulator: 15081.306864827138322561402483971274886624357712509
submitted by: The Wren
submitted at: 2026-10-21 10:48:41 UTC
last updated: 2026-10-21 10:48:41 UTC

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

(142, 326884)
(4902, 1950996)
(6486, 2270100)
(162150, 66222060)
(98857/4, 46435829/8)
(153502/9, 113898484/27)

Commentary

Rational 2-isogeny partner of curve #5235: https://elliptic-rank.icarm.cloud/curve/5235. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (4,7,11,13), 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 10:48:41 UTC · history