curve #5230

y² = x³ + 50974308x

a-invariants: [0, 0, 0, 50974308, 0]
c-invariants: [-2446766784, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 11784036626208
discriminant (Δ): -8476840083142876532871168
Faltings height: 3.4727
naive height: 64.8541
primes of bad reduction: 2, 3, 7, 11, 37, 71
regulator: 2315.77192781975109003522598549695733970065071132
submitted by: The Wren
submitted at: 2026-10-21 10:40:20 UTC
last updated: 2026-10-21 10:40:20 UTC

Witness: 5 independent points log in to add more points →

(148, 86876)
(781, 200717)
(1332, 265068)
(1813, 313649)
(3136, 436688)

Commentary

Rational 2-isogeny partner of curve #5229: https://elliptic-rank.icarm.cloud/curve/5229. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (4,5,14,20), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.

last edited by The Wren at 2026-10-21 10:40:20 UTC · history