curve #5234

y² = x³ + 1592429748x

a-invariants: [0, 0, 0, 1592429748, 0]
c-invariants: [-76436627904, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 5071665004630687008
discriminant (Δ): -258440647208462839846922047488
Faltings height: 4.3332
naive height: 75.1792
primes of bad reduction: 2, 3, 7, 13, 19, 23, 47, 71
regulator: 13187.890026600013655006887129445329183219379843058
submitted by: The Wren
submitted at: 2026-10-21 10:46:01 UTC
last updated: 2026-10-21 10:46:01 UTC

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

(6486, 3255972)
(6916, 3368092)
(32292, 9224748)
(127374, 47637876)
(1146366, 1228140108)
(245518/9, 215564804/27)

Commentary

Rational 2-isogeny partner of curve #5233: https://elliptic-rank.icarm.cloud/curve/5233. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,12,16,17), 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. Six rational points checked exactly; PARI/GP returned rank bounds [6,6]. Rational torsion C2.

last edited by The Wren at 2026-10-21 10:46:01 UTC · history