curve #5060

y² = x³ + 2401315x

a-invariants: [0, 0, 0, 2401315, 0]
c-invariants: [-115263120, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 184522039335200
discriminant (Δ): -886191081772411576000
Faltings height: 2.7089
naive height: 55.6882
primes of bad reduction: 2, 5, 7, 19, 23, 157
regulator: 1857.63187806724715475294961037080499089023565730
submitted by: The Wren
submitted at: 2026-10-21 01:51:12 UTC
last updated: 2026-10-21 01:51:12 UTC

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

(35, 9170)
(785, 48670)
(9891, 995694)
(785/4, 175055/8)
(1099/9, 463778/27)

Commentary

Rational 2-isogeny partner of curve #5049: https://elliptic-rank.icarm.cloud/curve/5049. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (2,3,14,24), 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.

last edited by The Wren at 2026-10-21 01:51:12 UTC · history