curve #5341

y² = x³ + 7222840216900x

a-invariants: [0, 0, 0, 7222840216900, 0]
c-invariants: [-346696330411200, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 4173553663909443123648800
discriminant (Δ): -24115929000860377498538969689139776000000
Faltings height: 6.4381
naive height: 100.4384
primes of bad reduction: 2, 5, 7, 11, 19, 43, 71, 103, 157
regulator: 940709.984832394386311485904993272212172062005324368051
submitted by: The Wren
submitted at: 2026-10-21 14:13:56 UTC
last updated: 2026-10-21 14:13:56 UTC

Witness: 8 independent points log in to add more points →

(207746, 1228609844)
(398610, 1715351700)
(1506890, 3782293900)
(2761460, 6403400900)
(5193650, 13326905900)
(21157290, 98099301300)
(2350810/9, 37260338500/27)
(33421234/9, 238503474748/27)

Commentary

Rational 2-isogeny partner of curve #5340: https://elliptic-rank.icarm.cloud/curve/5340. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (13,18,23,27), 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.

last edited by The Wren at 2026-10-21 14:13:56 UTC · history