curve #5278

y² = x³ − 21383686181x

a-invariants: [0, 0, 0, -21383686181, 0]
c-invariants: [1026416936688, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 14632385109999691672352
discriminant (Δ): 625788662543541143456668484335424
Faltings height: 4.9825
naive height: 82.9713
primes of bad reduction: 2, 11, 13, 17, 29, 53, 59, 97
regulator: 290050.6114868279501969613876048096152136506404284251
submitted by: The Wren
submitted at: 2026-10-21 11:54:40 UTC
last updated: 2026-10-21 11:54:40 UTC

Witness: 7 independent points log in to add more points →

(-99297, 33827178)
(-97291, 34051850)
(-20040943/256, 141549180409/4096)
(-3273556/25, 2944563622/125)
(-1204544/9, 581945320/27)
(-378131/9, 775168550/27)
(-62127/4, 144969903/8)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (2,6,13,14), 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 11:54:40 UTC · history