curve #5311

y² = x³ − 8081372x

a-invariants: [0, 0, 0, -8081372, 0]
c-invariants: [387905856, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 130617146804768
discriminant (Δ): 33778104093054130614272
Faltings height: 3.0123
naive height: 59.3288
primes of bad reduction: 2, 13, 23, 29, 233
regulator: 7065.3336253517796691711269526374116711846161054094
submitted by: The Wren
submitted at: 2026-10-21 13:01:06 UTC
last updated: 2026-10-21 13:01:06 UTC

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

(-2691, 47541)
(-2668, 50692)
(-667, 71369)
(4212, 201708)
(6032, 413192)
(-8671/4, 685009/8)

Commentary

Rational 2-isogeny partner of curve #5310: https://elliptic-rank.icarm.cloud/curve/5310. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (8,16,19,22), 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 13:01:07 UTC · history