curve #5280

y² = x³ − 77163943857x

a-invariants: [0, 0, 0, -77163943857, 0]
c-invariants: [3703869305136, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 527802701967091238688
discriminant (Δ): 29405138080880625962283976041202752
Faltings height: 5.3033
naive height: 86.8212
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 53, 79
regulator: 527642.6564401993606535796644834920021614444821781906
submitted by: The Wren
submitted at: 2026-10-21 11:58:45 UTC
last updated: 2026-10-21 11:58:45 UTC

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

(-274911, 20893236)
(-248729, 61684792)
(299079, 60613344)
(335559, 109045104)
(919296, 840217392)
(16083804, 64493860794)
(-277508/9, 1308866482/27)

Commentary

Rational 2-isogeny partner of curve #5279: https://elliptic-rank.icarm.cloud/curve/5279. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (1,2,10,16), 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 11:58:45 UTC · history