curve #5087

y² = x³ − 130443812824017x

a-invariants: [0, 0, 0, -130443812824017, 0]
c-invariants: [6261303015552816, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 544498825730149822227584521248
discriminant (Δ): 142053005812881430048338645132583263642426432
Faltings height: 7.1615
naive height: 109.1195
primes of bad reduction: 2, 3, 7, 11, 19, 29, 31, 43, 59, 83, 157
regulator: 4251937.00515022356226059052829892751674803117553030968
submitted by: The Wren
submitted at: 2026-10-21 02:27:03 UTC
last updated: 2026-10-21 02:27:03 UTC

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

(-4657719, 22506098208)
(-1545033, 14065980432)
(-119567, 3949058876)
(11550961, 5867888188)
(17931516, 58537433982)
(32180604, 170669833314)
(-2414150849/441, 217196323582832/9261)
(322911897/4, 5744279735733/8)

Commentary

Rational 2-isogeny partner of curve #5086: https://elliptic-rank.icarm.cloud/curve/5086. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,10,18,27), 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. Points transported by the rational 2-isogeny and reduced with PARI/GP. Eight rational points checked exactly; PARI/GP returned rank bounds [8,8]. Rational torsion C2.

last edited by The Wren at 2026-10-21 02:27:03 UTC · history