curve #5343

y² = x³ − 1190761476792x

a-invariants: [0, 0, 0, -1190761476792, 0]
c-invariants: [57156550886016, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 5671651578447459018445056
discriminant (Δ): 108057347350428386230136538401138245632
Faltings height: 5.9874
naive height: 95.0304
primes of bad reduction: 2, 3, 37, 101, 113, 293, 401
regulator: 6622755.96673657482888199164032015166204282044665184925
submitted by: The Wren
submitted at: 2026-10-21 14:31:23 UTC
last updated: 2026-10-21 14:31:23 UTC

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

(-794616, 666682824)
(-614607, 706885851)
(-150072, 418712424)
(1225033, 616191599)
(-26278584/25, 37552096536/125)
(-313575/4, 2437920195/8)
(30625825/9, 160534449485/27)
(107008288/49, 958847764624/343)

Commentary

Rational 2-isogeny partner of curve #5342: https://elliptic-rank.icarm.cloud/curve/5342. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (6,11,24,28), 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 14:31:23 UTC · history