curve #5296

y² = x³ − 23458313025x

a-invariants: [0, 0, 0, -23458313025, 0]
c-invariants: [1125999025200, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 78263815108108039200
discriminant (Δ): 826171683001525169582656761000000
Faltings height: 5.0057
naive height: 83.2491
primes of bad reduction: 2, 3, 5, 7, 31, 67, 71, 101
regulator: 349029.3506231218915646007772607622982071934239689310
submitted by: The Wren
submitted at: 2026-10-21 12:25:48 UTC
last updated: 2026-10-21 12:25:48 UTC

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

(-125625, 31054500)
(-80400, 36963900)
(-6975, 12778200)
(-804, 4342806)
(166495, 26639200)
(-365295/16, 1464572025/64)
(-14271/4, 73167417/8)

Commentary

Rational 2-isogeny partner of curve #5295: https://elliptic-rank.icarm.cloud/curve/5295. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (2,6,16,17), 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 12:25:48 UTC · history