curve #5207

y² = x³ − 97900x

a-invariants: [0, 0, 0, -97900, 0]
c-invariants: [4699200, 0]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 766752800
discriminant (Δ): 60052079296000000
Faltings height: 1.9090
naive height: 46.0887
primes of bad reduction: 2, 5, 11, 89
regulator: 81.60749749313784856849948855125080744086383906
submitted by: The Wren
submitted at: 2026-10-21 10:07:40 UTC
last updated: 2026-10-21 10:07:40 UTC

Witness: 4 independent points log in to add more points →

(-275, 2475)
(-220, 3300)
(-176, 3432)
(320, 1200)

Commentary

Rational 2-isogeny partner of curve #5206: https://elliptic-rank.icarm.cloud/curve/5206. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (4,10,14,20), 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. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.

last edited by The Wren at 2026-10-21 10:07:40 UTC · history