curve #5200

y² = x³ − 23100x

a-invariants: [0, 0, 0, -23100, 0]
c-invariants: [1108800, 0]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 42688800
discriminant (Δ): 788889024000000
Faltings height: 1.5479
naive height: 41.7564
primes of bad reduction: 2, 3, 5, 7, 11
regulator: 4.7653739841220882240356851219835838071127302
submitted by: The Wren
submitted at: 2026-10-21 09:39:16 UTC
last updated: 2026-10-21 09:39:16 UTC

Witness: 3 independent points log in to add more points →

(-150, 300)
(-140, 700)
(-110, 1100)

Commentary

Rational 2-isogeny partner of curve #5199: https://elliptic-rank.icarm.cloud/curve/5199. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (1,2,3,4), 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. Three rational points checked exactly; PARI/GP returned rank bounds [3,3]. Rational torsion C2.

last edited by The Wren at 2026-10-21 09:39:16 UTC · history