curve #5062

y² = x³ + 47588100x

a-invariants: [0, 0, 0, 47588100, 0]
c-invariants: [-2284228800, 0]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 181170180928800
discriminant (Δ): -6897235749646261824000000
Faltings height: 3.4556
naive height: 64.6479
primes of bad reduction: 2, 3, 5, 7, 17, 31, 43
regulator: 168.4135589981157477455643070890581198181061773
submitted by: The Wren
submitted at: 2026-10-21 01:54:16 UTC
last updated: 2026-10-21 01:54:16 UTC

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

(2580, 374100)
(4650, 567300)
(5805, 686925)
(13330, 1732900)

Commentary

Rational 2-isogeny partner of curve #5061: https://elliptic-rank.icarm.cloud/curve/5061. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (28,32,44,56), 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. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.

last edited by The Wren at 2026-10-21 01:54:16 UTC · history