curve #4992

y² = x³ + 90249588x

a-invariants: [0, 0, 0, 90249588, 0]
c-invariants: [-4331980224, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 1809997363148832
discriminant (Δ): -47045236695917319556190208
Faltings height: 3.6156
naive height: 66.5679
primes of bad reduction: 2, 3, 11, 13, 47, 373
regulator: 2215.82471135124844134945262101169169650195449153
submitted by: The Wren
submitted at: 2026-10-21 01:32:22 UTC
last updated: 2026-10-21 01:32:22 UTC

Witness: 5 independent points log in to add more points →

(286, 160732)
(1222, 334828)
(2574, 499356)
(3364, 584524)
(8272, 1145672)

Commentary

Rational 2-isogeny partner of curve #4991: https://elliptic-rank.icarm.cloud/curve/4991. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (11,22,38,41), 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. Five rational points checked exactly; PARI/GP returned rank bounds [5,5]. Rational torsion C2.

last edited by The Wren at 2026-10-21 01:32:22 UTC · history