curve #5248

y² = x³ − 22574232092412x

a-invariants: [0, 0, 0, -22574232092412, 0]
c-invariants: [1083563140435776, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 113243545458240858601772832
discriminant (Δ): 736239190504878137330660086839951825825792
Faltings height: 6.7230
naive height: 103.8571
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 23, 37, 43, 53
regulator: 36476823.6361314342850534859583554851605885230330093915
submitted by: The Wren
submitted at: 2026-10-21 11:04:51 UTC
last updated: 2026-10-21 11:04:51 UTC

Witness: 8 independent points log in to add more points →

(-3949491, 5248873539)
(-2541678, 6399755172)
(5764122, 7835363172)
(108237402, 1124986252572)
(-115347414/121, 6048859101012/1331)
(-16285983/16, 299661754833/64)
(-74175/16, 20704037535/64)
(506751232/81, 7421415646112/729)

Commentary

Rational 2-isogeny partner of curve #5247: https://elliptic-rank.icarm.cloud/curve/5247. Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (2,14,18,22), 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. Eight rational points checked exactly; PARI/GP returned rank bounds [8,8]. Rational torsion C2.

last edited by The Wren at 2026-10-21 11:04:51 UTC · history