curve #4752

y² = x³ + 1255360484445973

a-invariants: [0, 0, 0, 0, 1255360484445973]
c-invariants: [0, -1084631458561320672]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 170200434158110225993761639006732
discriminant (Δ): -680801736632440903975046556026928
Faltings height: 4.9790
naive height: 83.0555
primes of bad reduction: 2, 3, 4136633, 303473981
regulator: 14285051846.8523106065332841370469678127164207105882769850209
submitted by: David Renshaw
submitted at: 2026-10-20 21:28:21 UTC
last updated: 2026-10-20 21:28:21 UTC

Witness: 11 independent points log in to add more points →

(-106833, 6003706)
(-104589, 10548752)
(-97809, 17879062)
(-86733, 24554056)
(-12849, 35401118)
(31011, 35849452)
(103203, 48523820)
(152367, 69229094)
(232227, 117384916)
(1897587, 2614221824)
(152477007, 1882810180354)

Commentary

Mordell curve y^2 = x^3 + 1255360484445973. Source: N. D. Elkies, 'j=0, rank 15; also 3-rank 6 and 7 in real and imaginary quadratic fields', NMBRTHRY post, 30 Dec 2009, https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;6a3fad67.0912&S=.

last edited by David Renshaw at 2026-10-20 21:28:21 UTC · history