curve #4754

y² = x³ − 227298856834289587

a-invariants: [0, 0, 0, 0, -227298856834289587]
c-invariants: [0, 196386212304826203168]
rank (lower bound): ≥ 12
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 5579795194362886401899718369476101452
discriminant (Δ): -22319180777451545607598873477904405808
Faltings height: 5.8454
naive height: 93.4532
primes of bad reduction: 2, 3, 29, 26814493, 292300571
regulator: 597695300125.13768556744373620542983375312135303515473405691222
submitted by: David Renshaw
submitted at: 2026-10-20 21:28:29 UTC
last updated: 2026-10-20 21:28:29 UTC

Witness: 12 independent points log in to add more points →

(684683, 306062480)
(791687, 518560954)
(1218107, 1257024116)
(1253927, 1320716414)
(1459271, 1697108618)
(4358183, 9085756930)
(5259911, 12053915962)
(118158011, 1284383529412)
(165785351, 2134613338342)
(166020683, 2139160070680)
(4650833/4, 9276397063/8)
(11551913/4, 39077070923/8)

Commentary

Mordell curve y^2 = x^3 + -227298856834289587. 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 21:28:29 UTC · history