curve #4755

y² = x³ − 12397937643467665384

a-invariants: [0, 0, 0, 0, -12397937643467665384]
c-invariants: [0, 10711818123956062891776]
rank (lower bound): ≥ 13
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 4150139160905439335634474289855580421312
discriminant (Δ): -66402226574487029370151588637689286740992
Faltings height: 6.5119
naive height: 101.4513
primes of bad reduction: 2, 3, 174900953, 8860684741
regulator: 4056137380463.064421321640463527907924113791337808881329590870448
submitted by: David Renshaw
submitted at: 2026-10-20 21:28:33 UTC
last updated: 2026-10-20 21:28:33 UTC

Witness: 13 independent points log in to add more points →

(2361017, 873681023)
(2754494, 2915658020)
(2831369, 3209385895)
(3488990, 5483950796)
(3886025, 6803356921)
(4111370, 7556324704)
(4361897, 8401913417)
(5152202, 11152050032)
(6828062, 17491223788)
(7870910, 21799416796)
(8405057, 24111764197)
(9466622, 28913174908)
(16325630, 65869644796)

Commentary

Mordell curve y^2 = x^3 + -12397937643467665384. 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 21:28:33 UTC · history