curve #4751

y² = x³ − 998820191314747

a-invariants: [0, 0, 0, 0, -998820191314747]
c-invariants: [0, 862980645295941408]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 35915103884809000742847108264324 ☆ record for Mordell curves, rank ≥ 11
discriminant (Δ): -430981246617708008914165299171888 ☆ record for Mordell curves, rank ≥ 11
Faltings height: 4.9409 ☆ record for Mordell curves, rank ≥ 11
naive height: 82.5983 ☆ record for Mordell curves, rank ≥ 11
primes of bad reduction: 2, 3, 998820191314747
regulator: 10163250386.4394211480268174907473535028829836293200949058669
submitted by: David Renshaw
submitted at: 2026-10-20 21:28:17 UTC
last updated: 2026-10-20 21:28:17 UTC

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

(101411, 6641528)
(157331, 53810788)
(174691, 65819568)
(203411, 86125028)
(231967, 107158854)
(281363, 145860620)
(316963, 175627560)
(379711, 231836322)
(1137187, 1212272616)
(1432163, 1713621200)
(4961827, 11052503256)

Commentary

Mordell curve y^2 = x^3 + -998820191314747. 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 21:28:17 UTC · history