curve #5570

y² + y = x³ − 184171032636571580158919788829056861

a-invariants: [0, 0, 1, 0, -184171032636571580158919788829056861]
c-invariants: [0, 159123772197997845257306697548305127688]
rank (lower bound): ≥ 17
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 809086259038223489432482561001918463920931331342328985448022657409 ☆ record for Mordell curves, rank ≥ 17
discriminant (Δ): -14652994721365921301870978747705611431007831160047822180418730394070592723
Faltings height: 12.7181
naive height: 175.9255
primes of bad reduction: 3, 7, 13, 71, 1129, 41103847444286828222618671
regulator: 15395774741537029293.7910283088442656143016338206836916468938348948039903
submitted by: wgxli
submitted at: 2026-10-23 11:48:46 UTC
last updated: 2026-10-23 11:48:46 UTC

(568961592927, 3416832493460158)
(569630791977, 25735837872250291)
(569854221027, 29663326439016133)
(614613472123, 219086819404671522)
(778519948857, 536362471343157763)
(1014924496621, 928048491898953575)
(2102619715147, 3018531274155370578)
(2830301110023, 4742177919199706857)
(33077353259041, 190237014690205181835)
(283751913571273, 4779783181433260462892)
(6409176696013/9, 11358369920565050597/27)
(656590640751367, 16824494777157651102998)
(7645224533713/9, 17680456690884361601/27)
(42108737196379/9, 273003054272552940263/27)
(25134965194381/25, 114025242745926702096/125)
(47610045960009/64, 244211270084215875653/512)
(97375127268337/144, 611040884991487654231/1728)

Isogenous to curve #5569

last edited by wgxli at 2026-10-23 11:48:46 UTC · history