curve #5352

y² + y = x³ + 381642689963997214201514640090173223

a-invariants: [0, 0, 1, 0, 381642689963997214201514640090173223]
c-invariants: [0, -329739284128893593070108649037909664888]
rank (lower bound): ≥ 17
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 20973764563625620794533860687974151980778874013811982435979547707546385041
discriminant (Δ): -62921293690876862383601582063922455942336622041435947307938643122639155123
Faltings height: 12.8396
naive height: 177.3827
primes of bad reduction: 3, 5303, 287869273968694862682643515059531
regulator: 256945769481424703209.103135185085011652125192746974512678814595029274530
submitted by: wgxli
submitted at: 2026-10-21 15:58:25 UTC
last updated: 2026-10-21 15:58:25 UTC

(344193931713, 649937812481989079)
(418675354227, 674560520636571057)
(-316907573827, 591452054085428284)
(-566562762001, 446967340503281458)
(-658587387387, 309820502720844779)
(-696701109681, 208492784074842413)
(1176688279277, 1418054920927918387)
(5559205371057/4, 14008249860908946187/8)
(8171874651337/9, 28704207232915389613/27)
(96154176734743/9, 943018422641936168374/27)
(53129138088273/49, 441438309667081395761/343)
(257026621404353/64, 4132785239902042429919/512)
(-59489812133327/324, 3573510874235177960269/5832)
(1029422403239159/625, 34410233918570536268077/15625)
(1178823761955113/676, 41904879933651013808879/17576)
(5299085393662989/3481, 406076140331476111725169/205379)
(5444356192425863/17161, 1445740380308318760831974/2248091)

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