curve #5162

y² = x³ − 534055695522470539128

a-invariants: [0, 0, 0, 0, -534055695522470539128]
c-invariants: [0, 461424120931414545806592]
rank (lower bound): ≥ 13
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 3521178838518392087099172002181518259264
discriminant (Δ): -123213089917435575911774226700335686928165888
Faltings height: 7.1391
naive height: 108.9772
primes of bad reduction: 2, 3, 2143, 18097, 63753501523
regulator: 1914128631191089593.833936645342956702610276857152035249193549165
submitted by: hdeping
submitted at: 2026-10-21 06:38:18 UTC
last updated: 2026-10-21 06:38:18 UTC

(19779476449855194798/3212282329, 87967487380813546282687171440/182062525560733)
(19797495098794548882/42712075561, -88087483187852830661050858980/8827261944116309)
(19748411358395753598/62738727529, 87759578574133590447842924520/15714608255281333)
(19699033788931611822/117745745881, 87426405129393275042476938960/40403392987352221)
(18273071189194660014/827963505625, 76146886704277559432037575088/753384692855828125)
(21856920112523354514/1025530909225, -99325638758437899200554578588/1038539768808519125)
(30308242707553119342/3026135097241, -114198004903488993252204321600/5264201066323401539)
(42131672192243986098/4998680907529, -89904701451737682285584959980/11175915808668834917)
(19778860065843658162/6217480201, 87963374813063704069844699540/490254531329051)
(19840227066203030002/96963109321, -88370318444452821040087365580/30193245648356869)
(18942436473789474514/559676053225, 81873202745428346914405763588/418702050558420875)
(17418009706217766514/1117238430025, 67376742334064067621970409588/1180915434344274875)
(26216815478711958514/2179889838025, -111746483260066746271246494412/3218487451902821125)

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