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Properties

Label 2116800.nx
Number of curves $2$
Conductor $2116800$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("nx1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 2116800.nx have rank \(0\).

Complex multiplication

The elliptic curves in class 2116800.nx do not have complex multiplication.

Modular form 2116800.2.a.nx

Copy content sage:E.q_eigenform(10)
 
\(q - 3 q^{11} - 2 q^{13} + 6 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.

Elliptic curves in class 2116800.nx

Copy content sage:E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
2116800.nx1 \([0, 0, 0, -4895100, -4649022000]\) \(-2431344/343\) \(-1830021227322624000000\) \([]\) \(107495424\) \(2.8111\)
2116800.nx2 \([0, 0, 0, 396900, 18522000]\) \(11664/7\) \(-4149707998464000000\) \([]\) \(35831808\) \(2.2617\)