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Properties

Label 202160.cf
Number of curves $2$
Conductor $202160$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cf1")
 
E.isogeny_class()
 

Elliptic curves in class 202160.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
202160.cf1 202160bl2 \([0, 1, 0, -290725, -60432737]\) \(-225637236736/1715\) \(-20655023594240\) \([]\) \(1026432\) \(1.7298\)  
202160.cf2 202160bl1 \([0, 1, 0, -1925, -160177]\) \(-65536/875\) \(-10538277344000\) \([]\) \(342144\) \(1.1805\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 202160.cf have rank \(0\).

Complex multiplication

The elliptic curves in class 202160.cf do not have complex multiplication.

Modular form 202160.2.a.cf

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} - 2 q^{9} - 3 q^{11} + q^{13} + q^{15} - 3 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

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

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

The vertices are labelled with LMFDB labels.