Properties

Label 94864.cx
Number of curves $2$
Conductor $94864$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 94864.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
94864.cx1 94864cq2 [0, -1, 0, -239136, 176030912] [] 1520640  
94864.cx2 94864cq1 [0, -1, 0, -23536, -1382016] [] 138240 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 94864.cx have rank \(0\).

Complex multiplication

The elliptic curves in class 94864.cx do not have complex multiplication.

Modular form 94864.2.a.cx

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} + q^{9} + q^{13} - 2q^{15} - 5q^{17} - 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.