Properties

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

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

Elliptic curves in class 94864.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
94864.cx1 94864cq2 \([0, -1, 0, -239136, 176030912]\) \(-121\) \(-12498993425952968704\) \([]\) \(1520640\) \(2.3471\)  
94864.cx2 94864cq1 \([0, -1, 0, -23536, -1382016]\) \(-24729001\) \(-58308726784\) \([]\) \(138240\) \(1.1481\) \(\Gamma_0(N)\)-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)
 
\(q + 2 q^{3} - q^{5} + q^{9} + q^{13} - 2 q^{15} - 5 q^{17} - 6 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.