Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 94864cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
94864.cw2 94864cr1 [0, -1, 0, -1976, -131536] [] 138240 \(\Gamma_0(N)\)-optimal
94864.cw1 94864cr2 [0, -1, 0, -2847896, 1850854832] [] 1520640  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 94864.2.a.cr

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 Cremona 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 Cremona labels.