Properties

Label 55440.cv
Number of curves 4
Conductor 55440
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("55440.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 55440.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
55440.cv1 55440ec4 [0, 0, 0, -3760707, -2727523006] [2] 1990656  
55440.cv2 55440ec2 [0, 0, 0, -514947, 140966786] [2] 663552  
55440.cv3 55440ec1 [0, 0, 0, -8067, 5427074] [2] 331776 \(\Gamma_0(N)\)-optimal
55440.cv4 55440ec3 [0, 0, 0, 72573, -146192254] [2] 995328  

Rank

sage: E.rank()
 

The elliptic curves in class 55440.cv have rank \(0\).

Modular form 55440.2.a.cv

sage: E.q_eigenform(10)
 
\( q + q^{5} - q^{7} - q^{11} - 4q^{13} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.