Properties

Label 62.a
Number of curves 4
Conductor 62
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("62.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62.a1 62a4 [1, -1, 1, -331, 2397] [2] 8  
62.a2 62a3 [1, -1, 1, -31, 5] [2] 8  
62.a3 62a2 [1, -1, 1, -21, 41] [2, 2] 4  
62.a4 62a1 [1, -1, 1, -1, 1] [4] 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 62.a have rank \(0\).

Modular form 62.2.a.a

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - 2q^{5} + q^{8} - 3q^{9} - 2q^{10} + 2q^{13} + q^{16} - 6q^{17} - 3q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.