Properties

Label 58.b
Number of curves 2
Conductor 58
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("58.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58.b1 58b2 [1, 1, 1, -455, -3951] [] 20  
58.b2 58b1 [1, 1, 1, 5, 9] [5] 4 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 58.b have rank \(0\).

Modular form 58.2.a.b

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - 2q^{7} + q^{8} - 2q^{9} + q^{10} - 3q^{11} - q^{12} - q^{13} - 2q^{14} - q^{15} + q^{16} + 8q^{17} - 2q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.