Properties

Label 158.b
Number of curves 3
Conductor 158
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("158.b1")
sage: E.isogeny_class()

Elliptic curves in class 158.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
158.b1 158d2 [1, 0, 1, -5217, -145452] 1 120  
158.b2 158d1 [1, 0, 1, -82, -92] 3 40 \(\Gamma_0(N)\)-optimal
158.b3 158d3 [1, 0, 1, -47, 118] 3 120  

Rank

sage: E.rank()

The elliptic curves in class 158.b have rank \(0\).

Modular form 158.2.a.b

sage: E.q_eigenform(10)
\( q - q^{2} + q^{3} + q^{4} + 3q^{5} - q^{6} - q^{7} - q^{8} - 2q^{9} - 3q^{10} + q^{12} + 5q^{13} + q^{14} + 3q^{15} + q^{16} + 2q^{18} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.