Properties

Label 113.a
Number of curves 2
Conductor 113
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("113.a1")
sage: E.isogeny_class()

Elliptic curves in class 113.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
113.a1 113a2 [1, 1, 1, -2, -2] 2 12  
113.a2 113a1 [1, 1, 1, 3, -4] 2 6 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 113.a have rank \(0\).

Modular form 113.2.a.a

sage: E.q_eigenform(10)
\( q - q^{2} + 2q^{3} - q^{4} + 2q^{5} - 2q^{6} + 3q^{8} + q^{9} - 2q^{10} - 2q^{12} + 2q^{13} + 4q^{15} - q^{16} - 6q^{17} - q^{18} + 6q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.