Properties

Label 46.a
Number of curves 2
Conductor 46
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("46.a1")
sage: E.isogeny_class()

Elliptic curves in class 46.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
46.a1 46a2 [1, -1, 0, -170, -812] 2 10  
46.a2 46a1 [1, -1, 0, -10, -12] 2 5 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 46.a have rank \(0\).

Modular form 46.2.a.a

sage: E.q_eigenform(10)
\( q - q^{2} + q^{4} + 4q^{5} - 4q^{7} - q^{8} - 3q^{9} - 4q^{10} + 2q^{11} - 2q^{13} + 4q^{14} + q^{16} - 2q^{17} + 3q^{18} - 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.