Properties

Label 132.a
Number of curves 2
Conductor 132
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("132.a1")
sage: E.isogeny_class()

Elliptic curves in class 132.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
132.a1 132b2 [0, -1, 0, -1292, 18312] 2 60  
132.a2 132b1 [0, -1, 0, -77, 330] 2 30 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 132.a have rank \(0\).

Modular form 132.2.a.a

sage: E.q_eigenform(10)
\( q - q^{3} + 2q^{5} + 2q^{7} + q^{9} - q^{11} + 6q^{13} - 2q^{15} - 4q^{17} - 2q^{19} + O(q^{20}) \)

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.