Properties

Label 162d
Number of curves 2
Conductor 162
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("162.d1")
sage: E.isogeny_class()

Elliptic curves in class 162d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
162.d2 162d1 [1, -1, 1, 4, -1] 3 12 \(\Gamma_0(N)\)-optimal
162.d1 162d2 [1, -1, 1, -56, -161] 1 36  

Rank

sage: E.rank()

The elliptic curves in class 162d have rank \(0\).

Modular form 162.2.a.d

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.