Properties

Label 142d
Number of curves 2
Conductor 142
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("142.e1")
sage: E.isogeny_class()

Elliptic curves in class 142d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
142.e2 142d1 [1, 0, 0, -8, 8] 3 4 \(\Gamma_0(N)\)-optimal
142.e1 142d2 [1, 0, 0, -58, -170] 1 12  

Rank

sage: E.rank()

The elliptic curves in class 142d have rank \(0\).

Modular form 142.2.a.e

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

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.