Properties

Label 106.d
Number of curves 2
Conductor 106
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("106.d1")
sage: E.isogeny_class()

Elliptic curves in class 106.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
106.d1 106c2 [1, 0, 0, -24603, -1487407] 1 144  
106.d2 106c1 [1, 0, 0, -283, -2351] 3 48 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 106.d have rank \(0\).

Modular form 106.2.a.d

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} - 2q^{9} + q^{12} + 5q^{13} - 4q^{14} + q^{16} - 3q^{17} - 2q^{18} - q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.