Properties

Label 606.f
Number of curves 2
Conductor 606
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("606.f1")
sage: E.isogeny_class()

Elliptic curves in class 606.f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
606.f1 606f1 [1, 0, 0, -90, 324] 5 100 \(\Gamma_0(N)\)-optimal
606.f2 606f2 [1, 0, 0, 600, -10626] 1 500  

Rank

sage: E.rank()

The elliptic curves in class 606.f have rank \(0\).

Modular form 606.2.a.f

sage: E.q_eigenform(10)
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 2q^{7} + q^{8} + q^{9} + q^{10} + 2q^{11} + q^{12} + 4q^{13} - 2q^{14} + q^{15} + q^{16} - 2q^{17} + q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.