Properties

Label 9450.cl
Number of curves 3
Conductor 9450
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("9450.cl1")
sage: E.isogeny_class()

Elliptic curves in class 9450.cl

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
9450.cl1 9450dd3 [1, -1, 1, -26555, 1672197] 1 15552  
9450.cl2 9450dd1 [1, -1, 1, -305, 2697] 1 5184 \(\Gamma_0(N)\)-optimal
9450.cl3 9450dd2 [1, -1, 1, 2320, -27053] 1 15552  

Rank

sage: E.rank()

The elliptic curves in class 9450.cl have rank \(1\).

Modular form 9450.2.a.cl

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

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.