Properties

Label 9450.cf
Number of curves 2
Conductor 9450
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("9450.cf1")
sage: E.isogeny_class()

Elliptic curves in class 9450.cf

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
9450.cf1 9450df2 [1, -1, 1, -1355, 43647] 1 10368  
9450.cf2 9450df1 [1, -1, 1, 145, -1353] 1 3456 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

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

Modular form 9450.2.a.cf

sage: E.q_eigenform(10)
\( q + q^{2} + q^{4} - q^{7} + q^{8} - 3q^{11} + q^{13} - q^{14} + q^{16} - q^{19} + O(q^{20}) \)

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.