Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("9450.dl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9450.dl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9450.dl1 9450dw2 [1, -1, 1, -3368930, -2317366303] [3] 388800  
9450.dl2 9450dw1 [1, -1, 1, -3344555, -2353430053] [] 129600 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 9450.2.a.dl

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

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.