Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("9450.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9450.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9450.h1 9450f2 [1, -1, 0, -31767, -2171359] [] 23328  
9450.h2 9450f1 [1, -1, 0, -267, -4859] [] 7776 \(\Gamma_0(N)\)-optimal
9450.h3 9450f3 [1, -1, 0, 2358, 118516] [] 23328  

Rank

sage: E.rank()
 

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

Modular form 9450.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{7} - q^{8} - 3q^{11} + 4q^{13} + q^{14} + q^{16} - 6q^{17} - 7q^{19} + O(q^{20}) \)

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.