Properties

Label 9408.df
Number of curves $2$
Conductor $9408$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9408.df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.df1 9408dd2 [0, 1, 0, -7121, -233073] [2] 18432  
9408.df2 9408dd1 [0, 1, 0, -261, -6693] [2] 9216 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9408.df have rank \(0\).

Modular form 9408.2.a.df

sage: E.q_eigenform(10)
 
\( q + q^{3} + 4q^{5} + q^{9} + 2q^{11} - 6q^{13} + 4q^{15} + 4q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.