Properties

Label 9408.r
Number of curves $4$
Conductor $9408$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 9408.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.r1 9408bw4 \([0, -1, 0, -358353, -82449135]\) \(2640279346000/3087\) \(5950381473792\) \([2]\) \(55296\) \(1.7343\)  
9408.r2 9408bw3 \([0, -1, 0, -22213, -1304939]\) \(-10061824000/352947\) \(-42520434281472\) \([2]\) \(27648\) \(1.3878\)  
9408.r3 9408bw2 \([0, -1, 0, -5553, -49167]\) \(9826000/5103\) \(9836344885248\) \([2]\) \(18432\) \(1.1850\)  
9408.r4 9408bw1 \([0, -1, 0, 1307, -6635]\) \(2048000/1323\) \(-159385218048\) \([2]\) \(9216\) \(0.83846\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9408.r have rank \(1\).

Complex multiplication

The elliptic curves in class 9408.r do not have complex multiplication.

Modular form 9408.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - 6 q^{11} + 2 q^{13} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.