Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("9408.ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.ct1 9408bg3 [0, 1, 0, -6337, -196225] [2] 9216  
9408.ct2 9408bg2 [0, 1, 0, -457, -2185] [2, 2] 4608  
9408.ct3 9408bg1 [0, 1, 0, -212, 1098] [2] 2304 \(\Gamma_0(N)\)-optimal
9408.ct4 9408bg4 [0, 1, 0, 1503, -14337] [2] 9216  

Rank

sage: E.rank()
 

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

Modular form 9408.2.a.ct

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.