Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("9408.co1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.co

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.co1 9408bb4 [0, 1, 0, -358353, 82449135] [2] 55296  
9408.co2 9408bb3 [0, 1, 0, -22213, 1304939] [2] 27648  
9408.co3 9408bb2 [0, 1, 0, -5553, 49167] [2] 18432  
9408.co4 9408bb1 [0, 1, 0, 1307, 6635] [2] 9216 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 9408.2.a.co

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.