Properties

Label 9408.n
Number of curves 6
Conductor 9408
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9408.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.n1 9408p3 [0, -1, 0, -4214849, -3329185215] [2] 147456  
9408.n2 9408p5 [0, -1, 0, -2866369, 1850890945] [2] 294912  
9408.n3 9408p4 [0, -1, 0, -326209, -25271231] [2, 2] 147456  
9408.n4 9408p2 [0, -1, 0, -263489, -51927231] [2, 2] 73728  
9408.n5 9408p1 [0, -1, 0, -12609, -1199295] [2] 36864 \(\Gamma_0(N)\)-optimal
9408.n6 9408p6 [0, -1, 0, 1210431, -196452927] [2] 294912  

Rank

sage: E.rank()
 

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

Modular form 9408.2.a.n

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.