Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("9408.bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.bc1 9408ca3 [0, -1, 0, -29857, 1993153] [2] 24576  
9408.bc2 9408ca2 [0, -1, 0, -2417, 11985] [2, 2] 12288  
9408.bc3 9408ca1 [0, -1, 0, -1437, -20355] [2] 6144 \(\Gamma_0(N)\)-optimal
9408.bc4 9408ca4 [0, -1, 0, 9343, 84897] [2] 24576  

Rank

sage: E.rank()
 

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

Modular form 9408.2.a.bc

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

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.