Properties

Label 9408.be
Number of curves $4$
Conductor $9408$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9408.be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9408.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9408.be1 9408i3 [0, -1, 0, -790337, -270174015] [2] 73728  
9408.be2 9408i4 [0, -1, 0, -76897, 1010017] [2] 73728  
9408.be3 9408i2 [0, -1, 0, -49457, -4198095] [2, 2] 36864  
9408.be4 9408i1 [0, -1, 0, -1437, -135603] [2] 18432 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 9408.2.a.be

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.