Properties

Label 66654.j
Number of curves $6$
Conductor $66654$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("66654.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 66654.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
66654.j1 66654w4 [1, -1, 0, -6398883, 6231834121] [2] 1441792  
66654.j2 66654w6 [1, -1, 0, -4351653, -3459419429] [2] 2883584  
66654.j3 66654w3 [1, -1, 0, -495243, 47599825] [2, 2] 1441792  
66654.j4 66654w2 [1, -1, 0, -400023, 97399885] [2, 2] 720896  
66654.j5 66654w1 [1, -1, 0, -19143, 2256061] [2] 360448 \(\Gamma_0(N)\)-optimal
66654.j6 66654w5 [1, -1, 0, 1837647, 366272599] [2] 2883584  

Rank

sage: E.rank()
 

The elliptic curves in class 66654.j have rank \(0\).

Modular form 66654.2.a.j

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - 2q^{5} + q^{7} - q^{8} + 2q^{10} - 4q^{11} + 6q^{13} - q^{14} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.