Properties

Label 8670.g
Number of curves 8
Conductor 8670
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("8670.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8670.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8670.g1 8670e7 [1, 1, 0, -1541387, -737215371] [2] 110592  
8670.g2 8670e8 [1, 1, 0, -131067, -2540379] [2] 110592  
8670.g3 8670e6 [1, 1, 0, -96387, -11536371] [2, 2] 55296  
8670.g4 8670e5 [1, 1, 0, -83382, 9232614] [2] 36864  
8670.g5 8670e4 [1, 1, 0, -19802, -932094] [2] 36864  
8670.g6 8670e2 [1, 1, 0, -5352, 134316] [2, 2] 18432  
8670.g7 8670e3 [1, 1, 0, -3907, -309299] [2] 27648  
8670.g8 8670e1 [1, 1, 0, 428, 10624] [2] 9216 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8670.g have rank \(0\).

Modular form 8670.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 4q^{7} - q^{8} + q^{9} - q^{10} - q^{12} + 2q^{13} - 4q^{14} - q^{15} + q^{16} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.