Properties

Label 70602.bf
Number of curves $6$
Conductor $70602$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("70602.bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 70602.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
70602.bf1 70602bn4 [1, 0, 0, -2259299, 1306911333] [2] 1105920  
70602.bf2 70602bn6 [1, 0, 0, -1536469, -726140497] [2] 2211840  
70602.bf3 70602bn3 [1, 0, 0, -174859, 9945869] [2, 2] 1105920  
70602.bf4 70602bn2 [1, 0, 0, -141239, 20401689] [2, 2] 552960  
70602.bf5 70602bn1 [1, 0, 0, -6759, 471753] [2] 276480 \(\Gamma_0(N)\)-optimal
70602.bf6 70602bn5 [1, 0, 0, 648831, 76994235] [2] 2211840  

Rank

sage: E.rank()
 

The elliptic curves in class 70602.bf have rank \(0\).

Modular form 70602.2.a.bf

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - 2q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - 2q^{10} + 4q^{11} + q^{12} - 6q^{13} + q^{14} - 2q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.