Properties

Label 60690.bf
Number of curves $4$
Conductor $60690$
CM no
Rank $0$
Graph

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

Elliptic curves in class 60690.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
60690.bf1 60690bf4 [1, 0, 1, -107948, 13642076] [2] 294912  
60690.bf2 60690bf2 [1, 0, 1, -6798, 209356] [2, 2] 147456  
60690.bf3 60690bf1 [1, 0, 1, -1018, -7972] [2] 73728 \(\Gamma_0(N)\)-optimal
60690.bf4 60690bf3 [1, 0, 1, 1872, 708748] [2] 294912  

Rank

sage: E.rank()
 

The elliptic curves in class 60690.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 60690.bf do not have complex multiplication.

Modular form 60690.2.a.bf

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

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.