Properties

Label 61710.bs
Number of curves $2$
Conductor $61710$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 61710.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61710.bs1 61710bo2 [1, 1, 1, -17366, -569887] [2] 245760  
61710.bs2 61710bo1 [1, 1, 1, 3204, -59751] [2] 122880 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 61710.bs have rank \(1\).

Complex multiplication

The elliptic curves in class 61710.bs do not have complex multiplication.

Modular form 61710.2.a.bs

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.