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Properties

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

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

Elliptic curves in class 61710.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61710.bs1 61710bo2 \([1, 1, 1, -17366, -569887]\) \(326940373369/112003650\) \(198421298197650\) \([2]\) \(245760\) \(1.4454\)  
61710.bs2 61710bo1 \([1, 1, 1, 3204, -59751]\) \(2053225511/2098140\) \(-3716982996540\) \([2]\) \(122880\) \(1.0988\) \(\Gamma_0(N)\)-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)
 
\(q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2 q^{7} + q^{8} + q^{9} - q^{10} - q^{12} + 2 q^{14} + q^{15} + q^{16} - q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display

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.