Properties

Label 166410bs
Number of curves $2$
Conductor $166410$
CM no
Rank $0$
Graph

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

Elliptic curves in class 166410bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166410.bf2 166410bs1 \([1, -1, 0, -624384, 127618240]\) \(5841725401/1857600\) \(8560329155870529600\) \([2]\) \(4257792\) \(2.3366\) \(\Gamma_0(N)\)-optimal
166410.bf1 166410bs2 \([1, -1, 0, -3952584, -2927003720]\) \(1481933914201/53916840\) \(248463553749142121640\) \([2]\) \(8515584\) \(2.6832\)  

Rank

sage: E.rank()
 

The elliptic curves in class 166410bs have rank \(0\).

Complex multiplication

The elliptic curves in class 166410bs do not have complex multiplication.

Modular form 166410.2.a.bs

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