Properties

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

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

Elliptic curves in class 166410.bf

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

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 166410.2.a.bf

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