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Properties

Label 169065.bd
Number of curves $2$
Conductor $169065$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bd1")
 
E.isogeny_class()
 

Elliptic curves in class 169065.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169065.bd1 169065bi1 \([1, -1, 0, -2655, -10544]\) \(117649/65\) \(1143758707065\) \([2]\) \(245760\) \(1.0043\) \(\Gamma_0(N)\)-optimal
169065.bd2 169065bi2 \([1, -1, 0, 10350, -91175]\) \(6967871/4225\) \(-74344315959225\) \([2]\) \(491520\) \(1.3509\)  

Rank

sage: E.rank()
 

The elliptic curves in class 169065.bd have rank \(0\).

Complex multiplication

The elliptic curves in class 169065.bd do not have complex multiplication.

Modular form 169065.2.a.bd

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - q^{5} + 4 q^{7} - 3 q^{8} - q^{10} + 2 q^{11} - q^{13} + 4 q^{14} - q^{16} - 6 q^{19} + O(q^{20})\) 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 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.