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Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 169065.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169065.k1 169065k2 \([1, -1, 1, -570107, -118609136]\) \(43132764843/12138425\) \(5766962933273042475\) \([2]\) \(3538944\) \(2.3069\)  
169065.k2 169065k1 \([1, -1, 1, 93148, -12223034]\) \(188132517/244205\) \(-116021739485966535\) \([2]\) \(1769472\) \(1.9603\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 169065.2.a.k

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