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Properties

Label 16562.n
Number of curves $2$
Conductor $16562$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 16562.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16562.n1 16562b2 \([1, 0, 1, -4819715, -3706227458]\) \(2633034313/262144\) \(1232738785991464321024\) \([]\) \(943488\) \(2.7834\)  
16562.n2 16562b1 \([1, 0, 1, -1051860, 414298770]\) \(27369433/64\) \(300961617673697344\) \([3]\) \(314496\) \(2.2341\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 16562.n have rank \(1\).

Complex multiplication

The elliptic curves in class 16562.n do not have complex multiplication.

Modular form 16562.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} - q^{8} - 2 q^{9} + 3 q^{10} - 3 q^{11} + q^{12} - 3 q^{15} + q^{16} + 6 q^{17} + 2 q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.