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Properties

Label 16562q
Number of curves $2$
Conductor $16562$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 16562q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16562.e2 16562q1 \([1, 0, 1, 1010, -203136]\) \(68921/10816\) \(-17906920787392\) \([2]\) \(48384\) \(1.2223\) \(\Gamma_0(N)\)-optimal
16562.e1 16562q2 \([1, 0, 1, -46310, -3723744]\) \(6634074439/228488\) \(378283701633656\) \([2]\) \(96768\) \(1.5689\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16562q have rank \(0\).

Complex multiplication

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

Modular form 16562.2.a.q

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