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Properties

Label 16562l
Number of curves $2$
Conductor $16562$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 16562l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16562.k2 16562l1 \([1, 1, 0, -21466, -1217068]\) \(27369433/64\) \(2558131541056\) \([]\) \(44928\) \(1.2612\) \(\Gamma_0(N)\)-optimal
16562.k1 16562l2 \([1, 1, 0, -98361, 10763173]\) \(2633034313/262144\) \(10478106792165376\) \([]\) \(134784\) \(1.8105\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 16562.2.a.l

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 Cremona 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 Cremona labels.