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Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 16562.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16562.l1 16562d2 \([1, -1, 0, -19070, 1018772]\) \(-38575685889/16384\) \(-325757845504\) \([]\) \(24192\) \(1.1699\)  
16562.l2 16562d1 \([1, -1, 0, 40, -428]\) \(351/4\) \(-79530724\) \([]\) \(3456\) \(0.19693\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 16562.l have rank \(2\).

Complex multiplication

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

Modular form 16562.2.a.l

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.