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Properties

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

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Show commands: SageMath
E = EllipticCurve("bt1")
 
E.isogeny_class()
 

Elliptic curves in class 16562bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16562.bn1 16562bt1 \([1, 0, 0, -136809, 20477183]\) \(-226981/14\) \(-17466522454277078\) \([]\) \(149760\) \(1.8710\) \(\Gamma_0(N)\)-optimal
16562.bn2 16562bt2 \([1, 0, 0, 401456, -1242400160]\) \(5735339/537824\) \(-670993926603508228448\) \([]\) \(748800\) \(2.6757\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 16562.2.a.bt

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.