Properties

Label 2016n
Number of curves $2$
Conductor $2016$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2016n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2016.n2 2016n1 \([0, 0, 0, 1887, -45740]\) \(15926924096/28588707\) \(-1333834713792\) \([2]\) \(3840\) \(1.0114\) \(\Gamma_0(N)\)-optimal
2016.n1 2016n2 \([0, 0, 0, -13548, -477920]\) \(92100460096/20253807\) \(60477543641088\) \([2]\) \(7680\) \(1.3580\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2016n have rank \(0\).

Complex multiplication

The elliptic curves in class 2016n do not have complex multiplication.

Modular form 2016.2.a.n

sage: E.q_eigenform(10)
 
\(q + 4 q^{5} + q^{7} + 2 q^{11} - 2 q^{13} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.