Properties

Label 2016.e
Number of curves $2$
Conductor $2016$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 2016.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2016.e1 2016l2 \([0, 0, 0, -75, 142]\) \(125000/49\) \(18289152\) \([2]\) \(384\) \(0.092106\)  
2016.e2 2016l1 \([0, 0, 0, 15, 16]\) \(8000/7\) \(-326592\) \([2]\) \(192\) \(-0.25447\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2016.e have rank \(1\).

Complex multiplication

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

Modular form 2016.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{7} + 4 q^{11} - 4 q^{13} + 2 q^{17} - 6 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.