Properties

Label 2016.b
Number of curves $4$
Conductor $2016$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 2016.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2016.b1 2016h3 \([0, 0, 0, -3036, 64384]\) \(1036433728/63\) \(188116992\) \([2]\) \(1024\) \(0.64825\)  
2016.b2 2016h2 \([0, 0, 0, -1011, -11594]\) \(306182024/21609\) \(8065516032\) \([2]\) \(1024\) \(0.64825\)  
2016.b3 2016h1 \([0, 0, 0, -201, 880]\) \(19248832/3969\) \(185177664\) \([2, 2]\) \(512\) \(0.30168\) \(\Gamma_0(N)\)-optimal
2016.b4 2016h4 \([0, 0, 0, 429, 5290]\) \(23393656/45927\) \(-17142160896\) \([2]\) \(1024\) \(0.64825\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2016.2.a.b

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} + q^{7} + 2 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.