Properties

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

Related objects

Downloads

Learn more

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

Elliptic curves in class 2016.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2016.l1 2016g2 \([0, 0, 0, -2019, -34918]\) \(2438569736/21\) \(7838208\) \([2]\) \(1024\) \(0.49067\)  
2016.l2 2016g3 \([0, 0, 0, -444, 3008]\) \(3241792/567\) \(1693052928\) \([2]\) \(1024\) \(0.49067\)  
2016.l3 2016g1 \([0, 0, 0, -129, -520]\) \(5088448/441\) \(20575296\) \([2, 2]\) \(512\) \(0.14410\) \(\Gamma_0(N)\)-optimal
2016.l4 2016g4 \([0, 0, 0, 141, -2410]\) \(830584/7203\) \(-2688505344\) \([2]\) \(1024\) \(0.49067\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2016.2.a.l

sage: E.q_eigenform(10)
 
\(q + 2 q^{5} + q^{7} - 4 q^{11} - 6 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\)  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.