Properties

Label 20160.da
Number of curves $6$
Conductor $20160$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("20160.da1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160.da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.da1 20160cd5 [0, 0, 0, -377292, 89197936] [2] 131072  
20160.da2 20160cd3 [0, 0, 0, -24492, 1280176] [2, 2] 65536  
20160.da3 20160cd2 [0, 0, 0, -6492, -181424] [2, 2] 32768  
20160.da4 20160cd1 [0, 0, 0, -6312, -193016] [2] 16384 \(\Gamma_0(N)\)-optimal
20160.da5 20160cd4 [0, 0, 0, 8628, -901136] [2] 65536  
20160.da6 20160cd6 [0, 0, 0, 40308, 6904816] [2] 131072  

Rank

sage: E.rank()
 

The elliptic curves in class 20160.da have rank \(1\).

Modular form 20160.2.a.da

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.