Properties

Label 20160.dw
Number of curves $4$
Conductor $20160$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160.dw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.dw1 20160eu3 \([0, 0, 0, -40332, -3117616]\) \(303735479048/105\) \(2508226560\) \([2]\) \(49152\) \(1.1595\)  
20160.dw2 20160eu2 \([0, 0, 0, -2532, -48256]\) \(601211584/11025\) \(32920473600\) \([2, 2]\) \(24576\) \(0.81289\)  
20160.dw3 20160eu1 \([0, 0, 0, -327, 1136]\) \(82881856/36015\) \(1680315840\) \([2]\) \(12288\) \(0.46632\) \(\Gamma_0(N)\)-optimal
20160.dw4 20160eu4 \([0, 0, 0, -12, -139984]\) \(-8/354375\) \(-8465264640000\) \([2]\) \(49152\) \(1.1595\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20160.dw have rank \(0\).

Complex multiplication

The elliptic curves in class 20160.dw do not have complex multiplication.

Modular form 20160.2.a.dw

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.