Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("20160.dp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160.dp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.dp1 20160eo3 [0, 0, 0, -64812, -6350384] [2] 65536  
20160.dp2 20160eo2 [0, 0, 0, -4332, -84656] [2, 2] 32768  
20160.dp3 20160eo1 [0, 0, 0, -1452, 20176] [2] 16384 \(\Gamma_0(N)\)-optimal
20160.dp4 20160eo4 [0, 0, 0, 10068, -528176] [2] 65536  

Rank

sage: E.rank()
 

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

Modular form 20160.2.a.dp

sage: E.q_eigenform(10)
 
\( q + q^{5} - q^{7} + 6q^{13} - 2q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.