Properties

Label 28560.e
Number of curves 4
Conductor 28560
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("28560.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28560.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28560.e1 28560cf4 [0, -1, 0, -26976, -1696320] [2] 65536  
28560.e2 28560cf3 [0, -1, 0, -8576, 287040] [2] 65536  
28560.e3 28560cf2 [0, -1, 0, -1776, -23040] [2, 2] 32768  
28560.e4 28560cf1 [0, -1, 0, 224, -2240] [2] 16384 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28560.e have rank \(2\).

Modular form 28560.2.a.e

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} - q^{7} + q^{9} - 6q^{13} + q^{15} - q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.