Properties

Label 28594.e
Number of curves 4
Conductor 28594
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("28594.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28594.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28594.e1 28594f4 [1, 1, 0, -95050, -7833894] [2] 302400  
28594.e2 28594f3 [1, 1, 0, -86640, -9850612] [2] 151200  
28594.e3 28594f2 [1, 1, 0, -36180, 2633192] [2] 100800  
28594.e4 28594f1 [1, 1, 0, -2540, 29456] [2] 50400 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28594.e have rank \(0\).

Modular form 28594.2.a.e

sage: E.q_eigenform(10)
 
\( q - q^{2} + 2q^{3} + q^{4} - 2q^{6} - 4q^{7} - q^{8} + q^{9} - 6q^{11} + 2q^{12} + 2q^{13} + 4q^{14} + q^{16} + q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.