Properties

Label 28611.g
Number of curves 4
Conductor 28611
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("28611.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28611.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28611.g1 28611u4 [1, -1, 1, -381101, -90369790] [2] 245760  
28611.g2 28611u2 [1, -1, 1, -29966, -619684] [2, 2] 122880  
28611.g3 28611u1 [1, -1, 1, -16961, 847280] [2] 61440 \(\Gamma_0(N)\)-optimal
28611.g4 28611u3 [1, -1, 1, 113089, -4911334] [2] 245760  

Rank

sage: E.rank()
 

The elliptic curves in class 28611.g have rank \(1\).

Modular form 28611.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} - 2q^{5} - 4q^{7} + 3q^{8} + 2q^{10} + q^{11} - 2q^{13} + 4q^{14} - q^{16} + O(q^{20}) \)

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.