Properties

Label 53235.bg
Number of curves 4
Conductor 53235
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("53235.bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53235.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53235.bg1 53235bc4 [1, -1, 0, -171144, 27292383] [2] 245760  
53235.bg2 53235bc2 [1, -1, 0, -11439, 366120] [2, 2] 122880  
53235.bg3 53235bc1 [1, -1, 0, -3834, -85617] [2] 61440 \(\Gamma_0(N)\)-optimal
53235.bg4 53235bc3 [1, -1, 0, 26586, 2259765] [2] 245760  

Rank

sage: E.rank()
 

The elliptic curves in class 53235.bg have rank \(1\).

Modular form 53235.2.a.bg

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} + q^{5} - q^{7} - 3q^{8} + q^{10} - q^{14} - q^{16} - 2q^{17} + 8q^{19} + O(q^{20}) \)

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.