Properties

Label 8550x
Number of curves $4$
Conductor $8550$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("8550.x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8550x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8550.x3 8550x1 [1, -1, 1, -6980, -221353] [2] 12288 \(\Gamma_0(N)\)-optimal
8550.x2 8550x2 [1, -1, 1, -11480, 102647] [2, 2] 24576  
8550.x1 8550x3 [1, -1, 1, -139730, 20109647] [2] 49152  
8550.x4 8550x4 [1, -1, 1, 44770, 777647] [2] 49152  

Rank

sage: E.rank()
 

The elliptic curves in class 8550x have rank \(1\).

Modular form 8550.2.a.x

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{8} - 4q^{11} - 2q^{13} + q^{16} + 2q^{17} - q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.