Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("8550.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8550ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8550.t4 8550ba1 [1, -1, 1, -2255, -69753] [2] 18432 \(\Gamma_0(N)\)-optimal
8550.t3 8550ba2 [1, -1, 1, -42755, -3390753] [2, 2] 36864  
8550.t1 8550ba3 [1, -1, 1, -684005, -217568253] [2] 73728  
8550.t2 8550ba4 [1, -1, 1, -49505, -2243253] [2] 73728  

Rank

sage: E.rank()
 

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

Modular form 8550.2.a.t

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

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.