Properties

Label 8550.o
Number of curves $2$
Conductor $8550$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8550.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.o1 8550j2 \([1, -1, 0, -89442, -10259784]\) \(6947097508441/10687500\) \(121737304687500\) \([2]\) \(36864\) \(1.6021\)  
8550.o2 8550j1 \([1, -1, 0, -3942, -256284]\) \(-594823321/2166000\) \(-24672093750000\) \([2]\) \(18432\) \(1.2555\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 8550.o do not have complex multiplication.

Modular form 8550.2.a.o

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.