Properties

Label 8550.g
Number of curves $2$
Conductor $8550$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8550.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.g1 8550f2 \([1, -1, 0, -364167, -84494259]\) \(468898230633769/5540400\) \(63108618750000\) \([2]\) \(73728\) \(1.7980\)  
8550.g2 8550f1 \([1, -1, 0, -22167, -1388259]\) \(-105756712489/12476160\) \(-142111260000000\) \([2]\) \(36864\) \(1.4514\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 8550.g have rank \(0\).

Complex multiplication

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

Modular form 8550.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{7} - q^{8} + 6 q^{11} + 2 q^{14} + q^{16} + 2 q^{17} - q^{19} + O(q^{20})\)  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.