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Properties

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

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Show commands: SageMath
E = EllipticCurve("bg1")
 
E.isogeny_class()
 

Elliptic curves in class 8550.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.bg1 8550u2 \([1, -1, 1, -9980, 215647]\) \(260549802603/104256800\) \(43983337500000\) \([2]\) \(30720\) \(1.3160\)  
8550.bg2 8550u1 \([1, -1, 1, 2020, 23647]\) \(2161700757/1848320\) \(-779760000000\) \([2]\) \(15360\) \(0.96945\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8550.2.a.bg

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2 q^{7} + q^{8} - 2 q^{11} + 4 q^{13} + 2 q^{14} + q^{16} - 6 q^{17} + q^{19} + O(q^{20})\) Copy content 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.