Properties

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

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

Elliptic curves in class 8550x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.x3 8550x1 \([1, -1, 1, -6980, -221353]\) \(3301293169/22800\) \(259706250000\) \([2]\) \(12288\) \(1.0238\) \(\Gamma_0(N)\)-optimal
8550.x2 8550x2 \([1, -1, 1, -11480, 102647]\) \(14688124849/8122500\) \(92520351562500\) \([2, 2]\) \(24576\) \(1.3704\)  
8550.x1 8550x3 \([1, -1, 1, -139730, 20109647]\) \(26487576322129/44531250\) \(507238769531250\) \([2]\) \(49152\) \(1.7169\)  
8550.x4 8550x4 \([1, -1, 1, 44770, 777647]\) \(871257511151/527800050\) \(-6011972444531250\) \([2]\) \(49152\) \(1.7169\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8550.2.a.x

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