Properties

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

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

Elliptic curves in class 8550.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.t1 8550ba3 \([1, -1, 1, -684005, -217568253]\) \(3107086841064961/570\) \(6492656250\) \([2]\) \(73728\) \(1.7185\)  
8550.t2 8550ba4 \([1, -1, 1, -49505, -2243253]\) \(1177918188481/488703750\) \(5566641152343750\) \([2]\) \(73728\) \(1.7185\)  
8550.t3 8550ba2 \([1, -1, 1, -42755, -3390753]\) \(758800078561/324900\) \(3700814062500\) \([2, 2]\) \(36864\) \(1.3720\)  
8550.t4 8550ba1 \([1, -1, 1, -2255, -69753]\) \(-111284641/123120\) \(-1402413750000\) \([2]\) \(18432\) \(1.0254\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8550.2.a.t

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.