Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 8550e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.f2 8550e1 \([1, -1, 0, 42948, -214704]\) \(480705753733655/279172334592\) \(-5087915797939200\) \([]\) \(57600\) \(1.7033\) \(\Gamma_0(N)\)-optimal
8550.f1 8550e2 \([1, -1, 0, -4471992, 3641708916]\) \(-1389310279182025/267418692\) \(-1903791274101562500\) \([]\) \(288000\) \(2.5080\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8550.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2 q^{7} - q^{8} + 3 q^{11} - 6 q^{13} + 2 q^{14} + q^{16} + 2 q^{17} - q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.