Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8550.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.k1 8550p2 \([1, -1, 0, -23022, -1338764]\) \(14809006736693/34656\) \(3158028000\) \([2]\) \(15360\) \(1.0652\)  
8550.k2 8550p1 \([1, -1, 0, -1422, -21164]\) \(-3491055413/175104\) \(-15956352000\) \([2]\) \(7680\) \(0.71866\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8550.2.a.k

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