Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 8550.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.j1 8550q2 \([1, -1, 0, -176742, -14750834]\) \(428831641421/181752822\) \(258784779761718750\) \([2]\) \(107520\) \(2.0380\)  
8550.j2 8550q1 \([1, -1, 0, 37008, -1712084]\) \(3936827539/3158028\) \(-4496489085937500\) \([2]\) \(53760\) \(1.6914\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8550.2.a.j

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