Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8550.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.bb1 8550bj2 \([1, -1, 1, -575555, -167921053]\) \(14809006736693/34656\) \(49344187500000\) \([2]\) \(76800\) \(1.8700\)  
8550.bb2 8550bj1 \([1, -1, 1, -35555, -2681053]\) \(-3491055413/175104\) \(-249318000000000\) \([2]\) \(38400\) \(1.5234\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8550.2.a.bb

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.