Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8550.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.be1 8550bm2 \([1, -1, 1, -15305, 1186697]\) \(-1392225385/1316928\) \(-375015825000000\) \([3]\) \(34560\) \(1.4928\)  
8550.be2 8550bm1 \([1, -1, 1, 1570, -28303]\) \(1503815/2052\) \(-584339062500\) \([]\) \(11520\) \(0.94354\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 8550.2.a.be

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.