Properties

Label 5550.ba
Number of curves $2$
Conductor $5550$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5550.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.ba1 5550v2 \([1, 1, 1, -177213, -28823469]\) \(-39390416456458249/56832000000\) \(-888000000000000\) \([]\) \(51840\) \(1.7707\)  
5550.ba2 5550v1 \([1, 1, 1, 3162, -185469]\) \(223759095911/1094104800\) \(-17095387500000\) \([]\) \(17280\) \(1.2214\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5550.ba have rank \(0\).

Complex multiplication

The elliptic curves in class 5550.ba do not have complex multiplication.

Modular form 5550.2.a.ba

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + q^{7} + q^{8} + q^{9} + 3q^{11} - q^{12} + 7q^{13} + q^{14} + q^{16} + 3q^{17} + q^{18} - q^{19} + O(q^{20})\)  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.