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Properties

Label 54150.br
Number of curves $2$
Conductor $54150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("br1")
 
E.isogeny_class()
 

Elliptic curves in class 54150.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54150.br1 54150bo2 \([1, 1, 1, -32905338, 72638229531]\) \(781484460931/900\) \(4537795750017187500\) \([2]\) \(3502080\) \(2.8639\)  
54150.br2 54150bo1 \([1, 1, 1, -2039838, 1153731531]\) \(-186169411/6480\) \(-32672129400123750000\) \([2]\) \(1751040\) \(2.5174\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54150.br have rank \(0\).

Complex multiplication

The elliptic curves in class 54150.br do not have complex multiplication.

Modular form 54150.2.a.br

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