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Properties

Label 27225.bu
Number of curves $2$
Conductor $27225$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 27225.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27225.bu1 27225bj2 [1, -1, 0, -817317, -284208534] [] 221760  
27225.bu2 27225bj1 [1, -1, 0, -567, 20466] [] 20160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 27225.bu have rank \(1\).

Complex multiplication

The elliptic curves in class 27225.bu do not have complex multiplication.

Modular form 27225.2.a.bu

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} + 2q^{7} - 3q^{8} - q^{13} + 2q^{14} - q^{16} - 5q^{17} + 6q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.