Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 27225.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27225.g1 27225bm2 [1, -1, 1, -68630, -27034378] [] 221760  
27225.g2 27225bm1 [1, -1, 1, -6755, 215372] [] 20160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 27225.2.a.g

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.