Properties

Label 27.a
Number of curves 4
Conductor 27
CM -3
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("27.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 27.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27.a1 27a2 [0, 0, 1, -270, -1708] [] 3  
27.a2 27a4 [0, 0, 1, -30, 63] [3] 9  
27.a3 27a1 [0, 0, 1, 0, -7] [3] 1 \(\Gamma_0(N)\)-optimal
27.a4 27a3 [0, 0, 1, 0, 0] [3] 3  

Rank

sage: E.rank()
 

The elliptic curves in class 27.a have rank \(0\).

Modular form 27.2.a.a

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

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.

\(\left(\begin{array}{rrrr} 1 & 27 & 3 & 9 \\ 27 & 1 & 9 & 3 \\ 3 & 9 & 1 & 3 \\ 9 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.