Properties

Label 27.a
Number of curves 4
Conductor \(27\)
CM True
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 order Modular degree Optimality
27.a1 27a2 [0, 0, 1, -270, -1708] 1 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 27.2.1.a

sage: E.q_eigenform(10)
\( q - 2q^{4} - q^{7} + O(q^{10}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

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

Isogeny graph

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