Properties

Label 36.a
Number of curves 4
Conductor \(36\)
CM True
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("36.a1")
sage: E.isogeny_class()

Elliptic curves in class 36.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
36.a1 36a4 [0, 0, 0, -135, -594] 2 6  
36.a2 36a2 [0, 0, 0, -15, 22] 6 2  
36.a3 36a3 [0, 0, 0, 0, -27] 2 3  
36.a4 36a1 [0, 0, 0, 0, 1] 6 1 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 36.a have rank \(0\).

Modular form 36.2.1.a

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

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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