Properties

Label 66.b
Number of curves 4
Conductor \(66\)
CM no
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("66.b1")
sage: E.isogeny_class()

Elliptic curves in class 66.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
66.b1 66b3 [1, 1, 1, -352, -2689] 2 16  
66.b2 66b2 [1, 1, 1, -22, -49] 4 8  
66.b3 66b4 [1, 1, 1, -12, -81] 2 16  
66.b4 66b1 [1, 1, 1, -2, -1] 4 4 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 66.b have rank \(0\).

Modular form 66.2.1.b

sage: E.q_eigenform(10)
\( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} - 4q^{7} + q^{8} + q^{9} + 2q^{10} - q^{11} - q^{12} - 6q^{13} - 4q^{14} - 2q^{15} + q^{16} + 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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