Properties

Label 20.a
Number of curves 4
Conductor \(20\)
CM False
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("20.a1")
sage: E.isogeny_class()

Elliptic curves in class 20.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
20.a1 20a4 [0, 1, 0, -41, -116] 2 6  
20.a2 20a3 [0, 1, 0, -36, -140] 2 3  
20.a3 20a2 [0, 1, 0, -1, 0] 6 2  
20.a4 20a1 [0, 1, 0, 4, 4] 6 1 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 20.a have rank \(0\).

Modular form 20.2.1.a

sage: E.q_eigenform(10)
\( q - 2q^{3} - q^{5} + 2q^{7} + q^{9} + O(q^{10}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

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

Isogeny graph

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