Properties

Label 40.a
Number of curves 4
Conductor \(40\)
CM no
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("40.a1")
sage: E.isogeny_class()

Elliptic curves in class 40.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
40.a1 40a2 [0, 0, 0, -107, -426] 2 4  
40.a2 40a1 [0, 0, 0, -7, -6] 4 2 \(\Gamma_0(N)\)-optimal
40.a3 40a3 [0, 0, 0, -2, 1] 4 4  
40.a4 40a4 [0, 0, 0, 13, -34] 4 4  

Rank

sage: E.rank()

The elliptic curves in class 40.a have rank \(0\).

Modular form 40.2.1.a

sage: E.q_eigenform(10)
\( q + q^{5} - 4q^{7} - 3q^{9} + 4q^{11} - 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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)