Properties

Label 39.a
Number of curves 4
Conductor \(39\)
CM False
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("39.a1")
sage: E.isogeny_class()

Elliptic curves in class 39.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
39.a1 39a2 [1, 1, 0, -69, -252] 2 4  
39.a2 39a3 [1, 1, 0, -19, 22] 4 4  
39.a3 39a1 [1, 1, 0, -4, -5] 4 2 \(\Gamma_0(N)\)-optimal
39.a4 39a4 [1, 1, 0, 1, 0] 2 4  

Rank

sage: E.rank()

The elliptic curves in class 39.a have rank \(0\).

Modular form 39.2.1.a

sage: E.q_eigenform(10)
\( q + q^{2} - q^{3} - q^{4} + 2q^{5} - q^{6} - 4q^{7} - 3q^{8} + q^{9} + O(q^{10}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()

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

Isogeny graph

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