Properties

Label 38.a
Number of curves 3
Conductor \(38\)
CM False
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("38.a1")
sage: E.isogeny_class()

Elliptic curves in class 38.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
38.a1 38a2 [1, 0, 1, -86, -2456] 1 18  
38.a2 38a3 [1, 0, 1, -16, 22] 3 18  
38.a3 38a1 [1, 0, 1, 9, 90] 3 6 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 38.a have rank \(0\).

Modular form 38.2.1.a

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

Isogeny matrix

sage: E.isogeny_class().matrix()

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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