Properties

Label 37.a
Number of curves 1
Conductor \(37\)
CM no
Rank \(1\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("37.a1")
sage: E.isogeny_class()

Elliptic curves in class 37.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
37.a1 37a1 [0, 0, 1, -1, 0] 1 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 37.a have rank \(1\).

Modular form 37.2.1.a

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