Properties

Label 197.a
Number of curves 1
Conductor 197
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("197.a1")
sage: E.isogeny_class()

Elliptic curves in class 197.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
197.a1 197a1 [0, 0, 1, -5, 4] 1 10 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 197.a1 has rank \(1\).

Modular form 197.2.a.a

sage: E.q_eigenform(10)
\( q - 2q^{2} + 2q^{4} - 3q^{7} - 3q^{9} + 4q^{11} - 2q^{13} + 6q^{14} - 4q^{16} - 8q^{17} + 6q^{18} - 3q^{19} + O(q^{20}) \)