Properties

Label 58.a
Number of curves 1
Conductor 58
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("58.a1")
sage: E.isogeny_class()

Elliptic curves in class 58.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
58.a1 58a1 [1, -1, 0, -1, 1] 1 4 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 58.a1 has rank \(1\).

Modular form 58.2.a.a

sage: E.q_eigenform(10)
\( q - q^{2} - 3q^{3} + q^{4} - 3q^{5} + 3q^{6} - 2q^{7} - q^{8} + 6q^{9} + 3q^{10} - q^{11} - 3q^{12} + 3q^{13} + 2q^{14} + 9q^{15} + q^{16} - 4q^{17} - 6q^{18} - 8q^{19} + O(q^{20}) \)