Properties

Label 89.a
Number of curves 1
Conductor 89
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("89.a1")
sage: E.isogeny_class()

Elliptic curves in class 89.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
89.a1 89a1 [1, 1, 1, -1, 0] 1 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 89.a1 has rank \(1\).

Modular form 89.2.a.a

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