Properties

Label 1006.b
Number of curves 1
Conductor 1006
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("1006.b1")
sage: E.isogeny_class()

Elliptic curves in class 1006.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1006.b1 1006a1 [1, 0, 1, -2, 4] 1 48 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 1006.b1 has rank \(1\).

Modular form 1006.2.a.b

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