Properties

Label 1006d
Number of curves 1
Conductor 1006
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("1006.d1")
sage: E.isogeny_class()

Elliptic curves in class 1006d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1006.d1 1006d1 [1, 1, 1, -23, 45] 1 120 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 1006d1 has rank \(1\).

Modular form 1006.2.a.d

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