Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("1006.c1")
sage: E.isogeny_class()

Elliptic curves in class 1006e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1006.c1 1006e1 [1, -1, 1, -135, 639] 1 480 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 1006e1 has rank \(1\).

Modular form 1006.2.a.c

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