Properties

Label 1002e
Number of curves 1
Conductor 1002
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("1002.e1")
sage: E.isogeny_class()

Elliptic curves in class 1002e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1002.e1 1002e1 [1, 0, 0, -27, 81] 1 224 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 1002e1 has rank \(1\).

Modular form 1002.2.a.e

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