Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("1002.c1")
sage: E.isogeny_class()

Elliptic curves in class 1002c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1002.c1 1002c1 [1, 0, 1, -3264, 71590] 1 1008 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 1002c1 has rank \(1\).

Modular form 1002.2.a.c

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