Properties

Label 1001c
Number of curves 1
Conductor 1001
CM no
Rank 2

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Show commands for: SageMath

sage: E = EllipticCurve("1001.a1")
sage: E.isogeny_class()

Elliptic curves in class 1001c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1001.a1 1001c1 [0, 0, 1, -199, 1092] 1 1008 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 1001c1 has rank \(2\).

Modular form 1001.2.a.a

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