Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("1001.c1")
sage: E.isogeny_class()

Elliptic curves in class 1001.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1001.c1 1001a1 [0, -1, 1, -15881, 778423] 1 1680 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 1001.c1 has rank \(1\).

Modular form 1001.2.a.c

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