Properties

Label 10005c
Number of curves 1
Conductor 10005
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("10005.n1")
sage: E.isogeny_class()

Elliptic curves in class 10005c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
10005.n1 10005c1 [0, -1, 1, -16, -3] 1 1440 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 10005c1 has rank \(1\).

Modular form None

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