Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("10005.a1")
sage: E.isogeny_class()

Elliptic curves in class 10005k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
10005.a1 10005k1 [0, 1, 1, -31666, -2179460] 1 38880 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 10005k1 has rank \(1\).

Modular form None

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