Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("10005.f1")
sage: E.isogeny_class()

Elliptic curves in class 10005b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
10005.f1 10005b1 [0, -1, 1, -609991, 183560811] 1 84000 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 10005b1 has rank \(1\).

Modular form None

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