Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("10005.g1")
sage: E.isogeny_class()

Elliptic curves in class 10005m

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
10005.g1 10005m1 [0, 1, 1, -104207741, 135268278965] 1 2140320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 10005m1 has rank \(1\).

Modular form None

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