Properties

Label 10005.e
Number of curves 1
Conductor 10005
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("10005.e1")
sage: E.isogeny_class()

Elliptic curves in class 10005.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
10005.e1 10005a1 [0, -1, 1, -51, -124] 1 1632 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 10005.e1 has rank \(1\).

Modular form 10005.2.a.e

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