Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("10005.i1")
sage: E.isogeny_class()

Elliptic curves in class 10005l

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
10005.i1 10005l1 [0, 1, 1, -10597711, -13282563134] 1 349440 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 10005l1 has rank \(1\).

Modular form None

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