Properties

Label 100010k
Number of curves 1
Conductor 100010
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("100010.e1")
sage: E.isogeny_class()

Elliptic curves in class 100010k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100010.e1 100010k1 [1, 0, 0, -670, 6660] 1 51264 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 100010k1 has rank \(1\).

Modular form None

sage: E.q_eigenform(10)
\( q + q^{2} - 2q^{3} + q^{4} + q^{5} - 2q^{6} - q^{7} + q^{8} + q^{9} + q^{10} + 2q^{11} - 2q^{12} + 5q^{13} - q^{14} - 2q^{15} + q^{16} - 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)