Properties

Label 100010.b
Number of curves 1
Conductor 100010
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("100010.b1")
sage: E.isogeny_class()

Elliptic curves in class 100010.b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
100010.b1 100010b1 [1, 0, 1, -10709, 425632] 1 100224 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 100010.b1 has rank \(1\).

Modular form None

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