Properties

 Label 106b Number of curves 1 Conductor 106 CM no Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("106.a1")
sage: E.isogeny_class()

Elliptic curves in class 106b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
106.a1 106b1 [1, 1, 0, -7, 5] 1 8 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 106b1 has rank $$1$$.

Modular form106.2.a.a

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