Properties

 Label 101a Number of curves 1 Conductor 101 CM no Rank 1

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Show commands for: SageMath
sage: E = EllipticCurve("101.a1")

sage: E.isogeny_class()

Elliptic curves in class 101a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
101.a1 101a1 [0, 1, 1, -1, -1] [] 2 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 101a1 has rank $$1$$.

Modular form101.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{4} - q^{5} - 2q^{7} + q^{9} - 2q^{11} + 4q^{12} + q^{13} + 2q^{15} + 4q^{16} + 3q^{17} - 5q^{19} + O(q^{20})$$