Properties

Label 83.a
Number of curves 1
Conductor 83
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("83.a1")
sage: E.isogeny_class()

Elliptic curves in class 83.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
83.a1 83a1 [1, 1, 1, 1, 0] 1 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 83.a1 has rank \(1\).

Modular form 83.2.a.a

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