Properties

Label 43.a
Number of curves 1
Conductor \(43\)
CM no
Rank \(1\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("43.a1")
sage: E.isogeny_class()

Elliptic curves in class 43.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
43.a1 43a1 [0, 1, 1, 0, 0] 1 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 43.a have rank \(1\).

Modular form 43.2.1.a

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