Properties

Label 57a
Number of curves 1
Conductor 57
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("57.a1")
sage: E.isogeny_class()

Elliptic curves in class 57a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
57.a1 57a1 [0, -1, 1, -2, 2] 1 4 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 57a1 has rank \(1\).

Modular form 57.2.a.a

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