Properties

Label 27773.a
Number of curves 1
Conductor 27773
CM no
Rank 3

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Show commands for: SageMath

sage: E = EllipticCurve("27773.a1")
sage: E.isogeny_class()

Elliptic curves in class 27773.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
27773.a1 27773a1 [1, -1, 1, -21, 42] 1 5536 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 27773.a1 has rank \(3\).

Modular form None

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