Properties

Label 27747c
Number of curves 1
Conductor 27747
CM no
Rank 3

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Show commands for: SageMath

sage: E = EllipticCurve("27747.a1")
sage: E.isogeny_class()

Elliptic curves in class 27747c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
27747.a1 27747c1 [0, 0, 1, -327, 2286] 1 27776 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 27747c1 has rank \(3\).

Modular form None

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