Properties

Label 18745a
Number of curves 1
Conductor 18745
CM no
Rank 3

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Show commands for: SageMath

sage: E = EllipticCurve("18745.a1")
sage: E.isogeny_class()

Elliptic curves in class 18745a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
18745.a1 18745a1 [0, 1, 1, -146, 636] 1 10976 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 18745a1 has rank \(3\).

Modular form None

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