Properties

Label 4018.r
Number of curves 1
Conductor 4018
CM no
Rank 1

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Show commands for: SageMath

sage: E = EllipticCurve("4018.r1")
sage: E.isogeny_class()

Elliptic curves in class 4018.r

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4018.r1 4018l1 [1, 1, 1, 636, -32635] 1 5544 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curve 4018.r1 has rank \(1\).

Modular form 4018.2.a.r

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