Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 4018.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4018.r1 4018l1 \([1, 1, 1, 636, -32635]\) \(4934783/83968\) \(-484058810368\) \([]\) \(5544\) \(0.92264\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 4018.r do not have complex multiplication.

Modular form 4018.2.a.r

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