Properties

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

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 4018.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4018.b1 4018k1 \([1, -1, 0, -1969, 34117]\) \(7177888089/2296\) \(270122104\) \([]\) \(5760\) \(0.59266\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4018.b1 has rank \(1\).

Complex multiplication

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

Modular form 4018.2.a.b

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