Properties

Label 4008.b
Number of curves $1$
Conductor $4008$
CM no
Rank $1$

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

Elliptic curves in class 4008.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4008.b1 4008c1 \([0, 1, 0, -296, -2064]\) \(-1405190738/1503\) \(-3078144\) \([]\) \(576\) \(0.16131\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4008.b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4008.b do not have complex multiplication.

Modular form 4008.2.a.b

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} + q^{9} - 2q^{11} + 2q^{13} - q^{15} + O(q^{20})\)  Toggle raw display