Properties

Label 4008.a
Number of curves $1$
Conductor $4008$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 4008.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4008.a1 4008d1 \([0, -1, 0, 160, -2196]\) \(219804478/1095687\) \(-2243966976\) \([]\) \(1792\) \(0.47653\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4008.a1 has rank \(0\).

Complex multiplication

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

Modular form 4008.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 3 q^{7} + q^{9} + 4 q^{11} + 2 q^{13} - q^{15} - 6 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display