Properties

Label 588.a
Number of curves $1$
Conductor $588$
CM no
Rank $0$

Related objects

Downloads

Learn more

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

Elliptic curves in class 588.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
588.a1 588a1 \([0, -1, 0, 131, -167]\) \(401408/243\) \(-149361408\) \([]\) \(180\) \(0.25773\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 588.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 588.a do not have complex multiplication.

Modular form 588.2.a.a

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