Properties

Label 5586.s
Number of curves $1$
Conductor $5586$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 5586.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.s1 5586l1 \([1, 0, 1, -2623, -56206]\) \(-346016041/34656\) \(-199784943456\) \([]\) \(6720\) \(0.90862\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5586.s1 has rank \(0\).

Complex multiplication

The elliptic curves in class 5586.s do not have complex multiplication.

Modular form 5586.2.a.s

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