Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 5586.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.q1 5586n1 \([1, 0, 1, -24389923, 46360136414]\) \(-668286694038078762077641/413929046016\) \(-993843639484416\) \([]\) \(255360\) \(2.6332\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5586.q1 has rank \(1\).

Complex multiplication

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

Modular form 5586.2.a.q

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