Properties

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

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

Elliptic curves in class 5586b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5586.d1 5586b1 \([1, 1, 0, -1195106203, -15902721896291]\) \(-668286694038078762077641/413929046016\) \(-116924710341702057984\) \([]\) \(1787520\) \(3.6062\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5586b1 has rank \(0\).

Complex multiplication

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

Modular form 5586.2.a.b

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