Properties

Label 489566.bb
Number of curves $1$
Conductor $489566$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 489566.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
489566.bb1 489566bb1 \([1, 0, 1, -41823653, 104103767392]\) \(654699641761/112\) \(1384093740728764912\) \([]\) \(49351680\) \(2.8796\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 489566.bb1 has rank \(1\).

Complex multiplication

The elliptic curves in class 489566.bb do not have complex multiplication.

Modular form 489566.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 4 q^{5} - q^{6} - q^{7} - q^{8} - 2 q^{9} + 4 q^{10} + q^{12} + 2 q^{13} + q^{14} - 4 q^{15} + q^{16} + 2 q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display