Properties

Label 55506bb
Number of curves $1$
Conductor $55506$
CM no
Rank $1$

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

Elliptic curves in class 55506bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55506.x1 55506bb1 \([1, 1, 1, -283014, -46352325]\) \(5011452097/1054152\) \(527335756715664072\) \([]\) \(835200\) \(2.1153\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 55506bb1 has rank \(1\).

Complex multiplication

The elliptic curves in class 55506bb do not have complex multiplication.

Modular form 55506.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 2 q^{5} - q^{6} - 3 q^{7} + q^{8} + q^{9} - 2 q^{10} - q^{11} - q^{12} - 4 q^{13} - 3 q^{14} + 2 q^{15} + q^{16} - q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display