Properties

Label 221067bf
Number of curves $1$
Conductor $221067$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 221067bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.bi1 221067bf1 \([1, -1, 0, -1847511, 16366811764]\) \(-36883367257/6098396283\) \(-115310809763674414242507\) \([]\) \(13685760\) \(3.1045\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 221067bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 221067bf do not have complex multiplication.

Modular form 221067.2.a.bf

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