Properties

Label 169065.bf
Number of curves $1$
Conductor $169065$
CM no
Rank $1$

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

Elliptic curves in class 169065.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169065.bf1 169065u1 \([1, -1, 0, -1807749, 2653201930]\) \(-10730378053390609/43719326015625\) \(-2661930252722090390625\) \([]\) \(9160704\) \(2.7964\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 169065.bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 169065.bf do not have complex multiplication.

Modular form 169065.2.a.bf

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