Properties

Label 163170fb
Number of curves $1$
Conductor $163170$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("fb1")
 
E.isogeny_class()
 

Elliptic curves in class 163170fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163170.a1 163170fb1 \([1, -1, 0, 2376540, 527208016]\) \(353221512666239/233046720000\) \(-979388146122482880000\) \([]\) \(9580032\) \(2.7166\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 163170fb1 has rank \(1\).

Complex multiplication

The elliptic curves in class 163170fb do not have complex multiplication.

Modular form 163170.2.a.fb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 5 q^{11} + 5 q^{13} + q^{16} + 5 q^{17} + 5 q^{19} + O(q^{20})\) Copy content Toggle raw display