Properties

Label 163170.r
Number of curves $1$
Conductor $163170$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 163170.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163170.r1 163170em1 \([1, -1, 0, 788836095, 8479043901]\) \(263618634987871768031/152557238353920000\) \(-31415266396375632649912320000\) \([]\) \(114175488\) \(4.1576\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 163170.r1 has rank \(0\).

Complex multiplication

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

Modular form 163170.2.a.r

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