Properties

Label 169050gr
Number of curves $1$
Conductor $169050$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("gr1")
 
E.isogeny_class()
 

Elliptic curves in class 169050gr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.eb1 169050gr1 \([1, 0, 1, 11142574, -9606244252]\) \(83228502970940543/69854999176704\) \(-128412043720938264000000\) \([]\) \(20528640\) \(3.1218\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 169050gr1 has rank \(1\).

Complex multiplication

The elliptic curves in class 169050gr do not have complex multiplication.

Modular form 169050.2.a.gr

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