Properties

Label 169338.p
Number of curves $1$
Conductor $169338$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 169338.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169338.p1 169338h1 \([1, 1, 1, -257644, -95836915]\) \(-13719882553/20777472\) \(-2864350954354825728\) \([]\) \(3144960\) \(2.2332\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 169338.p1 has rank \(1\).

Complex multiplication

The elliptic curves in class 169338.p do not have complex multiplication.

Modular form 169338.2.a.p

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 2 q^{5} - q^{6} + 2 q^{7} + q^{8} + q^{9} - 2 q^{10} - 4 q^{11} - q^{12} + 2 q^{14} + 2 q^{15} + q^{16} - 2 q^{17} + q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display