Properties

Label 221067.n
Number of curves $1$
Conductor $221067$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 221067.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.n1 221067i1 \([1, -1, 1, -367177064, -2708128529994]\) \(-289531596860402017/17410522563\) \(-329204820740288072052627\) \([]\) \(42577920\) \(3.5737\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 221067.n1 has rank \(1\).

Complex multiplication

The elliptic curves in class 221067.n do not have complex multiplication.

Modular form 221067.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} + 2 q^{5} + q^{7} + 3 q^{8} - 2 q^{10} + 4 q^{13} - q^{14} - q^{16} - q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display