Properties

Label 422331.i
Number of curves $1$
Conductor $422331$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 422331.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422331.i1 422331i1 \([0, 1, 1, 2966450184, -532512251582398]\) \(177997182325354496/7656065368994259\) \(-124173063559026251250837364631259\) \([]\) \(1736616960\) \(4.8381\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 422331.i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 422331.i do not have complex multiplication.

Modular form 422331.2.a.i

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