Properties

Label 422331j
Number of curves $1$
Conductor $422331$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 422331j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422331.j1 422331j1 \([0, 1, 1, -188395510, -1440714096272]\) \(-1302227927110660096/825290486657091\) \(-468657091374515156618872731\) \([]\) \(263983104\) \(3.8191\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 422331j1 has rank \(1\).

Complex multiplication

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

Modular form 422331.2.a.j

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