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Properties

Label 422142x
Number of curves $1$
Conductor $422142$
CM no
Rank $2$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("x1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 422142x1 has rank \(2\).

Complex multiplication

The elliptic curves in class 422142x do not have complex multiplication.

Modular form 422142.2.a.x

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + 3 q^{10} - 2 q^{11} + q^{12} - 2 q^{13} - q^{14} - 3 q^{15} + q^{16} - 3 q^{17} - q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 422142x

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422142.x1 422142x1 \([1, 0, 1, -605475, 181253710]\) \(46404025484312948377/10403087412816\) \(5503233241379664\) \([]\) \(5870592\) \(2.0130\) \(\Gamma_0(N)\)-optimal