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Properties

Label 422142n
Number of curves $1$
Conductor $422142$
CM no
Rank $0$

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 422142n1 has rank \(0\).

Complex multiplication

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

Modular form 422142.2.a.n

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

Elliptic curves in class 422142n

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422142.n1 422142n1 \([1, 1, 0, -629563704, -25707687106752]\) \(-186412805526685980326617/1820685432230184941568\) \(-269526786549544680459431933952\) \([]\) \(669081600\) \(4.3295\) \(\Gamma_0(N)\)-optimal