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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("k1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 422142.k1 has rank \(2\).

Complex multiplication

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

Modular form 422142.2.a.k

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

Elliptic curves in class 422142.k

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422142.k1 422142k1 \([1, 1, 0, -17502, 883188]\) \(1120907693189209/1117863936\) \(591350022144\) \([]\) \(999936\) \(1.1784\) \(\Gamma_0(N)\)-optimal