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Properties

Label 422142p
Number of curves $1$
Conductor $422142$
CM no
Rank $1$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("p1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 422142p1 has rank \(1\).

Complex multiplication

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

Modular form 422142.2.a.p

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

Elliptic curves in class 422142p

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422142.p1 422142p1 \([1, 1, 0, -13139130879, 579687554152773]\) \(-3203324534532292752802873/52058248123392\) \(-4076732702545596783793152\) \([]\) \(456261120\) \(4.2673\) \(\Gamma_0(N)\)-optimal