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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("a1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 422142a1 has rank \(1\).

Complex multiplication

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

Modular form 422142.2.a.a

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

Elliptic curves in class 422142a

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422142.a1 422142a1 \([1, 1, 0, -85813597, -306014525315]\) \(-892420116098747161/21445337088\) \(-1679405477044451401728\) \([]\) \(82667520\) \(3.1834\) \(\Gamma_0(N)\)-optimal