Properties

Label 4022.a
Number of curves $1$
Conductor $4022$
CM no
Rank $0$

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

Elliptic curves in class 4022.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4022.a1 4022a1 \([1, -1, 0, -1, -195]\) \(-185193/16474112\) \(-16474112\) \([]\) \(754\) \(0.063664\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4022.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 4022.a do not have complex multiplication.

Modular form 4022.2.a.a

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