Properties

Label 3822.z
Number of curves $1$
Conductor $3822$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 3822.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.z1 3822z1 \([1, 1, 1, -182526, -30833349]\) \(-2380771254001/69009408\) \(-19493449708142592\) \([]\) \(64512\) \(1.9050\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3822.z1 has rank \(0\).

Complex multiplication

The elliptic curves in class 3822.z do not have complex multiplication.

Modular form 3822.2.a.z

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