Properties

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

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 3822.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.e1 3822h1 \([1, 1, 0, -368, 2976]\) \(-47045881/8736\) \(-1027781664\) \([]\) \(1920\) \(0.45370\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3822.e1 has rank \(1\).

Complex multiplication

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

Modular form 3822.2.a.e

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