Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 3822.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.f1 3822a1 \([1, 1, 0, 26533, 894237]\) \(358321516679/265814016\) \(-1532364905250816\) \([]\) \(19152\) \(1.6020\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3822.f1 has rank \(1\).

Complex multiplication

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

Modular form 3822.2.a.f

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