Properties

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

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 3822.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.u1 3822r1 \([1, 1, 1, -3823, -164347]\) \(-1071912625/1364688\) \(-7867154747088\) \([]\) \(10752\) \(1.1677\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3822.u1 has rank \(0\).

Complex multiplication

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

Modular form 3822.2.a.u

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