Properties

Label 2006d
Number of curves $1$
Conductor $2006$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 2006d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2006.a1 2006d1 \([1, 1, 0, -88, 284]\) \(-76711450249/68204\) \(-68204\) \([]\) \(384\) \(-0.14743\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 2006d1 has rank \(2\).

Complex multiplication

The elliptic curves in class 2006d do not have complex multiplication.

Modular form 2006.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 5 q^{7} - q^{8} - 2 q^{9} + q^{10} - 2 q^{11} - q^{12} - 4 q^{13} + 5 q^{14} + q^{15} + q^{16} + q^{17} + 2 q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display