Properties

Label 1006.d
Number of curves $1$
Conductor $1006$
CM no
Rank $1$

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

Elliptic curves in class 1006.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1006.d1 1006d1 \([1, 1, 1, -23, 45]\) \(-1349232625/515072\) \(-515072\) \([]\) \(120\) \(-0.19440\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1006.d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1006.d do not have complex multiplication.

Modular form 1006.2.a.d

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