Properties

Label 1666.a
Number of curves $1$
Conductor $1666$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 1666.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1666.a1 1666h1 \([1, -1, 0, -74881, -28409795]\) \(-164384733177/1140850688\) \(-322262082164621312\) \([]\) \(43680\) \(2.0428\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1666.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 1666.a do not have complex multiplication.

Modular form 1666.2.a.a

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