Counter, n = 66

Discriminant, d = 540365

3class group of type (3,3)

3class number, h = 9

Conductor, f = 1

Fundamental unit, e_{0} = (U_{0} + V_{0}*x)/T_{0}, with x^{2} = d, and regulator, R

U_{0}

V_{0}

T_{0}


R

15437

21

2


9.6

The nonGalois absolute cubic subfields (L_{1},L_{2},L_{3},L_{4})
of the four unramified cyclic cubic relative extensions NK

Regulators, R

39.1

116.3

118.9

131.6

Class numbers, h

9

3

3

3

Polynomials, p(X) = X^{3}  C*X  D, with d(p) = i^{2}*d

(C,D)

(122,499)

(68,163)

(768,7247)

(642,4961)

Indices, i

1

1

27

27

Fundamental units, e_{1} = (U_{1} + V_{1}*x + W_{1}*x^{2})/T_{1}, with P(x) = 0

U_{1}

16

1487

238

10294

V_{1}

3

394

32

812

W_{1}

0

60

1

41

T_{1}

1

1

9

9

Fundamental units, e_{2} = (U_{2} + V_{2}*x + W_{2}*x^{2})/T_{2}, with P(x) = 0

U_{2}

83

1936

2870111

462048

V_{2}

26

531

164494

75971

W_{2}

2

80

7840

2660

T_{2}

1

1

9

3

Splitting primes, q

31

97,181

19

67,229

Associated quadratic forms, F = a*X^{2} + b*X*Y + c*Y^{2}

(a,b,c)

(31,715,235)

(181,651,161)

(19,713,421)

(229,487,331)

Represented primes, q

31

181

19

229

Associated ideal cubes, (x + y*d^{1/2})/2, with 4*q^{3} = x^{2}  d*y^{2}

(x,y)

(649,1)

(1661,7)

(5143,7)

(241747,329)

Principalization

0

2

3

1

Capitulation type c.21: (0,2,3,1)

Group G in CBF^{2a}(5,6)

Contents
