Counter, n = 58

Discriminant, d = 494236

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

4872576100076

13861857765

1


29.9

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

Regulators, R

36.4

60.1

84.8

178.4

Class numbers, h

9

3

3

3

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

(C,D)

(547,4114)

(82,92)

(187,268)

(154,684)

Indices, i

20

2

7

2

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

U_{1}

162

7

23

9767

V_{1}

27

5

24

2886

W_{1}

1

1

2

203

T_{1}

20

1

7

1

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

U_{2}

7056

67

2409

63521

V_{2}

131

7

1849

2889

W_{2}

15

0

129

513

T_{2}

2

1

1

1

Splitting primes, q

37

139

307

181,523

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

(a,b,c)

(10,686,591)

(30,674,333)

(14,678,617)

(3,698,586)

Represented primes, q

37

139,173

307,197

523,113

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

(x,y)

(23204,33)

(210252,299)

(5706,2)

(11502,16)

Principalization

3

0

0

0

Capitulation type a.3: (3,0,0,0)

Group G in CF^{2a}(6)

Contents
