Counter, n = 21

Discriminant, d = 214712

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

6315163023

27257524

1


23.3

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

Regulators, R

39.2

65.4

73.9

107.1

Class numbers, h

6

3

3

3

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

(C,D)

(83,230)

(993,358)

(1137,8534)

(74,168)

Indices, i

2

135

135

2

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

U_{1}

19244

104

44655919

38613970

V_{1}

8819

248

7157054

21044036

W_{1}

859

8

193522

2199288

T_{1}

2

360

45

2

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

U_{2}

72

3762479

21503471

143

V_{2}

3

1288

3446386

84

W_{2}

1

3792

93188

9

T_{2}

2

15

45

1

Splitting primes, q

13

43

103

7

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

(a,b,c)

(13,440,406)

(41,404,314)

(17,436,362)

(7,454,307)

Represented primes, q

13

43

103

7

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

(x,y)

(769658,1661)

(328530,709)

(2328898,5026)

(926,2)

Principalization

4

3

2

1

Capitulation type G.19: (4,3,2,1)

Group G in CBF^{1b}(5,6)

Contents
