Counter, n = 94

Discriminant, d = 710652

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

473767

1124

1


13.8

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

Regulators, R

35.2

68.0

198.7

222.0

Class numbers, h

18

9

3

3

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

(C,D)

(330,2092)

(186,76)

(690,6908)

(807,8770)

Indices, i

6

6

6

6

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

U_{1}

13

77

13889

473

V_{1}

1

194

538

62

W_{1}

0

14

33

2

T_{1}

1

3

1

3

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

U_{2}

31

23

1034201

1777628

V_{2}

4

42

137434

660107

W_{2}

0

3

4536

35471

T_{2}

1

1

1

6

Splitting primes, q

31,577

103,109

73

37

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

(a,b,c)

(577,378,246)

(109,772,263)

(73,786,318)

(37,794,542)

Represented primes, q

577

109

73

37

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

(x,y)

(94414,112)

(59054,70)

(31216,37)

(5078,6)

Principalization

0

0

4

3

Capitulation type b.10: (0,0,4,3)

Group G in CBF^{1b}(6,8)

Contents
