Let a Module in an Integral Domain for be expressed using a two-element basis as

where and are in . Then the Different of the Module is defined as

and the discriminant is defined as the square of the Different (Cohn 1980).

For Imaginary Quadratic Fields (with ), the discriminants are given in the following table.

The discriminants of Real Quadratic Fields () are given in the following table.

2 | 34 | 67 | |||

3 | 35 | 69 | |||

5 | 5 | 37 | 37 | 70 | |

6 | 38 | 71 | |||

7 | 39 | 73 | 73 | ||

10 | 41 | 41 | 74 | ||

11 | 42 | 77 | |||

13 | 13 | 43 | 78 | ||

14 | 46 | 79 | |||

15 | 47 | 82 | |||

17 | 17 | 51 | 83 | ||

19 | 53 | 53 | 85 | ||

21 | 55 | 86 | |||

22 | 57 | 87 | |||

23 | 58 | 89 | 89 | ||

26 | 59 | 91 | |||

29 | 29 | 61 | 61 | 93 | |

30 | 62 | 94 | |||

31 | 65 | 95 | |||

33 | 66 | 97 | 97 |

**References**

Cohn, H. *Advanced Number Theory.* New York: Dover, pp. 72-73 and 261-274, 1980.

© 1996-9

1999-05-24