Let a Module in an Integral Domain for be expressed using a two-element basis as
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 |
See also Different, Fundamental Discriminant, Module
References
Cohn, H. Advanced Number Theory. New York: Dover, pp. 72-73 and 261-274, 1980.
© 1996-9 Eric W. Weisstein