Petits Discriminants de Polynômes Irréductibles
Cette page contient des listes de polynômes irréductibles de Z[X]
de petits discriminants.
, ce n'est pas une liste de discriminants de corps de nombres.
Une
table de corps de nombres est disponible sur le site
de l'Université de Bordeaux.
Vous y trouverez aussi les
bornes d'Odlyzko.
Les polynômes sont triés suivant leur signature d.r1
où d est le degré et r1 est le nombre de
racines réelles.
Cette liste est une mise à jour des résultats de ma
thèse.
(dernière mise à jour : 12/11/2023)
Si vous connaissez des polynômes qui ont naturellement leur place
dans ces listes, écrivez-moi !
Si vous voulez davantage de polynômes, ou de plus grand degré,
n'hésitez pas à m'en demander !
d.r1 =
3.1,
3.3,
d.r1 =
4.0,
4.2,
4.4.
d.r1 =
5.1,
5.3,
5.5.
d.r1 =
6.0,
6.2,
6.4,
6.6.
d.r1 =
7.1,
7.3,
7.5,
7.7.
d.r1 =
8.0,
8.2,
8.4,
8.6,
8.8.
d.r1 =
9.1,
9.3,
9.5,
9.7,
9.9.
d.r1 =
10.0,
10.2,
10.4,
10.6,
10.8,
10.10.
d.r1 =
11.1,
11.3,
11.5,
11.7,
11.9,
11.11.
d.r1 =
12.0,
12.2,
12.4,
12.6,
12.8,
12.10,
12.12.
d.r1 =
13.1,
13.3,
13.5,
13.7,
13.9,
13.11,
13.13.
d.r1 =
14.0,
14.2,
14.4,
14.6,
14.8,
14.10,
14.12,
14.14.
d.r1 =
15.1,
15.3,
15.5,
15.7,
15.9,
15.11,
15.13,
15.15.
d.r1 =
16.0,
16.2,
16.4,
16.6,
16.8,
16.10,
16.12,
16.14,
16.16.
d.r1 =
17.1,
17.3,
17.5,
17.7,
17.9,
17.11,
17.13,
17.15,
17.17.
d.r1 =
18.0,
18.2,
18.4,
18.6,
18.8,
18.10,
18.12,
18.14,
18.16,
18.18.
d.r1 =
19.1,
19.3,
19.5,
19.7,
19.9,
19.11,
19.13,
19.15,
19.17,
19.19.
d.r1 =
20.0,
20.2,
20.4,
20.6,
20.8,
20.10,
20.12,
20.14,
20.16,
20.18,
20.20.
d.r1 =
21.1,
21.3,
21.5,
21.7,
21.9,
21.11,
21.13,
21.15,
21.17,
21.19,
21.21.
d.r1 =
22.0,
22.2,
22.4,
22.6,
22.8,
22.10,
22.12,
22.14,
22.16,
22.18,
22.20,
22.22.
d.r1 =
23.1,
23.3,
23.5,
23.7,
23.9,
23.11,
23.13,
23.15,
23.17,
23.19,
23.21,
23.23.
d.r1 =
24.0,
24.2,
24.4,
24.6,
24.8,
24.10,
24.12,
24.14,
24.16,
24.18,
24.20,
24.22,
24.24.
d.r1 =
25.1,
25.3,
25.5,
25.7,
25.9,
25.11,
25.13,
25.15,
25.17,
25.19,
25.21,
25.23,
25.25.
d.r1 =
26.0,
26.2,
26.4,
26.6,
26.8,
26.10,
26.12,
26.14,
26.16,
26.18,
26.20,
26.22,
26.24,
26.26.
d.r1 =
27.1,
27.3,
27.5,
27.7,
27.9,
27.11,
27.13,
27.15,
27.17,
27.19,
27.21,
27.23,
27.25,
27.27.
d.r1 =
28.0,
28.2,
28.4,
28.6,
28.8,
28.10,
28.12,
28.14,
28.16,
28.18,
28.20,
28.22,
28.24,
28.26,
28.28.
d.r1 =
29.1,
29.3,
29.5,
29.7,
29.9,
29.11,
29.13,
29.15,
29.17,
29.19,
29.21,
29.23,
29.25,
29.27,
29.29.
Les fichiers suivants sont compressés au format .gz
d.r1 =
30.0,
30.2,
30.4,
30.6,
30.8,
30.10,
30.12,
30.14,
30.16,
30.18,
30.20,
30.22,
30.24,
30.26,
30.28,
30.30.
d.r1 =
31.1,
31.3,
31.5,
31.7,
31.9,
31.11,
31.13,
31.15,
31.17,
31.19,
31.21,
31.23,
31.25,
31.27,
31.29,
31.31.
d.r1 =
32.0,
32.2,
32.4,
32.6,
32.8,
32.10,
32.12,
32.14,
32.16,
32.18,
32.20,
32.22,
32.24,
32.26,
32.28,
32.30,
32.32.
d.r1 =
33.1,
33.3,
33.5,
33.7,
33.9,
33.11,
33.13,
33.15,
33.17,
33.19,
33.21,
33.23,
33.25,
33.27,
33.29,
33.31,
33.33.
d.r1 =
34.0,
34.2,
34.4,
34.6,
34.8,
34.10,
34.12,
34.14,
34.16,
34.18,
34.20,
34.22,
34.24,
34.26,
34.28,
34.30,
34.32,
34.34.
d.r1 =
35.1,
35.3,
35.5,
35.7,
35.9,
35.11,
35.13,
35.15,
35.17,
35.19,
35.21,
35.23,
35.25,
35.27,
35.29,
35.31,
35.33,
35.35.
d.r1 =
36.0,
36.2,
36.4,
36.6,
36.8,
36.10,
36.12,
36.14,
36.16,
36.18,
36.20,
36.22,
36.24,
36.26,
36.28,
36.30,
36.32,
36.34,
36.36.
d.r1 =
37.1,
37.3,
37.5,
37.7,
37.9,
37.11,
37.13,
37.15,
37.17,
37.19,
37.21,
37.23,
37.25,
37.27,
37.29,
37.31,
37.33,
37.35,
37.37.
d.r1 =
38.0,
38.2,
38.4,
38.6,
38.8,
38.10,
38.12,
38.14,
38.16,
38.18,
38.20,
38.22,
38.24,
38.26,
38.28,
38.30,
38.32,
38.34,
38.36,
38.38.
d.r1 =
39.1,
39.3,
39.5,
39.7,
39.9,
39.11,
39.13,
39.15,
39.17,
39.19,
39.21,
39.23,
39.25,
39.27,
39.29,
39.31,
39.33,
39.35,
39.37,
39.39.
d.r1 =
40.0,
40.2,
40.4,
40.6,
40.8,
40.10,
40.12,
40.14,
40.16,
40.18,
40.20,
40.22,
40.24,
40.26,
40.28,
40.30,
40.32,
40.34,
40.36,
40.38,
40.40.
d.r1 =
41.1,
41.3,
41.5,
41.7,
41.9,
41.11,
41.13,
41.15,
41.17,
41.19,
41.21,
41.23,
41.25,
41.27,
41.29,
41.31,
41.33,
41.35,
41.37,
41.39,
41.41.
d.r1 =
42.0,
42.2,
42.4,
42.6,
42.8,
42.10,
42.12,
42.14,
42.16,
42.18,
42.20,
42.22,
42.24,
42.26,
42.28,
42.30,
42.32,
42.34,
42.36,
42.38,
42.40,
42.42.
d.r1 =
43.1,
43.3,
43.5,
43.7,
43.9,
43.11,
43.13,
43.15,
43.17,
43.19,
43.21,
43.23,
43.25,
43.27,
43.29,
43.31,
43.33,
43.35,
43.37,
43.39,
43.41,
43.43.
d.r1 =
44.0,
44.2,
44.4,
44.6,
44.8,
44.10,
44.12,
44.14,
44.16,
44.18,
44.20,
44.22,
44.24,
44.26,
44.28,
44.30,
44.32,
44.34,
44.36,
44.38,
44.40,
44.42,
44.44.
d.r1 =
45.1,
45.3,
45.5,
45.7,
45.9,
45.11,
45.13,
45.15,
45.17,
45.19,
45.21,
45.23,
45.25,
45.27,
45.29,
45.31,
45.33,
45.35,
45.37,
45.39,
45.41,
45.43,
45.45.
d.r1 =
46.0,
46.2,
46.4,
46.6,
46.8,
46.10,
46.12,
46.14,
46.16,
46.18,
46.20,
46.22,
46.24,
46.26,
46.28,
46.30,
46.32,
46.34,
46.36,
46.38,
46.40,
46.42,
46.44,
46.46.
d.r1 =
47.1,
47.3,
47.5,
47.7,
47.9,
47.11,
47.13,
47.15,
47.17,
47.19,
47.21,
47.23,
47.25,
47.27,
47.29,
47.31,
47.33,
47.35,
47.37,
47.39,
47.41,
47.43,
47.45,
47.47.
d.r1 =
48.0,
48.2,
48.4,
48.6,
48.8,
48.10,
48.12,
48.14,
48.16,
48.18,
48.20,
48.22,
48.24,
48.26,
48.28,
48.30,
48.32,
48.34,
48.36,
48.38,
48.40,
48.42,
48.44,
48.46,
48.48.
d.r1 =
49.1,
49.3,
49.5,
49.7,
49.9,
49.11,
49.13,
49.15,
49.17,
49.19,
49.21,
49.23,
49.25,
49.27,
49.29,
49.31,
49.33,
49.35,
49.37,
49.39,
49.41,
49.43,
49.45,
49.47,
49.49.
d.r1 =
50.0,
50.2,
50.4,
50.6,
50.8,
50.10,
50.12,
50.14,
50.16,
50.18,
50.20,
50.22,
50.24,
50.26,
50.28,
50.30,
50.32,
50.34,
50.36,
50.38,
50.40,
50.42,
50.44,
50.46,
50.48,
50.50.
d.r1 =
51.1,
51.3,
51.5,
51.7,
51.9,
51.11,
51.13,
51.15,
51.17,
51.19,
51.21,
51.23,
51.25,
51.27,
51.29,
51.31,
51.33,
51.35,
51.37,
51.39,
51.41,
51.43,
51.45,
51.47,
51.49,
51.51.
d.r1 =
52.0,
52.2,
52.4,
52.6,
52.8,
52.10,
52.12,
52.14,
52.16,
52.18,
52.20,
52.22,
52.24,
52.26,
52.28,
52.30,
52.32,
52.34,
52.36,
52.38,
52.40,
52.42,
52.44,
52.46,
52.48,
52.50,
52.52.
d.r1 =
53.1,
53.3,
53.5,
53.7,
53.9,
53.11,
53.13,
53.15,
53.17,
53.19,
53.21,
53.23,
53.25,
53.27,
53.29,
53.31,
53.33,
53.35,
53.37,
53.39,
53.41,
53.43,
53.45,
53.47,
53.49,
53.51,
53.53.
d.r1 =
54.0,
54.2,
54.4,
54.6,
54.8,
54.10,
54.12,
54.14,
54.16,
54.18,
54.20,
54.22,
54.24,
54.26,
54.28,
54.30,
54.32,
54.34,
54.36,
54.38,
54.40,
54.42,
54.44,
54.46,
54.48,
54.50,
54.52,
54.54.
d.r1 =
55.1,
55.3,
55.5,
55.7,
55.9,
55.11,
55.13,
55.15,
55.17,
55.19,
55.21,
55.23,
55.25,
55.27,
55.29,
55.31,
55.33,
55.35,
55.37,
55.39,
55.41,
55.43,
55.45,
55.47,
55.49,
55.51,
55.53,
55.55.
d.r1 =
56.0,
56.2,
56.4,
56.6,
56.8,
56.10,
56.12,
56.14,
56.16,
56.18,
56.20,
56.22,
56.24,
56.26,
56.28,
56.30,
56.32,
56.34,
56.36,
56.38,
56.40,
56.42,
56.44,
56.46,
56.48,
56.50,
56.52,
56.54,
56.56.
d.r1 =
57.1,
57.3,
57.5,
57.7,
57.9,
57.11,
57.13,
57.15,
57.17,
57.19,
57.21,
57.23,
57.25,
57.27,
57.29,
57.31,
57.33,
57.35,
57.37,
57.39,
57.41,
57.43,
57.45,
57.47,
57.49,
57.51,
57.53,
57.55,
57.57.
d.r1 =
58.0,
58.2,
58.4,
58.6,
58.8,
58.10,
58.12,
58.14,
58.16,
58.18,
58.20,
58.22,
58.24,
58.26,
58.28,
58.30,
58.32,
58.34,
58.36,
58.38,
58.40,
58.42,
58.44,
58.46,
58.48,
58.50,
58.52,
58.54,
58.56,
58.58.
d.r1 =
59.1,
59.3,
59.5,
59.7,
59.9,
59.11,
59.13,
59.15,
59.17,
59.19,
59.21,
59.23,
59.25,
59.27,
59.29,
59.31,
59.33,
59.35,
59.37,
59.39,
59.41,
59.43,
59.45,
59.47,
59.49,
59.51,
59.53,
59.55,
59.57,
59.59.
d.r1 =
60.0,
60.2,
60.4,
60.6,
60.8,
60.10,
60.12,
60.14,
60.16,
60.18,
60.20,
60.22,
60.24,
60.26,
60.28,
60.30,
60.32,
60.34,
60.36,
60.38,
60.40,
60.42,
60.44,
60.46,
60.48,
60.50,
60.52,
60.54,
60.56,
60.58,
60.60.
d.r1 =
61.1,
61.3,
61.5,
61.7,
61.9,
61.11,
61.13,
61.15,
61.17,
61.19,
61.21,
61.23,
61.25,
61.27,
61.29,
61.31,
61.33,
61.35,
61.37,
61.39,
61.41,
61.43,
61.45,
61.47,
61.49,
61.51,
61.53,
61.55,
61.57,
61.59,
61.61.
d.r1 =
62.0,
62.2,
62.4,
62.6,
62.8,
62.10,
62.12,
62.14,
62.16,
62.18,
62.20,
62.22,
62.24,
62.26,
62.28,
62.30,
62.32,
62.34,
62.36,
62.38,
62.40,
62.42,
62.44,
62.46,
62.48,
62.50,
62.52,
62.54,
62.56,
62.58,
62.60,
62.62.
d.r1 =
63.1,
63.3,
63.5,
63.7,
63.9,
63.11,
63.13,
63.15,
63.17,
63.19,
63.21,
63.23,
63.25,
63.27,
63.29,
63.31,
63.33,
63.35,
63.37,
63.39,
63.41,
63.43,
63.45,
63.47,
63.49,
63.51,
63.53,
63.55,
63.57,
63.59,
63.61,
63.63.
d.r1 =
64.0,
64.2,
64.4,
64.6,
64.8,
64.10,
64.12,
64.14,
64.16,
64.18,
64.20,
64.22,
64.24,
64.26,
64.28,
64.30,
64.32,
64.34,
64.36,
64.38,
64.40,
64.42,
64.44,
64.46,
64.48,
64.50,
64.52,
64.54,
64.56,
64.58,
64.60,
64.62,
64.64.
d.r1 =
65.1,
65.3,
65.5,
65.7,
65.9,
65.11,
65.13,
65.15,
65.17,
65.19,
65.21,
65.23,
65.25,
65.27,
65.29,
65.31,
65.33,
65.35,
65.37,
65.39,
65.41,
65.43,
65.45,
65.47,
65.49,
65.51,
65.53,
65.55,
65.57,
65.59,
65.61,
65.63,
65.65.
d.r1 =
66.0,
66.2,
66.4,
66.6,
66.8,
66.10,
66.12,
66.14,
66.16,
66.18,
66.20,
66.22,
66.24,
66.26,
66.28,
66.30,
66.32,
66.34,
66.36,
66.38,
66.40,
66.42,
66.44,
66.46,
66.48,
66.50,
66.52,
66.54,
66.56,
66.58,
66.60,
66.62,
66.64,
66.66.
d.r1 =
67.1,
67.3,
67.5,
67.7,
67.9,
67.11,
67.13,
67.15,
67.17,
67.19,
67.21,
67.23,
67.25,
67.27,
67.29,
67.31,
67.33,
67.35,
67.37,
67.39,
67.41,
67.43,
67.45,
67.47,
67.49,
67.51,
67.53,
67.55,
67.57,
67.59,
67.61,
67.63,
67.65,
67.67.
d.r1 =
68.0,
68.2,
68.4,
68.6,
68.8,
68.10,
68.12,
68.14,
68.16,
68.18,
68.20,
68.22,
68.24,
68.26,
68.28,
68.30,
68.32,
68.34,
68.36,
68.38,
68.40,
68.42,
68.44,
68.46,
68.48,
68.50,
68.52,
68.54,
68.56,
68.58,
68.60,
68.62,
68.64,
68.66,
68.68.
d.r1 =
69.1,
69.3,
69.5,
69.7,
69.9,
69.11,
69.13,
69.15,
69.17,
69.19,
69.21,
69.23,
69.25,
69.27,
69.29,
69.31,
69.33,
69.35,
69.37,
69.39,
69.41,
69.43,
69.45,
69.47,
69.49,
69.51,
69.53,
69.55,
69.57,
69.59,
69.61,
69.63,
69.65,
69.67,
69.69.
d.r1 =
70.0,
70.2,
70.4,
70.6,
70.8,
70.10,
70.12,
70.14,
70.16,
70.18,
70.20,
70.22,
70.24,
70.26,
70.28,
70.30,
70.32,
70.34,
70.36,
70.38,
70.40,
70.42,
70.44,
70.46,
70.48,
70.50,
70.52,
70.54,
70.56,
70.58,
70.60,
70.62,
70.64,
70.66,
70.68,
70.70.
d.r1 =
71.1,
71.3,
71.5,
71.7,
71.9,
71.11,
71.13,
71.15,
71.17,
71.19,
71.21,
71.23,
71.25,
71.27,
71.29,
71.31,
71.33,
71.35,
71.37,
71.39,
71.41,
71.43,
71.45,
71.47,
71.49,
71.51,
71.53,
71.55,
71.57,
71.59,
71.61,
71.63,
71.65,
71.67,
71.69,
71.71.
d.r1 =
72.0,
72.2,
72.4,
72.6,
72.8,
72.10,
72.12,
72.14,
72.16,
72.18,
72.20,
72.22,
72.24,
72.26,
72.28,
72.30,
72.32,
72.34,
72.36,
72.38,
72.40,
72.42,
72.44,
72.46,
72.48,
72.50,
72.52,
72.54,
72.56,
72.58,
72.60,
72.62,
72.64,
72.66,
72.68,
72.70,
72.72.
d.r1 =
73.1,
73.3,
73.5,
73.7,
73.9,
73.11,
73.13,
73.15,
73.17,
73.19,
73.21,
73.23,
73.25,
73.27,
73.29,
73.31,
73.33,
73.35,
73.37,
73.39,
73.41,
73.43,
73.45,
73.47,
73.49,
73.51,
73.53,
73.55,
73.57,
73.59,
73.61,
73.63,
73.65,
73.67,
73.69,
73.71,
73.73.
d.r1 =
74.0,
74.2,
74.4,
74.6,
74.8,
74.10,
74.12,
74.14,
74.16,
74.18,
74.20,
74.22,
74.24,
74.26,
74.28,
74.30,
74.32,
74.34,
74.36,
74.38,
74.40,
74.42,
74.44,
74.46,
74.48,
74.50,
74.52,
74.54,
74.56,
74.58,
74.60,
74.62,
74.64,
74.66,
74.68,
74.70,
74.72,
74.74.
d.r1 =
75.1,
75.3,
75.5,
75.7,
75.9,
75.11,
75.13,
75.15,
75.17,
75.19,
75.21,
75.23,
75.25,
75.27,
75.29,
75.31,
75.33,
75.35,
75.37,
75.39,
75.41,
75.43,
75.45,
75.47,
75.49,
75.51,
75.53,
75.55,
75.57,
75.59,
75.61,
75.63,
75.65,
75.67,
75.69,
75.71,
75.73,
75.75.
d.r1 =
76.0,
76.2,
76.4,
76.6,
76.8,
76.10,
76.12,
76.14,
76.16,
76.18,
76.20,
76.22,
76.24,
76.26,
76.28,
76.30,
76.32,
76.34,
76.36,
76.38,
76.40,
76.42,
76.44,
76.46,
76.48,
76.50,
76.52,
76.54,
76.56,
76.58,
76.60,
76.62,
76.64,
76.66,
76.68,
76.70,
76.72,
76.74,
76.76.
d.r1 =
77.1,
77.3,
77.5,
77.7,
77.9,
77.11,
77.13,
77.15,
77.17,
77.19,
77.21,
77.23,
77.25,
77.27,
77.29,
77.31,
77.33,
77.35,
77.37,
77.39,
77.41,
77.43,
77.45,
77.47,
77.49,
77.51,
77.53,
77.55,
77.57,
77.59,
77.61,
77.63,
77.65,
77.67,
77.69,
77.71,
77.73,
77.75,
77.77.
d.r1 =
78.0,
78.2,
78.4,
78.6,
78.8,
78.10,
78.12,
78.14,
78.16,
78.18,
78.20,
78.22,
78.24,
78.26,
78.28,
78.30,
78.32,
78.34,
78.36,
78.38,
78.40,
78.42,
78.44,
78.46,
78.48,
78.50,
78.52,
78.54,
78.56,
78.58,
78.60,
78.62,
78.64,
78.66,
78.68,
78.70,
78.72,
78.74,
78.76,
78.78.
d.r1 =
79.1,
79.3,
79.5,
79.7,
79.9,
79.11,
79.13,
79.15,
79.17,
79.19,
79.21,
79.23,
79.25,
79.27,
79.29,
79.31,
79.33,
79.35,
79.37,
79.39,
79.41,
79.43,
79.45,
79.47,
79.49,
79.51,
79.53,
79.55,
79.57,
79.59,
79.61,
79.63,
79.65,
79.67,
79.69,
79.71,
79.73,
79.75,
79.77,
79.79.