Low Degree Fields Unramified Outside of {∞, 73, 83}

Discriminant class: −6059

∞ 73 83 a_{1} a_{2} a_{3}  Over p = 73  Over p = 83 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
1. 1_{k} 1_{−} 1_{k} 0 6059  1^{2} 1_{−} 73∗ 73∗ 1^{2} 1_{k} 83 83 2  2 2  2 2
C_{2} 26  2 2

Discriminant class: −83

∞ 73 83 a_{1} a_{2} a_{3} Over p = 73  Over p = 83  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 31 37 41 43 47 53
2. 1_{k} 0_{+} 1_{i} 0 83  2 0_{+} ∗ ∗ 1^{2} 1_{i} 83∗ 83∗ 2  2  2  2
C_{2} 3  2 2 2
3. 1_{k} 0_{+} 1_{i} -1 1 -2 2 0_{+} ∗ ∗ 1^{2} 1_{i} 83∗ 83∗ 2 3 2 3 3 2 3 2
S_{3} 3 3 3 2 2 2

Discriminant class: 1

∞ 73 83 a_{1} a_{2} a_{3} Over p = 73 Over p = 83 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
4. 0_{+} 2_{+} 0_{+} -1 -24 27 1^{3} 2_{+} 1  3  3  3 3  3
C_{3}  3 3 3 3 3  3 3

Discriminant class: 73

∞ 73 83 a_{1} a_{2} a_{3} Over p = 73 Over p = 83 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
5. 0_{+} 1_{+} 0_{+} 0 -73  1^{2} 1_{+} 73 73 2 0_{+} ∗ ∗  2 2 2 2 2
C_{2}  2 2  2 2 2