Low Degree Fields Unramified Outside of {∞, 37, 59}

Discriminant class: −2183

∞ 37 59 a_{1} a_{2} a_{3}  Over p = 37  Over p = 59 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 41 43 47 53 61
1. 1_{k} 1_{−} 1_{k} 0 2183  1^{2} 1_{−} 37∗ 37∗ 1^{2} 1_{k} 59 59  2  2  2 2
C_{2} 42  2  2
2. 1_{k} 1_{−} 1_{k} 0  -1 -9 1^{2} 1_{−} 37∗ 37∗ 1^{2} 1_{k} 59 59 3  2 3 2 3 2 2
S_{3} 2  2 3 3  2 3 3

Discriminant class: −59

∞ 37 59 a_{1} a_{2} a_{3} Over p = 37  Over p = 59  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 41 43 47 53 61
3. 1_{k} 0_{+} 1_{i} 0 59  2 0_{+} ∗ ∗ 1^{2} 1_{i} 59∗ 59∗ 2  2 2
C_{2} 3  2  2  2 2  2
4. 1_{k} 0_{+} 1_{i} 0 2 -1 2 0_{+} ∗ ∗ 1^{2} 1_{i} 59∗ 59∗ 2 3 3 3 2 2  3
S_{3}  2 3 2 3 2 2 3 2

Discriminant class: 1

∞ 37 59 a_{1} a_{2} a_{3} Over p = 37 Over p = 59 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 41 43 47 53 61
5. 0_{+} 2_{+} 0_{+} 1 -12 11 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3  3 3 3
C_{3}  3  3 3

Discriminant class: 37

∞ 37 59 a_{1} a_{2} a_{3} Over p = 37 Over p = 59 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 41 43 47 53 61
6. 0_{+} 1_{+} 0_{+} 0 -37  1^{2} 1_{+} 37 37 2 0_{+} ∗ ∗ 2  2  2 2 2
C_{2}  2 2 2  2  2