Low Degree Fields Unramified Outside of {∞, 7, 11, 17}

Discriminant class: −187

∞ 7 11 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 11  Over p = 17  2 3 5 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
1. 1_{k} 0_{+} 1_{k} 1_{−} 0 187  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2 2 2 2 2  2
C_{2} 2  2  2
2. 1_{k} 2_{+} 1_{k} 1_{−} -1 12 -76 1^{3} 2_{+} 1  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2 2 2 2 2 3 2
S_{3} 6 2 3 2 3 3 3 3

Discriminant class: −119

∞ 7 11 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 11  Over p = 17  2 3 5 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
3. 1_{k} 1_{k} 0_{+} 1_{−} 0 119  1^{2} 1_{k} 7 7 2 0_{+} ∗ ∗ 1^{2} 1_{−} 17∗ 17∗  2 2 2 2
C_{2} 10  2  2  2
4. 1_{k} 1_{k} 2_{+} 1_{−} 0 11 -44 1^{2} 1_{k} 7 7 1^{3} 2_{+} ∗  1^{2} 1_{−} 17∗ 17∗  3 3 2 2 2 2 3
S_{3}  2  3 2 3 2 3 3

Discriminant class: −11

∞ 7 11 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 11  Over p = 17 2 3 5 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
5. 1_{k} 0_{+} 1_{i} 0_{+} -1 3  2 0_{+} ∗ ∗ 1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 2  2 2  2
C_{2}  2 2  2
6. 1_{k} 0_{+} 1_{i} 2_{+} -1 -11 22 2 0_{+} ∗ ∗ 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 3 3 2 2 3 2
S_{3} 3 2 2 3 3 2

Discriminant class: −7

∞ 7 11 17 a_{1} a_{2} a_{3} Over p = 7 Over p = 11 Over p = 17 2 3 5 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
7. 1_{k} 1_{i} 0_{+} 0_{+} 1 2  1^{2} 1_{i} 7∗ 7∗  2 0_{+} ∗ ∗  2 2 2 2  2
C_{2}  2  2  2 2
8. 1_{k} 1_{i} 0_{+} 2_{+} -1 6 5 1^{2} 1_{i} 7∗ 7∗  1^{3} 2_{+} ∗  3 2 2 2 2 3 3 2
S_{3}  3 2 3 2 3 2 2

Discriminant class: 1

∞ 7 11 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 11 Over p = 17 2 3 5 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
9. 0_{+} 2_{+} 0_{+} 0_{+} -1 -2 1 1^{3} 2_{+} 1  3 0_{+} 1  3 0_{+} 1  3 3 3  3 3  3
C_{3}  3  3 3 3 3 3

Discriminant class: 17

∞ 7 11 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 11  Over p = 17 2 3 5 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
10. 0_{+} 0_{+} 0_{+} 1_{+} 1 -4  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17  2 2  2 2 2
C_{2}  2 2  2
11. 0_{+} 0_{+} 2_{+} 1_{+} 0 -11 -11 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 3 2 2 3 3 2 2 2
S_{3}  2 2 3 3  2 3

Discriminant class: 77

∞ 7 11 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 11  Over p = 17 2 3 5 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
12. 0_{+} 1_{k} 1_{i} 0_{+} 0 -77  1^{2} 1_{k} 7 7 1^{2} 1_{i} 11∗ 11∗  2 2 2  2 2
C_{2}  2 2  2

Discriminant class: 1309

∞ 7 11 17 a_{1}  a_{2} a_{3}  Over p = 7  Over p = 11  Over p = 17 2 3 5 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
13. 0_{+} 1_{i} 1_{k} 1_{+} 0 -1309  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 11 11 1^{2} 1_{+} 17 17 2  2
C_{2} 2  2 2 2 2  2 2