Low Degree Fields Unramified Outside of {∞, 11, 17, 19}

Discriminant class: −323

∞ 11 17 19 a_{1} a_{2} a_{3} Over p = 11  Over p = 17  Over p = 19  2 3 5 7 13 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_{+} 1_{i} 0 323  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17 1^{2} 1_{i} 19∗ 19∗ 2  2 2 2 2
C_{2} 4  2 2 2 2
2. 1_{k} 2_{+} 1_{+} 1_{i} 0 -22 -55 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 1^{2} 1_{i} 19∗ 19∗ 2 3 2 2 2 2
S_{3} 3 3 3 2 2 2 2

Discriminant class: −187

∞ 11 17 19 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 19 2 3 5 7 13 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} 1_{−} 0_{+} 0 187  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 0_{+} ∗ ∗ 2 2 2  2 2  2
C_{2} 2  2  2

Discriminant class: −19

∞ 11 17 19 a_{1} a_{2} a_{3} Over p = 11 Over p = 17  Over p = 19  2 3 5 7 13 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
4. 1_{k} 0_{+} 0_{+} 1_{i} -1 5  1^{2} 1_{i} 19∗ 19∗ 2 2  2  2 2
C_{2}  2 2  2 2  2

Discriminant class: −11

∞ 11 17 19 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17 Over p = 19 2 3 5 7 13 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} 1_{i} 0_{+} 0_{+} -1 3  1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 2  2 2  2
C_{2}  2 2  2
6. 1_{k} 1_{i} 2_{+} 0_{+} -1 -11 22 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 2 3 3 2 2 3 2
S_{3} 3 2 2 3 3 2

Discriminant class: 1

∞ 11 17 19 a_{1} a_{2} a_{3} Over p = 11 Over p = 17 Over p = 19 2 3 5 7 13 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. 0_{+} 0_{+} 0_{+} 2_{+} -1 -6 7 3 0_{+} 1 1^{3} 2_{+} 1 3 3 3 3 3 3
C_{3}  3 3 3 3 3 3 3

Discriminant class: 17

∞ 11 17 19 a_{1} a_{2} a_{3} Over p = 11  Over p = 17  Over p = 19 2 3 5 7 13 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
8. 0_{+} 0_{+} 1_{+} 0_{+} 1 -4  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17  2 2 2  2 2 2
C_{2}  2 2  2
9. 0_{+} 2_{+} 1_{+} 0_{+} 0 -11 -11 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 3 0_{+} 1  3 2 2 2 3 2 2 2
S_{3}  2 2 3 3  2 3

Discriminant class: 209

∞ 11 17 19 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 19 2 3 5 7 13 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_{+} 1_{i} 0_{+} 1_{k} 0 -209  1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 1^{2} 1_{k} 19 19  2  2  2
C_{2}  2  2  2 2 2 2

Discriminant class: 3553

∞ 11 17 19 a_{1}  a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 19 2 3 5 7 13 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
11. 0_{+} 1_{k} 1_{−} 1_{k} 0 -3553  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 19 19  2  2 2
C_{2} 2  2 2  2 2  2