Low Degree Fields Unramified Outside of {∞, 17, 19, 29}

Discriminant class: −9367

∞ 17 19 29 a_{1} a_{2} a_{3}  Over p = 17  Over p = 19  Over p = 29 2 3 5 7 11 13 23 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} 1_{−} 1_{k} 1_{+} 0 9367  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 19 19 1^{2} 1_{+} 29 29  2 2 2  2 2 2
C_{2} 28  2 2 2 2 2 2  2

Discriminant class: −551

∞ 17 19 29 a_{1} a_{2} a_{3} Over p = 17  Over p = 19  Over p = 29  2 3 5 7 11 13 23 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
2. 1_{k} 0_{+} 1_{k} 1_{−} 0 551  2 0_{+} ∗ ∗ 1^{2} 1_{k} 19 19 1^{2} 1_{−} 29∗ 29∗  2 2
C_{2} 26  2 2 2 2 2 2
3. 1_{k} 2_{+} 1_{k} 1_{−} 0 17 -306 1^{3} 2_{+} ∗  1^{2} 1_{k} 19 19 1^{2} 1_{−} 29∗ 29∗  3 3 2 2 3 3
S_{3}  3  2 2 2 2 2 2

Discriminant class: −323

∞ 17 19 29 a_{1} a_{2} a_{3}  Over p = 17  Over p = 19  Over p = 29 2 3 5 7 11 13 23 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} 1_{+} 1_{i} 0_{+} 0 323  1^{2} 1_{+} 17 17 1^{2} 1_{i} 19∗ 19∗  2  2 2 2 2 2
C_{2} 4  2 2 2 2

Discriminant class: −19

∞ 17 19 29 a_{1} a_{2} a_{3} Over p = 17  Over p = 19  Over p = 29 2 3 5 7 11 13 23 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 5  1^{2} 1_{i} 19∗ 19∗ 2 0_{+} ∗ ∗ 2 2  2  2
C_{2}  2 2  2 2  2
6. 1_{k} 0_{+} 1_{i} 2_{+} -1 10 44  1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 2 3 3  2  2
S_{3}  2 2 3 3 2 2 3 2

Discriminant class: 1

∞ 17 19 29 a_{1} a_{2} a_{3} Over p = 17 Over p = 19 Over p = 29 2 3 5 7 11 13 23 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_{+} 2_{+} 0_{+} -1 -6 7 3 0_{+} 1 1^{3} 2_{+} 1 3 0_{+} 1 3 3 3 3 3
C_{3}  3 3 3 3 3 3 3

Discriminant class: 17

∞ 17 19 29 a_{1} a_{2}  a_{3}  Over p = 17  Over p = 19 Over p = 29 2 3 5 7 11 13 23 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_{+} 1_{+} 0_{+} 0_{+} 1 -4  1^{2} 1_{+} 17 17  2 0_{+} ∗ ∗  2 2 2 2  2 2
C_{2}  2 2  2
9. 0_{+} 1_{+} 2_{+} 2_{+} 0 -551 -4959 1^{2} 1_{+} 17 17 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  3 2 2 2 2 3 2 2
S_{3} 3  2 2 3 3 3 3 2

Discriminant class: 29

∞ 17 19 29 a_{1} a_{2} a_{3} Over p = 17 Over p = 19  Over p = 29 2 3 5 7 11 13 23 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_{+} 0 -29  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29 2 2  2  2
C_{2}  2 2 2 2  2

Discriminant class: 493

∞ 17 19 29 a_{1} a_{2} a_{3}  Over p = 17  Over p = 19  Over p = 29  2 3 5 7 11 13 23 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_{−} 0_{+} 1_{−} 0 -493  1^{2} 1_{−} 17∗ 17∗ 2 0_{+} ∗ ∗ 1^{2} 1_{−} 29∗ 29∗ 2  2 2  2
C_{2} 2  2 2