Low Degree Fields Unramified Outside of {∞, 13, 19, 29}

Discriminant class: −7163

∞ 13 19 29 a_{1} a_{2} a_{3}  Over p = 13  Over p = 19  Over p = 29  2 3 5 7 11 17 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_{i} 1_{−} 0 7163  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{−} 29∗ 29∗ 2  2 2  2  2
C_{2} 20  2 2 2  2  2

Discriminant class: −551

∞ 13 19 29 a_{1} a_{2} a_{3} Over p = 13  Over p = 19  Over p = 29  2 3 5 7 11 17 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

Discriminant class: −247

∞ 13 19 29 a_{1} a_{2} a_{3}  Over p = 13  Over p = 19  Over p = 29 2 3 5 7 11 17 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
3. 1_{k} 1_{−} 1_{k} 0_{+} 0 247  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{k} 19 19 2 0_{+} ∗ ∗  2 2 2 2
C_{2} 6  2 2
4. 1_{k} 1_{−} 1_{k} 0_{+} 0 1 -3 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{k} 19 19 2 0_{+} ∗ ∗ 3 2 2 2 2 3 3 3
S_{3}  3 3 3 2 2 3 3 3

Discriminant class: −19

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

Discriminant class: 1

∞ 13 19 29 a_{1} a_{2} a_{3} Over p = 13 Over p = 19 Over p = 29 2 3 5 7 11 17 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_{+} 2_{+} 0_{+} 0_{+} -1 -4 -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
8. 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
9. 0_{+} 2_{+} 2_{+} 0_{+} -1 -82 64 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3 3
C_{3} 3  3  3 3 3 3  3
10. 0_{+} 2_{+} 2_{+} 0_{+} -1 -82 311 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3
C_{3} 3  3 3  3 3  3

Discriminant class: 13

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

Discriminant class: 29

∞ 13 19 29 a_{1} a_{2} a_{3} Over p = 13 Over p = 19  Over p = 29 2 3 5 7 11 17 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
12. 0_{+} 0_{+} 0_{+} 1_{+} 0 -29  2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29 2 2  2 2  2
C_{2}  2 2 2 2  2

Discriminant class: 377

∞ 13 19 29 a_{1} a_{2} a_{3}  Over p = 13  Over p = 19  Over p = 29 2 3 5 7 11 17 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
13. 0_{+} 1_{+} 0_{+} 1_{+} 0 -377  1^{2} 1_{+} 13 13  1^{2} 1_{+} 29 29  2 2 2  2
C_{2} 2  2  2 2 2