Low Degree Fields Unramified Outside of {∞, 13, 17, 29}

Discriminant class: 1

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

Discriminant class: 13

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

Discriminant class: 17

∞ 13 17 29 a_{1} a_{2} a_{3} Over p = 13 Over p = 17 Over p = 29 2 3 5 7 11 19 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. 0_{+} 0_{+} 1_{+} 0_{+} 1 -4  1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗  2 2 2 2  2 2
C_{2}  2 2  2
4. 0_{+} 2_{+} 1_{+} 2_{+} 0 -377 -1885 1^{3} 2_{+} 1  1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  3 2 2 2 2  2 2
S_{3} 3  2 2 3 3 3  2

Discriminant class: 29

∞ 13 17 29 a_{1} a_{2} a_{3} Over p = 13 Over p = 17  Over p = 29 2 3 5 7 11 19 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. 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
6. 0_{+} 2_{+} 2_{+} 1_{+} -1 -147 90 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  1^{2} 1_{+} 29 29 2 2  3 2 2  2
S_{3} 3  2 2 2 2 3 3 2

Discriminant class: 221

∞ 13 17 29 a_{1} a_{2} a_{3} Over p = 13 Over p = 17 Over p = 29 2 3 5 7 11 19 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_{+} 1_{+} 1_{+} 0_{+} 0 -221  1^{2} 1_{+} 13 13 1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗ 2 2  2 2
C_{2} 2  2  2 2 2

Discriminant class: 377

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

Discriminant class: 493

∞ 13 17 29 a_{1} a_{2} a_{3} Over p = 13  Over p = 17  Over p = 29  2 3 5 7 11 19 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
9. 0_{+} 0_{+} 1_{−} 1_{−} 0 -493  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 29∗ 29∗ 2  2 2  2 2
C_{2} 2  2 2

Discriminant class: 6409

∞ 13 17 29 a_{1}  a_{2} a_{3}  Over p = 13  Over p = 17  Over p = 29  2 3 5 7 11 19 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_{+} 1_{+} 1_{−} 1_{−} 0 -6409  1^{2} 1_{+} 13 13 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 29∗ 29∗  2  2 2
C_{2} 8  2 2 2  2  2