Low Degree Fields Unramified Outside of {∞, 5, 17, 29}

Discriminant class: 5

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

Discriminant class: 17

∞ 5 17 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 17 Over p = 29 2 3 7 11 13 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_{+} 0_{+} 1_{+} 0_{+} 1 -4  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗  2 2 2  2 2
C_{2}  2 2  2
3. 0_{+} 2_{+} 1_{+} 2_{+} -1 -48 -43 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  3 2 2 2  3 2 2
S_{3}  2 2  3 3 2 3

Discriminant class: 29

∞ 5 17 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 17 Over p = 29 2 3 7 11 13 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
4. 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: 85

∞ 5 17 29 a_{1} a_{2} a_{3}  Over p = 5  Over p = 17  Over p = 29 2 3 7 11 13 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_{+} 1_{−} 1_{−} 0_{+} 0 -85  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 17∗ 17∗ 2 0_{+} ∗ ∗ 2  2 2  2
C_{2} 2  2 2 2 2  2 2

Discriminant class: 145

∞ 5 17 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 17 Over p = 29 2 3 7 11 13 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
6. 0_{+} 1_{+} 0_{+} 1_{+} 0 -145  1^{2} 1_{+} 5 5  1^{2} 1_{+} 29 29  2 2 2 2 2 2
C_{2} 4  2  2  2 2

Discriminant class: 493

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

Discriminant class: 493 (continued)

∞ 5 17 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 17  Over p = 29  2 3 7 11 13 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_{+} 2_{+} 1_{−} 1_{−} -1 -33 82 1^{3} 2_{+} ∗  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 29∗ 29∗ 2 3 2 3 3 2 2 3
S_{3}  3  2 2  3 3

Discriminant class: 2465

∞ 5 17 29 a_{1}  a_{2} a_{3}  Over p = 5  Over p = 17  Over p = 29  2 3 7 11 13 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_{+} 1_{−} 1_{+} 1_{−} 0 -2465  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{+} 17 17 1^{2} 1_{−} 29∗ 29∗  2  2 2
C_{2} 4  2  2  2