Low Degree Fields Unramified Outside of {∞, 11, 17, 29}

Discriminant class: −5423

∞ 11 17 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 29 2 3 5 7 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. 1_{k} 1_{i} 1_{+} 1_{+} 0 5423  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29  2  2  2
C_{2} 68  2  2  2

Discriminant class: −319

∞ 11 17 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 29  2 3 5 7 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. 1_{k} 1_{k} 0_{+} 1_{−} 0 319  1^{2} 1_{k} 11 11  1^{2} 1_{−} 29∗ 29∗  2  2 2  2
C_{2} 10  2  2

Discriminant class: −187

∞ 11 17 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 29 2 3 5 7 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
3. 1_{k} 1_{k} 1_{−} 0_{+} 0 187  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗  2 2 2  2 2 2 2
C_{2} 2  2  2

Discriminant class: −11

∞ 11 17 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17 Over p = 29 2 3 5 7 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. 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
5. 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 2 3
S_{3}  3 2 2 3  3 2
6. 1_{k} 1_{i} 0_{+} 2_{+} -1 -19 44 1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 3  2 2 2 3 3
S_{3} 2  3 2 2  3 3 2 3
7. 1_{k} 1_{i} 2_{+} 2_{+} -1 329 1552 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2  3 2 2 2  3
S_{3} 6  2 2 3 3 3 2 3
8. 1_{k} 1_{i} 2_{+} 2_{+} -1 -164 1552 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 3 3 2 2 2 3 3
S_{3} 3  3 2 2 3 3  2 3

Discriminant class: 17

∞ 11 17 29 a_{1} a_{2} a_{3} Over p = 11 Over p = 17 Over p = 29 2 3 5 7 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_{+} 0_{+} 1_{+} 0_{+} 1 -4  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗  2 2 2  2 2
C_{2}  2 2  2
10. 0_{+} 2_{+} 1_{+} 0_{+} 0 -11 -11 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗ 3 2 2 2 3 3 2 2
S_{3}  2 2 3 3  2 3

Discriminant class: 29

∞ 11 17 29 a_{1} a_{2} a_{3} Over p = 11 Over p = 17  Over p = 29 2 3 5 7 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
11. 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
12. 0_{+} 2_{+} 2_{+} 1_{+} -1 -249 1586 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{+} 29 29 2 2 3  2 3 2
S_{3} 2  2 2 2 2 3 3 2 3

Discriminant class: 493

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