Low Degree Fields Unramified Outside of {∞, 5, 11, 29}

Discriminant class: −1595

∞ 5 11 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 29  2 3 7 13 17 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_{+} 1_{k} 1_{−} 0 1595  1^{2} 1_{+} 5 5 1^{2} 1_{k} 11 11 1^{2} 1_{−} 29∗ 29∗ 2  2  2 2
C_{2} 16  2  2  2

Discriminant class: −319

∞ 5 11 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 29  2 3 7 13 17 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} 0_{+} 1_{k} 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: −55

∞ 5 11 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 29 2 3 7 13 17 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_{+} 1_{i} 0_{+} 0 55  1^{2} 1_{+} 5 5 1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗  2  2 2
C_{2} 4  2 2  2 2  2 2
4. 1_{k} 1_{+} 1_{i} 2_{+} -1 10 -43 1^{2} 1_{+} 5 5 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  3 2 3 3 3 2 2 3
S_{3} 2 2 2 2 3 2 2

Discriminant class: −11

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

Discriminant class: 5

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

Discriminant class: 29

∞ 5 11 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 29 2 3 7 13 17 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_{+} 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: 145

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