Low Degree Fields Unramified Outside of {∞, 11, 13, 23}

Discriminant class: −299

∞ 11 13 23 a_{1} a_{2} a_{3} Over p = 11  Over p = 13  Over p = 23  2 3 5 7 17 19 29 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} 0_{+} 1_{+} 1_{i} 0 299  1^{2} 1_{+} 13 13 1^{2} 1_{i} 23∗ 23∗ 2  2  2
C_{2} 8  2 2 2 2 2 2

Discriminant class: −143

∞ 11 13 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 23 2 3 5 7 17 19 29 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} 1_{−} 0_{+} 0 143  1^{2} 1_{k} 11 11 1^{2} 1_{−} 13∗ 13∗  2  2  2 2
C_{2} 10  2  2 2  2 2 2

Discriminant class: −23

∞ 11 13 23 a_{1} a_{2}  a_{3} Over p = 11 Over p = 13  Over p = 23  2 3 5 7 17 19 29 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} 0_{+} 0_{+} 1_{i} 0 23  2 0_{+} ∗ ∗  1^{2} 1_{i} 23∗ 23∗  2 2 2 2
C_{2} 3  2  2  2  2 2
4. 1_{k} 0_{+} 0_{+} 1_{i} -1 0  1 2 0_{+} ∗ ∗ 3 0_{+} 1  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 2 2 3 3
S_{3}  2 3 2 3 2  2 2
5. 1_{k} 2_{+} 2_{+} 1_{i} -1 48 -53 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 2 2 3 3
S_{3} 3  2  2  2 3 2 2
6. 1_{k} 2_{+} 2_{+} 1_{i} 0 143 1144 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗  3 2 2 2 2 3
S_{3} 3  2 3 2 3 2 3 2 2
7. 1_{k} 2_{+} 2_{+} 1_{i} -1 48 -1197 1^{3} 2_{+} ∗ 1^{3} 2_{+} 1 1^{2} 1_{i} 23∗ 23∗ 3 2 2 2 2 3
S_{3} 3  2 3 2 3 2 3 2 2

Discriminant class: −11

∞ 11 13 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13 Over p = 23 2 3 5 7 17 19 29 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. 1_{k} 1_{i} 0_{+} 0_{+} -1 3  1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗  2  2 2 2 2
C_{2}  2 2  2

Discriminant class: 1

∞ 11 13 23 a_{1} a_{2} a_{3} Over p = 11 Over p = 13 Over p = 23 2 3 5 7 17 19 29 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_{+} 2_{+} 0_{+} -1 -4 -1 3 0_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3 3  3 3 3 3
C_{3}  3 3 3  3 3 3

Discriminant class: 13

∞ 11 13 23 a_{1} a_{2} a_{3} Over p = 11  Over p = 13  Over p = 23 2 3 5 7 17 19 29 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_{+} 0_{+} 1_{+} 0_{+} 1 -3  2 0_{+} ∗ ∗ 1^{2} 1_{+} 13 13  2  2 2  2  2
C_{2}  2 2  2  2  2
11. 0_{+} 2_{+} 1_{+} 0_{+} -1 -7 2 1^{3} 2_{+} ∗  1^{2} 1_{+} 13 13 3 0_{+} 1  2 3 2 2 3 2 3 2
S_{3}  2 2 3 2 3 2 3 2

Discriminant class: 253

∞ 11 13 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 23  2 3 5 7 17 19 29 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_{+} 1_{k} 0_{+} 1_{i} 0 -253  1^{2} 1_{k} 11 11 2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗ 2  2  2
C_{2}  2 2  2  2

Discriminant class: 3289

∞ 11 13 23 a_{1}  a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 23  2 3 5 7 17 19 29 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_{i} 1_{−} 1_{i} 0 -3289  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{i} 23∗ 23∗  2  2 2 2
C_{2} 2  2 2 2