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

Discriminant class: −143

∞ 11 13 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13  2 3 5 7 17 19 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
1. 1_{k} 1_{k} 1_{−} 0 143  1^{2} 1_{k} 11 11 1^{2} 1_{−} 13∗ 13∗  2  2  2
C_{2} 10  2 2  2 2  2 2

Discriminant class: −11

∞ 11 13 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13 2 3 5 7 17 19 23 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
2. 1_{k} 1_{i} 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 a_{1} a_{2} a_{3} Over p = 11 Over p = 13 2 3 5 7 17 19 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 0_{+} 0_{+} 2_{+} -1 -4 -1 3 0_{+} 1  1^{3} 2_{+} 1  3 3  3 3 3 3 3
C_{3}  3 3 3  3 3

Discriminant class: 13

∞ 11 13 a_{1} a_{2} a_{3} Over p = 11  Over p = 13 2 3 5 7 17 19 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
4. 0_{+} 0_{+} 1_{+} 1 -3  2 0_{+} ∗ ∗ 1^{2} 1_{+} 13 13 2  2 2  2
C_{2}  2 2 2  2  2
5. 0_{+} 2_{+} 1_{+} -1 -7 2 1^{3} 2_{+} ∗  1^{2} 1_{+} 13 13 2 3 2 2 3 2 3 3
S_{3}  2 2 2 3 2 3 2 3