Low Degree Fields Ramifying Above {2, 7, 11}

Discriminant class: −154

∞ 2 7 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7  Over p = 11  3 5 13 17 19 23 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} 3_{k} 1_{i} 1_{i} 0 154  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{i} 11∗ 11∗ 2  2  2
C_{2} 8  2  2  2 2 2

Discriminant class: −77

∞ 2 7 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7  Over p = 11 3 5 13 17 19 23 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} 2_{i} 1_{i} 1_{k} 0 77  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 11 11  2  2 2 2
C_{2} 8  2

Discriminant class: −14

∞ 2 7 11 a_{1} a_{2} a_{3} Over p = 2 Over p = 7 Over p = 11 3 5 13 17 19 23 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} 3_{+} 1_{i} 2_{+} -1 -7 35 1^{2} 3_{+} 2 2 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  3  3 2 3 3 2 2
S_{3}  2 2 2 2 2 3  2

Discriminant class: 2

∞ 2 7 11 a_{1} a_{2} a_{3} Over p = 2 Over p = 7 Over p = 11 3 5 13 17 19 23 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
4. 0_{+} 3_{+} 2_{+} 2_{+} -1 -51 -97 1^{2} 3_{+} 2 2 1^{3} 2_{+} 1 1^{3} 2_{+} ∗ 2 2 2 3 2 2 3
S_{3} 3  2 3 2 3 2 2 2 2

Discriminant class: 22

∞ 2 7 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7  Over p = 11  3 5 13 17 19 23 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
5. 0_{+} 3_{k} 2_{+} 1_{i} -1 -16 8 1^{2} 3_{k} −2∗ −2∗ 1^{3} 2_{+} 1  1^{2} 1_{i} 11∗ 11∗ 3 2 3 2 2 2 3 2
S_{3} 3  2 2 2 2 2 3 3 3

Discriminant class: 154

∞ 2 7 11 a_{1} a_{2} a_{3} Over p = 2 Over p = 7 Over p = 11 3 5 13 17 19 23 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
6. 0_{+} 3_{−} 1_{k} 1_{k} 0 -154  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 7 7 1^{2} 1_{k} 11 11  2  2  2
C_{2} 2  2  2 2  2 2