Low Degree Fields Ramifying Above {2, 67}

Discriminant class: −134

∞ 2 67 a_{1} a_{2} a_{3} Over p = 2 Over p = 67 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
1. 1_{k} 3_{−} 1_{k} 0 134  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 67 67  2  2
C_{2} 14  2 2 2 2  2

Discriminant class: −67

∞ 2 67 a_{1} a_{2} a_{3} Over p = 2  Over p = 67  3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
2. 1_{k} 2_{+} 1_{i} -1 -3 5 1^{3} 2_{+} ∗  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 3 3 3
S_{3}  3 2 3 2 2 3 2 3

Discriminant class: −2

∞ 2 67 a_{1} a_{2} a_{3}  Over p = 2  Over p = 67 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
3. 1_{k} 3_{i} 2_{+} -1 -22 62 1^{2} 3_{i} −2 −2 1^{3} 2_{+} 1  3 2 2  2 3 3 2
S_{3} 9  2 2 2  3 2 2 3

Discriminant class: 67

∞ 2 67 a_{1} a_{2} a_{3}  Over p = 2  Over p = 67 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
4. 0_{+} 2_{i} 1_{k} 0 -67  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 67 67  2  2  2 2
C_{2}  2  2 2 2

Discriminant class: 134

∞ 2 67 a_{1} a_{2} a_{3}  Over p = 2  Over p = 67  3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
5. 0_{+} 3_{k} 1_{i} 0 -134  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 67∗ 67∗ 2  2  2
C_{2}  2  2 2 2 2