Low Degree Fields Ramifying Above {2, 17, 23}

Discriminant class: −782

∞ 2 17 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 23 3 5 7 11 13 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} 3_{+} 1_{−} 1_{k} 0 782  1^{2} 3_{+} 2 2 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23  2  2 2  2
C_{2} 24  2 2  2 2
2. 1_{k} 3_{+} 1_{−} 1_{k} -1 13 -17 1^{2} 3_{+} 2 2 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23 3 2 3 2 2 3  2
S_{3} 2 2 3 3 2 2 3

Discriminant class: −46

∞ 2 17 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 23  3 5 7 11 13 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} 3_{+} 2_{+} 1_{i} -1 6 -46 1^{2} 3_{+} 2 2 1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 2  2 3 2 3 2 3
S_{3}  3  3 3 3 2 3

Discriminant class: 46

∞ 2 17 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 23 3 5 7 11 13 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
4. 0_{+} 3_{i} 2_{+} 1_{k} -1 -62 -114 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  1^{2} 1_{k} 23 23  3 3 2 2 2 2 2
S_{3}  3 3 2 2 3 3  2

Discriminant class: 391

∞ 2 17 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 23  3 5 7 11 13 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
5. 0_{+} 2_{i} 1_{−} 1_{i} 0 -391  1^{2} 2_{i} −1 −1 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{i} 23∗ 23∗  2 2  2
C_{2} 2  2  2 2 2

Discriminant class: 782

∞ 2 17 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 23  3 5 7 11 13 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
6. 0_{+} 3_{i} 1_{−} 1_{i} 0 -782  1^{2} 3_{i} −2 −2 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{i} 23∗ 23∗ 2 2 2  2 2
C_{2} 2  2 2 2 2  2 2