Low Degree Fields Ramifying Above {2, 23, 29}

Discriminant class: −1334

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29  3 5 7 11 13 17 19 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_{i} 1_{−} 0 1334  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{−} 29∗ 29∗  2 2 2  2 2
C_{2} 32  2 2 2 2  2 2

Discriminant class: −667

∞ 2 23 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 23  Over p = 29 3 5 7 11 13 17 19 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_{+} 1_{i} 1_{+} 0 -2 -10 1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2  3 3 3 2
S_{3}  3 2 3 2 2 3  2

Discriminant class: −58

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29  3 5 7 11 13 17 19 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_{k} 2_{+} 1_{−} -1 8 132 1^{2} 3_{k} −2∗ −2∗ 1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 2 2 2 2 2 2 2 3
S_{3} 3 2 2 3 2 3 3

Discriminant class: −46

∞ 2 23 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 23  Over p = 29 3 5 7 11 13 17 19 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. 1_{k} 3_{+} 1_{i} 2_{+} -1 -19 -449 1^{2} 3_{+} 2 2 1^{2} 1_{i} 23∗ 23∗ 1^{3} 2_{+} ∗  2 3 2 3 2 2 3 3
S_{3} 3 3 2 3

Discriminant class: −2

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23 Over p = 29 3 5 7 11 13 17 19 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. 1_{k} 3_{i} 2_{+} 2_{+} -1 -222 3582 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 2 3 3 2
S_{3} 3  2 3  2 2 3 2 3
6. 1_{k} 3_{i} 2_{+} 2_{+} -1 445 247 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  3 2 2 3 2 3  2
S_{3} 3  2 3 3 2 2 3 2 3

Discriminant class: 667

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29 3 5 7 11 13 17 19 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
7. 0_{+} 2_{i} 1_{k} 1_{+} 0 -667  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 23 23 1^{2} 1_{+} 29 29  2  2  2
C_{2} 2  2 2  2 2

Discriminant class: 1334

∞ 2 23 29 a_{1}  a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29  3 5 7 11 13 17 19 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. 0_{+} 3_{k} 1_{k} 1_{−} 0 -1334  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 23 23 1^{2} 1_{−} 29∗ 29∗ 2  2
C_{2} 2  2 2  2 2