Old Sextic Fields Unramified Outside of {∞, 2, 17}

Discriminant class: −17

∞  2 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17 3 5 7 11 13 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 3_{i} 12_{i} 5_{−} -2 13 -36 1^{4} 9_{−} 2∗ −1 1^{6} 5_{−} 17  33 4 5 5 5 4 5 6
S_{5} 2 128 -212 110 1^{2} 3_{k} −2∗ −2∗ 33 6 222 6 6 33 4 4

Discriminant class: 1

∞ 2 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 17 3 5 7 11 13 19 23 29
G h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
2. 2_{−} 6_{−} 4_{+} -2 3 0 3^{2} 6_{−} 1  1^{3} 2_{+} ∗  5 5 5 33 5 5 5 5
A_{5}  -4 4 -3  1^{3} 2_{+} ∗  33 22 22 33 33 5 22 33

Discriminant class: 2

∞  2 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17 3 5 7 11 13 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 2_{−} 13_{−} 4_{+} -2 8 16 1^{4} 11_{i} −2 2 1^{3} 2_{+} ∗  6 4 33 4 6 6 5 4
S_{5} -3 -38 -22 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗ 22 4 5 4 33 4 4 222

Discriminant class: 34

∞  2 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17 3 5 7 11 13 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
4. 2_{−} 13_{+} 5_{−} -2 13 -36 1^{4} 10_{k} −1 2 1^{6} 5_{−} 17  33 5 6 5 4 6 4 33
S_{5}  2  -25 94 59 1^{2} 3_{i} −2 −2  4 5 6 222 22 6 4 33