New Sextic Fields Unramified Outside of {∞, 5, 19}

Discriminant class: −95

∞ 5 19  a_{1} a_{2}  a_{3} Over p = 5  Over p = 19  2 3 7 11 13 17 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} 9_{−} 3_{i}  2  -5  5 1^{5} 9_{−} 5  1^{3} 2_{+} 1  5 22 4 5 5 4 6 4
S_{6}  200 -384 307  1^{2} 1_{i} 19∗ 19∗ 6 42 32 6 32 5 32 22
2. 1_{k} 9_{−} 5_{k}  -3 75 -50 1^{5} 9_{−} 5  1^{6} 5_{k} 19∗  5 22 4 5 5 4 32 4
S_{6} 3  -2950 9140 -7095  32 42 6 32 6 5 6 22

Discriminant class: 5

∞ 5 19 a_{1}  a_{2} a_{3} Over p = 5  Over p = 19 2 3 7 11 13 17 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_{−} 9_{−} 2_{+} 3  -5  0 1^{5} 9_{−} 5  1^{3} 2_{+} 1  6 4 32 33 32 32 6 33
S_{6}  45  42 61  3 0_{+} 1  3 4 22 32 2 32 42 5
4. 2_{−} 9_{−} 4_{+} 0 -10 -55 1^{5} 9_{−} 5  1^{5} 4_{+} 1  32 6 4 5 6 32 32 42
S_{6}  -20 -1637 1705  3 32 33 6 4 6 5 5
5. 2_{−} 9_{−} 4_{+} 0 -10 -55 1^{5} 9_{−} 5  1^{5} 4_{+} 1  6 32 4 5 32 6 6 42
S_{6}  -20 358 755  33 6 3 32 4 32 5 5
6. 2_{−} 9_{−} 4_{+} 0  25  0 1^{5} 9_{−} 5  1^{3} 2_{+} 1  32 4 6 3 6 6 32 3
S_{6} 3  50 -95 -125  1^{3} 2_{+} 1  33 4 22 6 222 6 42 5