Low Degree Fields Unramified Outside of {∞, 2, 59}

Discriminant class: −118

∞ 2 59 a_{1} a_{2} a_{3} Over p = 2 Over p = 59 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 61
1. 1_{k} 3_{−} 1_{k} 0 118  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 59 59 2 2  2 2
C_{2} 6  2 2  2 2
2. 1_{k} 3_{−} 1_{k} 0 -5 -6 1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 59 59 2 2 3 3 3 3 2 2
S_{3}  2 2 3 3 3 2 2

Discriminant class: −59

∞ 2 59 a_{1} a_{2} a_{3} Over p = 2  Over p = 59  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 61
3. 1_{k} 0_{+} 1_{i} 0 59  2 0_{+} ∗ ∗ 1^{2} 1_{i} 59∗ 59∗  2 2  2
C_{2} 3  2 2  2 2  2
4. 1_{k} 0_{+} 1_{i} 0 2 -1 2 0_{+} ∗ ∗ 1^{2} 1_{i} 59∗ 59∗ 3 3 3 2 2  3 2
S_{3}  3 2 2 3 2 2 3 2

Discriminant class: −2

∞ 2 59 a_{1} a_{2} a_{3}  Over p = 2  Over p = 59 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 61
5. 1_{k} 3_{i} 0_{+} 0 2  1^{2} 3_{i} −2 −2  2 2  2  2
C_{2}  2 2 2  2 2 2

Discriminant class: −1

∞ 2 59 a_{1} a_{2} a_{3}  Over p = 2  Over p = 59 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 61
6. 1_{k} 2_{i} 0_{+} 0 1  1^{2} 2_{i} −1 −1 2 0_{+} ∗ ∗ 2  2 2  2 2
C_{2}  2  2 2
7. 1_{k} 2_{i} 2_{+} -1 20 24 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  2 3 2 2 3  2 2
S_{3} 2  2 3 3 2 2 3 3

Discriminant class: 2

∞ 2 59 a_{1} a_{2} a_{3} Over p = 2  Over p = 59 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 61
8. 0_{+} 3_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2 2 0_{+} ∗ ∗ 2 2  2 2  2
C_{2}  2  2  2  2 2
9. 0_{+} 3_{+} 2_{+} -1 -39 83 1^{2} 3_{+} 2 2 1^{3} 2_{+} ∗  2 2 3 2 2 3 2 3
S_{3}  2 3 2  2  2 2

Discriminant class: 59

∞ 2 59 a_{1} a_{2} a_{3}  Over p = 2  Over p = 59 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 61
10. 0_{+} 2_{i} 1_{k} 0 -59  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 59 59 2  2  2  2
C_{2}  2  2

Discriminant class: 118

∞ 2 59 a_{1} a_{2} a_{3}  Over p = 2  Over p = 59  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 61
11. 0_{+} 3_{k} 1_{i} 0 -118  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 59∗ 59∗  2 2 2
C_{2}  2  2  2