Low Degree Fields Unramified Outside of {∞, 7, 61}

Discriminant class: −427

∞ 7 61 a_{1} a_{2} a_{3} Over p = 7  Over p = 61  2 3 5 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 59
1. 1_{k} 1_{k} 1_{−} 0 427  1^{2} 1_{k} 7 7 1^{2} 1_{−} 61∗ 61∗ 2 2 2 2 2  2 2
C_{2} 2  2  2 2 2 2 2

Discriminant class: −7

∞ 7 61 a_{1} a_{2} a_{3} Over p = 7 Over p = 61 2 3 5 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 59
2. 1_{k} 1_{i} 0_{+} 1 2  1^{2} 1_{i} 7∗ 7∗ 2 0_{+} ∗ ∗  2 2  2 2 2
C_{2}  2  2  2  2

Discriminant class: 1

∞ 7 61 a_{1} a_{2} a_{3} Over p = 7  Over p = 61 2 3 5 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 59
3. 0_{+} 2_{+} 0_{+} -1 -2  1 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3  3 3 3
C_{3}  3 3  3 3 3
4. 0_{+} 0_{+} 2_{+} -1 -20  9 3 0_{+} 1  1^{3} 2_{+} 1  3  3  3 3 3
C_{3}  3 3  3 3  3
5. 0_{+} 2_{+} 2_{+} -1 -142 -601 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3  3
C_{3} 3  3 3 3  3  3
6. 0_{+} 2_{+} 2_{+} -1 -142 680 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3  3 3
C_{3} 3  3  3  3 3 3 3

Discriminant class: 61

∞ 7 61 a_{1} a_{2} a_{3} Over p = 7  Over p = 61 2 3 5 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 59
7. 0_{+} 0_{+} 1_{+} 0 -61  2 0_{+} ∗ ∗ 1^{2} 1_{+} 61 61 2  2  2  2
C_{2}  2 2 2  2  2 2