Label |
Base field |
Field degree |
Field discriminant |
Level |
Level norm |
Weight |
Dimension |
CM |
Base change |
1.1-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[1, 1, 1]$ |
$1$ |
$[2, 2, 2, 2]$ |
$2$ |
✓ |
✓ |
1.1-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[1, 1, 1]$ |
$1$ |
$[2, 2, 2, 2]$ |
$2$ |
✓ |
✓ |
1.1-c |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[1, 1, 1]$ |
$1$ |
$[2, 2, 2, 2]$ |
$4$ |
|
✓ |
1.1-d |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[1, 1, 1]$ |
$1$ |
$[2, 2, 2, 2]$ |
$4$ |
|
✓ |
2.1-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[2, 2, \frac{4}{9}w^{3} - \frac{2}{3}w^{2} - \frac{47}{9}w + \frac{20}{9}]$ |
$2$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
2.2-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[2,2,-\frac{4}{9}w^{3} + \frac{2}{3}w^{2} + \frac{47}{9}w - \frac{29}{9}]$ |
$2$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
4.1-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[4, 2, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{28}{9}]$ |
$4$ |
$[2, 2, 2, 2]$ |
$1$ |
|
|
4.1-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[4, 2, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{28}{9}]$ |
$4$ |
$[2, 2, 2, 2]$ |
$1$ |
|
|
4.2-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[4, 2, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{19}{9}w + \frac{10}{9}]$ |
$4$ |
$[2, 2, 2, 2]$ |
$1$ |
|
✓ |
4.2-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[4, 2, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{19}{9}w + \frac{10}{9}]$ |
$4$ |
$[2, 2, 2, 2]$ |
$1$ |
|
✓ |
4.2-c |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[4, 2, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{19}{9}w + \frac{10}{9}]$ |
$4$ |
$[2, 2, 2, 2]$ |
$4$ |
|
✓ |
4.3-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[4,2,-\frac{2}{9}w^{3} + \frac{1}{3}w^{2} + \frac{28}{9}w - \frac{1}{9}]$ |
$4$ |
$[2, 2, 2, 2]$ |
$1$ |
|
|
4.3-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[4,2,-\frac{2}{9}w^{3} + \frac{1}{3}w^{2} + \frac{28}{9}w - \frac{1}{9}]$ |
$4$ |
$[2, 2, 2, 2]$ |
$1$ |
|
|
8.1-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8, 2, w^{3} - 2w^{2} - 11w + 12]$ |
$8$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
8.1-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8, 2, w^{3} - 2w^{2} - 11w + 12]$ |
$8$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
8.2-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8,2,-w^{3} + w^{2} + 12w]$ |
$8$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
8.2-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8,2,-w^{3} + w^{2} + 12w]$ |
$8$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
8.3-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8, 4, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} - \frac{4}{9}w + \frac{4}{9}]$ |
$8$ |
$[2, 2, 2, 2]$ |
$1$ |
|
✓ |
8.3-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8, 4, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} - \frac{4}{9}w + \frac{4}{9}]$ |
$8$ |
$[2, 2, 2, 2]$ |
$1$ |
|
✓ |
8.3-c |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8, 4, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} - \frac{4}{9}w + \frac{4}{9}]$ |
$8$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
8.3-d |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8, 4, -\frac{1}{9}w^{3} + \frac{2}{3}w^{2} - \frac{4}{9}w + \frac{4}{9}]$ |
$8$ |
$[2, 2, 2, 2]$ |
$4$ |
|
|
8.4-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8,4,\frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{5}{9}w + \frac{5}{9}]$ |
$8$ |
$[2, 2, 2, 2]$ |
$1$ |
|
✓ |
8.4-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8,4,\frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{5}{9}w + \frac{5}{9}]$ |
$8$ |
$[2, 2, 2, 2]$ |
$1$ |
|
✓ |
8.4-c |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8,4,\frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{5}{9}w + \frac{5}{9}]$ |
$8$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
8.4-d |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[8,4,\frac{1}{9}w^{3} + \frac{1}{3}w^{2} - \frac{5}{9}w + \frac{5}{9}]$ |
$8$ |
$[2, 2, 2, 2]$ |
$4$ |
|
|
9.1-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[9, 3, \frac{1}{3}w^{3} - \frac{11}{3}w - \frac{1}{3}]$ |
$9$ |
$[2, 2, 2, 2]$ |
$2$ |
|
✓ |
9.1-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[9, 3, \frac{1}{3}w^{3} - \frac{11}{3}w - \frac{1}{3}]$ |
$9$ |
$[2, 2, 2, 2]$ |
$2$ |
|
✓ |
9.1-c |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[9, 3, \frac{1}{3}w^{3} - \frac{11}{3}w - \frac{1}{3}]$ |
$9$ |
$[2, 2, 2, 2]$ |
$10$ |
|
|
9.1-d |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[9, 3, \frac{1}{3}w^{3} - \frac{11}{3}w - \frac{1}{3}]$ |
$9$ |
$[2, 2, 2, 2]$ |
$10$ |
|
|
9.2-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[9,3,-\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{7}{3}]$ |
$9$ |
$[2, 2, 2, 2]$ |
$2$ |
|
✓ |
9.2-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[9,3,-\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{7}{3}]$ |
$9$ |
$[2, 2, 2, 2]$ |
$2$ |
|
✓ |
9.2-c |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[9,3,-\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{7}{3}]$ |
$9$ |
$[2, 2, 2, 2]$ |
$10$ |
|
|
9.2-d |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[9,3,-\frac{1}{3}w^{3} + \frac{11}{3}w + \frac{7}{3}]$ |
$9$ |
$[2, 2, 2, 2]$ |
$10$ |
|
|
16.1-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 2, 2]$ |
$16$ |
$[2, 2, 2, 2]$ |
$1$ |
|
✓ |
16.1-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 2, 2]$ |
$16$ |
$[2, 2, 2, 2]$ |
$1$ |
|
✓ |
16.1-c |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 2, 2]$ |
$16$ |
$[2, 2, 2, 2]$ |
$4$ |
|
✓ |
16.2-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{1}{3}w^{3} - w^{2} - \frac{8}{3}w + \frac{14}{3}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
16.2-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{1}{3}w^{3} - w^{2} - \frac{8}{3}w + \frac{14}{3}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
16.2-c |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{1}{3}w^{3} - w^{2} - \frac{8}{3}w + \frac{14}{3}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$4$ |
|
|
16.2-d |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{1}{3}w^{3} - w^{2} - \frac{8}{3}w + \frac{14}{3}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$4$ |
|
|
16.3-a |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{10}{9}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$1$ |
|
|
16.3-b |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{10}{9}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$1$ |
|
✓ |
16.3-c |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{10}{9}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$1$ |
|
✓ |
16.3-d |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{10}{9}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$1$ |
|
|
16.3-e |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{10}{9}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
16.3-f |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{10}{9}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$2$ |
✓ |
✓ |
16.3-g |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{10}{9}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$2$ |
|
|
16.3-h |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{10}{9}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$2$ |
✓ |
✓ |
16.3-i |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{10}{9}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$4$ |
|
✓ |
16.3-j |
\(\Q(\sqrt{2}, \sqrt{17})\) |
$4$ |
$18496$ |
$[16, 4, \frac{2}{9}w^{3} - \frac{1}{3}w^{2} - \frac{28}{9}w + \frac{10}{9}]$ |
$16$ |
$[2, 2, 2, 2]$ |
$4$ |
|
|