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Results (displaying matches 1-50 of 21871)
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| Label |
Polynomial |
Discriminant |
Galois group |
Class group |
| 4.0.125.1 |
x4 - x3 + x2 - x + 1 |
\( 5^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.1125.1 |
x4 - x3 - 4x2 + 4x + 1 |
\( 3^{2}\cdot 5^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.2000.1 |
x4 - 5x2 + 5 |
\( 2^{4}\cdot 5^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.2048.1 |
x4 - 4x2 + 2 |
\( 2^{11} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.2048.2 |
x4 + 4x2 + 2 |
\( 2^{11} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.2197.1 |
x4 - x3 + 2x2 + 4x + 3 |
\( 13^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.4913.1 |
x4 - x3 - 6x2 + x + 1 |
\( 17^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.6125.1 |
x4 - x3 - 9x2 + 9x + 11 |
\( 5^{3}\cdot 7^{2} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.8000.1 |
x4 - 10x2 + 20 |
\( 2^{6}\cdot 5^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.8000.2 |
x4 + 10x2 + 20 |
\( 2^{6}\cdot 5^{3} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.4.15125.1 |
x4 - x3 - 14x2 + 14x + 31 |
\( 5^{3}\cdot 11^{2} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.18000.1 |
x4 + 15x2 + 45 |
\( 2^{4}\cdot 3^{2}\cdot 5^{3} \) |
$C_4$ (as 4T1) |
$[2, 2]$
|
| 4.4.18432.1 |
x4 - 12x2 + 18 |
\( 2^{11}\cdot 3^{2} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.18432.2 |
x4 + 12x2 + 18 |
\( 2^{11}\cdot 3^{2} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.4.19773.1 |
x4 - x3 - 11x2 - 9x + 3 |
\( 3^{2}\cdot 13^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.21125.1 |
x4 - x3 + 16x2 - 16x + 61 |
\( 5^{3}\cdot 13^{2} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.0.24389.1 |
x4 - x3 + 4x2 - 20x + 23 |
\( 29^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.35152.1 |
x4 - 13x2 + 13 |
\( 2^{4}\cdot 13^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.36125.1 |
x4 - x3 + 21x2 - 21x + 101 |
\( 5^{3}\cdot 17^{2} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.0.44217.1 |
x4 - x3 + 11x2 + x + 52 |
\( 3^{2}\cdot 17^{3} \) |
$C_4$ (as 4T1) |
$[10]$
|
| 4.4.45125.1 |
x4 - x3 - 24x2 + 24x + 101 |
\( 5^{3}\cdot 19^{2} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.50653.1 |
x4 - x3 + 5x2 - 7x + 49 |
\( 37^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.51200.1 |
x4 - 20x2 + 50 |
\( 2^{11}\cdot 5^{2} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.0.51200.2 |
x4 + 20x2 + 50 |
\( 2^{11}\cdot 5^{2} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.0.54925.1 |
x4 - x3 + 15x2 + 17x + 29 |
\( 5^{2}\cdot 13^{3} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.0.55125.1 |
x4 - x3 + 26x2 - 26x + 151 |
\( 3^{2}\cdot 5^{3}\cdot 7^{2} \) |
$C_4$ (as 4T1) |
$[2, 2]$
|
| 4.4.66125.1 |
x4 - x3 - 29x2 + 29x + 151 |
\( 5^{3}\cdot 23^{2} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.68921.1 |
x4 - x3 - 15x2 - 18x - 4 |
\( 41^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.72000.1 |
x4 - 30x2 + 180 |
\( 2^{6}\cdot 3^{2}\cdot 5^{3} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.0.72000.2 |
x4 + 30x2 + 180 |
\( 2^{6}\cdot 3^{2}\cdot 5^{3} \) |
$C_4$ (as 4T1) |
$[2, 2]$
|
| 4.0.78608.1 |
x4 + 17x2 + 68 |
\( 2^{4}\cdot 17^{3} \) |
$C_4$ (as 4T1) |
$[2, 2]$
|
| 4.0.98000.1 |
x4 + 35x2 + 245 |
\( 2^{4}\cdot 5^{3}\cdot 7^{2} \) |
$C_4$ (as 4T1) |
$[2, 2]$
|
| 4.4.100352.1 |
x4 - 28x2 + 98 |
\( 2^{11}\cdot 7^{2} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.100352.5 |
x4 + 28x2 + 98 |
\( 2^{11}\cdot 7^{2} \) |
$C_4$ (as 4T1) |
$[2, 2]$
|
| 4.0.105125.2 |
x4 - x3 + 36x2 - 36x + 281 |
\( 5^{3}\cdot 29^{2} \) |
$C_4$ (as 4T1) |
$[2, 2]$
|
| 4.4.107653.1 |
x4 - x3 - 24x2 - 22x + 29 |
\( 7^{2}\cdot 13^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.120125.1 |
x4 - x3 - 39x2 + 39x + 281 |
\( 5^{3}\cdot 31^{2} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.122825.1 |
x4 - x3 - 23x2 + x + 86 |
\( 5^{2}\cdot 17^{3} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.0.136125.2 |
x4 - x3 + 41x2 - 41x + 361 |
\( 3^{2}\cdot 5^{3}\cdot 11^{2} \) |
$C_4$ (as 4T1) |
$[2, 2, 2]$
|
| 4.4.140608.1 |
x4 - 26x2 + 52 |
\( 2^{6}\cdot 13^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.140608.2 |
x4 + 26x2 + 52 |
\( 2^{6}\cdot 13^{3} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.0.148877.1 |
x4 - x3 + 7x2 + 43x + 47 |
\( 53^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.171125.1 |
x4 - x3 + 46x2 - 46x + 451 |
\( 5^{3}\cdot 37^{2} \) |
$C_4$ (as 4T1) |
$[10]$
|
| 4.4.190125.1 |
x4 - x3 - 49x2 + 49x + 451 |
\( 3^{2}\cdot 5^{3}\cdot 13^{2} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.0.210125.1 |
x4 - x3 + 51x2 - 51x + 551 |
\( 5^{3}\cdot 41^{2} \) |
$C_4$ (as 4T1) |
$[2, 4]$
|
| 4.4.219501.1 |
x4 - x3 - 25x2 + 67x - 35 |
\( 3^{2}\cdot 29^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.226981.1 |
x4 - x3 + 8x2 - 42x + 117 |
\( 61^{3} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.4.231125.1 |
x4 - x3 - 54x2 + 54x + 551 |
\( 5^{3}\cdot 43^{2} \) |
$C_4$ (as 4T1) |
Trivial
|
| 4.0.240737.1 |
x4 - x3 + 28x2 + x + 239 |
\( 7^{2}\cdot 17^{3} \) |
$C_4$ (as 4T1) |
$[2]$
|
| 4.0.242000.2 |
x4 + 55x2 + 605 |
\( 2^{4}\cdot 5^{3}\cdot 11^{2} \) |
$C_4$ (as 4T1) |
$[2, 2, 2]$
|
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