## Refine search

Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|

4.0.117.1 | x^{4} - x^{3} - x^{2} + x + 1 |
\( 3^{2}\cdot 13 \) | $D_{4}$ (as 4T3) | trivial |

4.0.125.1 | x^{4} - x^{3} + x^{2} - x + 1 |
\( 5^{3} \) | $C_4$ (as 4T1) | trivial |

4.0.144.1 | x^{4} - x^{2} + 1 |
\( 2^{4}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | trivial |

4.0.189.1 | x^{4} - x^{3} + 2x + 1 |
\( 3^{3}\cdot 7 \) | $D_{4}$ (as 4T3) | trivial |

4.0.225.1 | x^{4} - x^{3} + 2x^{2} + x + 1 |
\( 3^{2}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | trivial |

4.0.229.1 | x^{4} - x + 1 |
\( 229 \) | $S_4$ (as 4T5) | trivial |

4.0.256.1 | x^{4} + 1 |
\( 2^{8} \) | $C_2^2$ (as 4T2) | trivial |

4.0.257.1 | x^{4} + x^{2} - x + 1 |
\( 257 \) | $S_4$ (as 4T5) | trivial |

4.0.272.1 | x^{4} + x^{2} - 2x + 1 |
\( 2^{4}\cdot 17 \) | $D_{4}$ (as 4T3) | trivial |

4.0.320.1 | x^{4} - 2x^{3} + 2 |
\( 2^{6}\cdot 5 \) | $D_{4}$ (as 4T3) | trivial |

4.0.333.1 | x^{4} - x^{3} - 2x^{2} + 3 |
\( 3^{2}\cdot 37 \) | $D_{4}$ (as 4T3) | trivial |

4.0.392.1 | x^{4} - x^{3} + x + 1 |
\( 2^{3}\cdot 7^{2} \) | $D_{4}$ (as 4T3) | trivial |

4.0.400.1 | x^{4} + 3x^{2} + 1 |
\( 2^{4}\cdot 5^{2} \) | $C_2^2$ (as 4T2) | trivial |

4.0.432.1 | x^{4} - 3x^{2} + 3 |
\( 2^{4}\cdot 3^{3} \) | $D_{4}$ (as 4T3) | trivial |

4.0.441.1 | x^{4} - x^{3} - x^{2} - 2x + 4 |
\( 3^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | trivial |

4.0.512.1 | x^{4} - 2x^{2} + 2 |
\( 2^{9} \) | $D_{4}$ (as 4T3) | trivial |

4.0.513.1 | x^{4} - x^{3} - 3x^{2} + 2x + 4 |
\( 3^{3}\cdot 19 \) | $D_{4}$ (as 4T3) | trivial |

4.0.549.1 | x^{4} - 2x^{3} - 2x^{2} + 3x + 3 |
\( 3^{2}\cdot 61 \) | $D_{4}$ (as 4T3) | trivial |

4.0.576.1 | x^{4} - 2x^{2} + 4 |
\( 2^{6}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | trivial |

4.0.576.2 | x^{4} + 2x^{2} + 4 |
\( 2^{6}\cdot 3^{2} \) | $C_2^2$ (as 4T2) | trivial |

4.0.592.1 | x^{4} + 2x^{2} - 2x + 1 |
\( 2^{4}\cdot 37 \) | $S_4$ (as 4T5) | trivial |

4.0.605.1 | x^{4} - x^{3} + x^{2} + x + 1 |
\( 5\cdot 11^{2} \) | $D_{4}$ (as 4T3) | trivial |

4.0.656.1 | x^{4} - 2x^{3} - x^{2} + 2x + 2 |
\( 2^{4}\cdot 41 \) | $D_{4}$ (as 4T3) | trivial |

4.0.657.1 | x^{4} - x^{3} + 5x^{2} - 2x + 4 |
\( 3^{2}\cdot 73 \) | $D_{4}$ (as 4T3) | trivial |

4.0.697.1 | x^{4} - x^{3} + 2x^{2} - x + 2 |
\( 17\cdot 41 \) | $S_4$ (as 4T5) | trivial |

4.0.761.1 | x^{4} - x^{3} + x^{2} + 2x + 1 |
\( 761 \) | $S_4$ (as 4T5) | trivial |

4.0.784.1 | x^{4} - 3x^{2} + 4 |
\( 2^{4}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | trivial |

4.0.788.1 | x^{4} - x^{3} + 2x^{2} - 2x + 2 |
\( 2^{2}\cdot 197 \) | $S_4$ (as 4T5) | trivial |

4.0.832.1 | x^{4} - 2x^{3} - 2x + 5 |
\( 2^{6}\cdot 13 \) | $D_{4}$ (as 4T3) | trivial |

4.0.837.1 | x^{4} - x^{3} - 3x^{2} - x + 7 |
\( 3^{3}\cdot 31 \) | $D_{4}$ (as 4T3) | trivial |

4.0.873.1 | x^{4} - x^{3} - 4x^{2} + x + 7 |
\( 3^{2}\cdot 97 \) | $D_{4}$ (as 4T3) | trivial |

4.0.892.1 | x^{4} - x^{3} - x^{2} + 2 |
\( 2^{2}\cdot 223 \) | $S_4$ (as 4T5) | trivial |

4.0.981.1 | x^{4} - x^{3} - 4x^{2} + 4x + 7 |
\( 3^{2}\cdot 109 \) | $D_{4}$ (as 4T3) | trivial |

4.0.985.1 | x^{4} - x^{3} + 2x^{2} - 3x + 2 |
\( 5\cdot 197 \) | $S_4$ (as 4T5) | trivial |

4.0.1008.1 | x^{4} - 5x^{2} + 7 |
\( 2^{4}\cdot 3^{2}\cdot 7 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1008.2 | x^{4} + 5x^{2} + 7 |
\( 2^{4}\cdot 3^{2}\cdot 7 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1016.1 | x^{4} - x^{3} + x^{2} - 2x + 2 |
\( 2^{3}\cdot 127 \) | $S_4$ (as 4T5) | trivial |

4.0.1025.1 | x^{4} - x^{3} + 3x^{2} - 2x + 4 |
\( 5^{2}\cdot 41 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1040.1 | x^{4} - 3x^{2} - 2x + 5 |
\( 2^{4}\cdot 5\cdot 13 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1040.2 | x^{4} + x^{2} - 4x + 4 |
\( 2^{4}\cdot 5\cdot 13 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1076.1 | x^{4} - x^{3} + 3x^{2} - 3x + 2 |
\( 2^{2}\cdot 269 \) | $S_4$ (as 4T5) | trivial |

4.0.1088.1 | x^{4} - 2x^{3} + x^{2} - 2x + 3 |
\( 2^{6}\cdot 17 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1088.2 | x^{4} - 2x^{3} + 5x^{2} - 4x + 2 |
\( 2^{6}\cdot 17 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1089.1 | x^{4} - x^{3} - 2x^{2} - 3x + 9 |
\( 3^{2}\cdot 11^{2} \) | $C_2^2$ (as 4T2) | trivial |

4.0.1129.1 | x^{4} - x^{3} - x + 2 |
\( 1129 \) | $S_4$ (as 4T5) | trivial |

4.0.1161.1 | x^{4} - x^{3} + 6x^{2} - x + 7 |
\( 3^{3}\cdot 43 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1168.1 | x^{4} - x^{2} - 4x + 5 |
\( 2^{4}\cdot 73 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1197.1 | x^{4} - 2x^{3} - 4x^{2} + 5x + 7 |
\( 3^{2}\cdot 7\cdot 19 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1197.2 | x^{4} - x^{3} - 5x^{2} + 3x + 9 |
\( 3^{2}\cdot 7\cdot 19 \) | $D_{4}$ (as 4T3) | trivial |

4.0.1225.1 | x^{4} - x^{3} + 5x^{2} + 2x + 4 |
\( 5^{2}\cdot 7^{2} \) | $C_2^2$ (as 4T2) | trivial |