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Label Polynomial Discriminant Galois group Class group
4.2.2312.1 x4 - 3x2 - 2 \( -\,2^{3}\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.0.2312.1 x4 - x3 - 2x + 4 \( 2^{3}\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.0.2601.1 x4 - x3 + 5x2 + 4x + 16 \( 3^{2}\cdot 17^{2} \) $C_2^2$ (as 4T2) trivial
4.2.5491.1 x4 - 2x3 - 2x2 + 3x - 2 \( -\,17^{2}\cdot 19 \) $D_{4}$ (as 4T3) trivial
4.4.7225.1 x4 - 11x2 + 9 \( 5^{2}\cdot 17^{2} \) $C_2^2$ (as 4T2) trivial
4.2.9248.1 x4 + 3x2 - 2 \( -\,2^{5}\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.4.9248.1 x4 - 5x2 + 2 \( 2^{5}\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.2.10404.1 x4 - x3 - x2 + 7x - 2 \( -\,2^{2}\cdot 3^{2}\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.2.12427.1 x4 - 2x3 + 4x2 - 3x - 2 \( -\,17^{2}\cdot 43 \) $D_{4}$ (as 4T3) trivial
4.0.14161.1 x4 - 5x2 + 36 \( 7^{2}\cdot 17^{2} \) $C_2^2$ (as 4T2) $[5]$
4.4.15317.1 x4 - 2x3 - 4x2 + 5x + 2 \( 17^{2}\cdot 53 \) $D_{4}$ (as 4T3) trivial
4.2.17051.1 x4 - 2x3 + x - 4 \( -\,17^{2}\cdot 59 \) $D_{4}$ (as 4T3) trivial
4.2.17051.2 x4 - x3 + 4x2 - 4x - 1 \( -\,17^{2}\cdot 59 \) $S_4$ (as 4T5) $[2]$
4.0.21964.1 x4 - x3 + 5x2 - 13x + 16 \( 2^{2}\cdot 17^{2}\cdot 19 \) $D_{4}$ (as 4T3) $[4]$
4.4.21964.1 x4 - x3 - 11x2 + 12x + 8 \( 2^{2}\cdot 17^{2}\cdot 19 \) $D_{4}$ (as 4T3) trivial
4.0.23409.1 x4 - x3 + 6x2 - 5x + 8 \( 3^{4}\cdot 17^{2} \) $A_4$ (as 4T4) $[2]$
4.2.23987.1 x4 - x3 - 19x - 13 \( -\,17^{2}\cdot 83 \) $D_{4}$ (as 4T3) trivial
4.2.28900.1 x4 - x3 - 3x2 - 9x - 4 \( -\,2^{2}\cdot 5^{2}\cdot 17^{2} \) $D_{4}$ (as 4T3) $[2]$
4.2.30056.1 x4 - x3 - x2 - 10x - 2 \( -\,2^{3}\cdot 13\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.2.30056.2 x4 - x3 + 6x2 - 22x + 8 \( -\,2^{3}\cdot 13\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.4.30056.1 x4 - 11x2 + 26 \( 2^{3}\cdot 13\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.4.30056.2 x4 - x3 - 9x2 - 6x + 2 \( 2^{3}\cdot 13\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.4.33813.1 x4 - x3 - 13x2 + 13x + 16 \( 3^{2}\cdot 13\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.0.33813.2 x4 - x3 - 29x2 + 21x + 237 \( 3^{2}\cdot 13\cdot 17^{2} \) $D_{4}$ (as 4T3) $[2]$
4.0.33813.3 x4 - 2x3 - 4x2 + 5x + 19 \( 3^{2}\cdot 13\cdot 17^{2} \) $D_{4}$ (as 4T3) $[2]$
4.0.34969.1 x4 - 3x2 + 49 \( 11^{2}\cdot 17^{2} \) $C_2^2$ (as 4T2) trivial
4.2.36703.1 x4 - x3 - 3x2 + 25x - 38 \( -\,17^{2}\cdot 127 \) $D_{4}$ (as 4T3) trivial
4.0.41616.1 x4 + 7x2 + 25 \( 2^{4}\cdot 3^{2}\cdot 17^{2} \) $C_2^2$ (as 4T2) $[4]$
4.4.41616.1 x4 - 2x3 - 13x2 + 14x - 2 \( 2^{4}\cdot 3^{2}\cdot 17^{2} \) $C_2^2$ (as 4T2) trivial
4.0.41616.3 x4 - 17x2 + 289 \( 2^{4}\cdot 3^{2}\cdot 17^{2} \) $C_2^2$ (as 4T2) $[4]$
4.2.43639.1 x4 - 2x3 + 7x2 - 6x - 8 \( -\,17^{2}\cdot 151 \) $D_{4}$ (as 4T3) $[3]$
4.0.49708.1 x4 - x3 + 8x2 + 11x + 19 \( 2^{2}\cdot 17^{2}\cdot 43 \) $D_{4}$ (as 4T3) $[2]$
4.4.49708.1 x4 - x3 - 9x2 + 11x + 2 \( 2^{2}\cdot 17^{2}\cdot 43 \) $D_{4}$ (as 4T3) trivial
4.2.51731.1 x4 - x3 - x2 - 27x - 36 \( -\,17^{2}\cdot 179 \) $D_{4}$ (as 4T3) trivial
4.0.54621.1 x4 - x3 + 39x2 - 13x + 373 \( 3^{3}\cdot 7\cdot 17^{2} \) $D_{4}$ (as 4T3) $[2]$
4.2.56644.1 x4 - x3 + 15x - 13 \( -\,2^{2}\cdot 7^{2}\cdot 17^{2} \) $D_{4}$ (as 4T3) trivial
4.2.61268.1 x4 - x3 - 13x2 - 21x - 18 \( -\,2^{2}\cdot 17^{2}\cdot 53 \) $D_{4}$ (as 4T3) $[2]$
4.2.61268.2 x4 - x3 + 4x2 - 21x - 1 \( -\,2^{2}\cdot 17^{2}\cdot 53 \) $D_{4}$ (as 4T3) $[2]$
4.2.64447.1 x4 - 2x3 + 5x2 - 4x - 13 \( -\,17^{2}\cdot 223 \) $D_{4}$ (as 4T3) trivial
4.0.65025.3 x4 + 23x2 + 196 \( 3^{2}\cdot 5^{2}\cdot 17^{2} \) $C_2^2$ (as 4T2) $[12]$
4.0.65025.4 x4 - x3 + 22x2 + 21x + 441 \( 3^{2}\cdot 5^{2}\cdot 17^{2} \) $C_2^2$ (as 4T2) $[12]$
4.0.66181.1 x4 - 2x3 + 16x2 - 15x + 18 \( 17^{2}\cdot 229 \) $D_{4}$ (as 4T3) $[5]$
4.0.68204.1 x4 - x3 + 6x2 - 5x + 25 \( 2^{2}\cdot 17^{2}\cdot 59 \) $D_{4}$ (as 4T3) $[2]$
4.4.68204.1 x4 - x3 - 11x2 - 5x + 8 \( 2^{2}\cdot 17^{2}\cdot 59 \) $D_{4}$ (as 4T3) trivial
4.2.71383.1 x4 - 2x3 - x2 + 2x - 16 \( -\,13\cdot 17^{2}\cdot 19 \) $D_{4}$ (as 4T3) trivial
4.2.71383.2 x4 - 2x3 - 13x2 + 14x - 19 \( -\,13\cdot 17^{2}\cdot 19 \) $D_{4}$ (as 4T3) trivial
4.0.74273.1 x4 - 2x3 + 13x2 - 12x + 19 \( 17^{2}\cdot 257 \) $D_{4}$ (as 4T3) trivial
4.2.76007.1 x4 - 2x3 + 3x2 - 2x - 16 \( -\,17^{2}\cdot 263 \) $D_{4}$ (as 4T3) trivial
4.4.81209.1 x4 - 2x3 - 17x2 + 18x + 13 \( 17^{2}\cdot 281 \) $D_{4}$ (as 4T3) trivial
4.0.85833.2 x4 - 2x3 + 3x2 - 2x + 52 \( 3^{3}\cdot 11\cdot 17^{2} \) $D_{4}$ (as 4T3) $[2]$
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