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Label Polynomial Discriminant Galois group Class group
5.1.2209.1 x5 - 2x4 + 2x3 - x2 + 1 \( 47^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.6241.1 x5 - x4 + x3 - 2x2 + 3x - 1 \( 79^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.10609.1 x5 - 2x4 + 3x3 - 3x2 + x + 1 \( 103^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.14161.1 x5 - x4 - x2 + 3x - 1 \( 7^{2}\cdot 17^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.16129.1 x5 - x4 - 2x3 + x2 + 3x - 1 \( 127^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.17161.1 x5 - x4 + 2x3 - x2 + x + 2 \( 131^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.20449.1 x5 - x4 - x3 + 3x - 1 \( 11^{2}\cdot 13^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.25281.1 x5 + x3 - 3x2 + x - 3 \( 3^{2}\cdot 53^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.32041.1 x5 - x4 + 3x2 - x + 2 \( 179^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.51529.1 x5 - x3 - 2x2 + 3x + 4 \( 227^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.57121.1 x5 - 2x4 + 4x3 - 5x2 + 2x + 1 \( 239^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.87616.1 x5 - x4 + 3x3 - 3x2 + 2x + 2 \( 2^{6}\cdot 37^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.91809.1 x5 + 3x3 - x2 + 3x + 3 \( 3^{2}\cdot 101^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.101761.1 x5 - x4 - x3 - 3x2 + 6x + 1 \( 11^{2}\cdot 29^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.118336.1 x5 - x4 - x3 + 5x2 - 2x + 2 \( 2^{6}\cdot 43^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.120409.1 x5 - x4 + 4x3 - x2 + 5x - 4 \( 347^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.140625.1 x5 - 5x2 - 3 \( 3^{2}\cdot 5^{6} \) $D_{5}$ (as 5T2) Trivial
5.5.160801.1 x5 - x4 - 5x3 + 4x2 + 3x - 1 \( 401^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.172225.1 x5 - x4 - 9x2 + 13x - 1 \( 5^{2}\cdot 83^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.192721.1 x5 - 3x3 - 4x2 + 8x + 1 \( 439^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.196249.1 x5 - x4 - x3 + 5x2 + 3x - 5 \( 443^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.207025.1 x5 - 2x4 + 3x3 - 9x2 + 5x - 5 \( 5^{2}\cdot 7^{2}\cdot 13^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.229441.1 x5 - 2x4 + 5x3 - 7x2 + 3x + 1 \( 479^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.238144.1 x5 - 2x4 + 3x3 + 10x + 8 \( 2^{6}\cdot 61^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.250000.1 x5 - 5x3 + 10x - 4 \( 2^{4}\cdot 5^{6} \) $D_{5}$ (as 5T2) Trivial
5.1.273529.1 x5 - x4 + 3x3 + 5x2 - x + 3 \( 523^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.326041.1 x5 - x4 - 2x3 + 7x2 - 3x + 2 \( 571^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.358801.1 x5 - x4 + 3x3 - 9x2 + 6x - 5 \( 599^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.373321.1 x5 + 3x3 - 6x2 - x - 4 \( 13^{2}\cdot 47^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.378225.1 x5 - x4 + 7x3 + 2x2 - 5x + 5 \( 3^{2}\cdot 5^{2}\cdot 41^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.383161.1 x5 - x4 + 4x3 - 5x2 + 3x + 2 \( 619^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.403225.1 x5 - x4 + 3x3 - 7x2 - x - 5 \( 5^{2}\cdot 127^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.440896.1 x5 - x4 - 4x2 - x - 27 \( 2^{6}\cdot 83^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.450241.1 x5 - x4 + 2x3 + 7x2 - 9x + 7 \( 11^{2}\cdot 61^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.466489.1 x5 - 2x4 + 5x3 + 6x2 - 7x + 2 \( 683^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.477481.1 x5 - 2x4 + 3x3 - 8x2 - x - 6 \( 691^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.488601.1 x5 - 2x4 - x3 + 8x2 + 3x - 6 \( 3^{2}\cdot 233^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.524176.1 x5 - 2x4 + 3x3 + 6x2 - 10x + 8 \( 2^{4}\cdot 181^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.546121.1 x5 - 4x3 - x2 + 10x - 4 \( 739^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.564001.1 x5 - x3 - 7x2 - x - 3 \( 751^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.602176.1 x5 - x4 + 7x3 + 5x2 + 8x - 4 \( 2^{6}\cdot 97^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.606841.1 x5 - 2x4 - 3x3 + 15x - 4 \( 19^{2}\cdot 41^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.619369.1 x5 + 2x3 - 7x2 + 10x - 4 \( 787^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.620944.1 x5 - 2x3 - 2x2 - 3x - 10 \( 2^{4}\cdot 197^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.644809.1 x5 - x4 + 2x3 - 19x2 + 33x - 20 \( 11^{2}\cdot 73^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.664225.1 x5 - 2x4 + 5x3 - 12x2 + 8x - 7 \( 5^{2}\cdot 163^{2} \) $D_{5}$ (as 5T2) Trivial
5.5.667489.1 x5 - x4 - 6x3 + 5x2 + 3x - 1 \( 19^{2}\cdot 43^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.678976.2 x5 + x3 - 6x2 + 10x - 4 \( 2^{6}\cdot 103^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.698896.1 x5 - x4 - 3x3 + 9x2 - 4x + 2 \( 2^{4}\cdot 11^{2}\cdot 19^{2} \) $D_{5}$ (as 5T2) Trivial
5.1.717409.1 x5 - 2x4 + 6x3 - 9x2 + 4x + 1 \( 7^{2}\cdot 11^{4} \) $D_{5}$ (as 5T2) $[5]$
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