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Label Polynomial Discriminant Galois group Class group Regulator
4.2.2312.1 $x^{4} - 3 x^{2} - 2$ $-\,2^{3}\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $2.47168963566$
4.0.2312.1 $x^{4} - x^{3} - 2 x + 4$ $2^{3}\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $4.18942509452$
4.0.2601.1 $x^{4} - x^{3} + 5 x^{2} + 4 x + 16$ $3^{2}\cdot 17^{2}$ $C_2^2$ (as 4T2) trivial $4.18942509452$
4.2.5491.1 $x^{4} - 2 x^{3} - 2 x^{2} + 3 x - 2$ $-\,17^{2}\cdot 19$ $D_{4}$ (as 4T3) trivial $6.45204286808$
4.4.7225.1 $x^{4} - 11 x^{2} + 9$ $5^{2}\cdot 17^{2}$ $C_2^2$ (as 4T2) trivial $4.45404695945$
4.2.9248.1 $x^{4} + 3 x^{2} - 2$ $-\,2^{5}\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $8.14015932466$
4.4.9248.1 $x^{4} - 5 x^{2} + 2$ $2^{5}\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $9.93835336634$
4.2.10404.1 $x^{4} - x^{3} - x^{2} + 7 x - 2$ $-\,2^{2}\cdot 3^{2}\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $13.5401509297$
4.2.12427.1 $x^{4} - 2 x^{3} + 4 x^{2} - 3 x - 2$ $-\,17^{2}\cdot 43$ $D_{4}$ (as 4T3) trivial $10.7705254206$
4.0.14161.1 $x^{4} - 5 x^{2} + 36$ $7^{2}\cdot 17^{2}$ $C_2^2$ (as 4T2) $[5]$ $4.18942509452$
4.4.15317.1 $x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 2$ $17^{2}\cdot 53$ $D_{4}$ (as 4T3) trivial $15.164099755$
4.2.17051.1 $x^{4} - 2 x^{3} + x - 4$ $-\,17^{2}\cdot 59$ $D_{4}$ (as 4T3) trivial $13.3907143433$
4.2.17051.2 $x^{4} - x^{3} + 4 x^{2} - 4 x - 1$ $-\,17^{2}\cdot 59$ $S_4$ (as 4T5) $[2]$ $2.8636187974$
4.0.21964.1 $x^{4} - x^{3} + 5 x^{2} - 13 x + 16$ $2^{2}\cdot 17^{2}\cdot 19$ $D_{4}$ (as 4T3) $[4]$ $4.18942509452$
4.4.21964.1 $x^{4} - x^{3} - 11 x^{2} + 12 x + 8$ $2^{2}\cdot 17^{2}\cdot 19$ $D_{4}$ (as 4T3) trivial $12.3769974688$
4.0.23409.1 $x^{4} - x^{3} + 6 x^{2} - 5 x + 8$ $3^{4}\cdot 17^{2}$ $A_4$ (as 4T4) $[2]$ $5.93153383032$
4.2.23987.1 $x^{4} - x^{3} - 19 x - 13$ $-\,17^{2}\cdot 83$ $D_{4}$ (as 4T3) trivial $16.4244197849$
4.2.28900.1 $x^{4} - x^{3} - 3 x^{2} - 9 x - 4$ $-\,2^{2}\cdot 5^{2}\cdot 17^{2}$ $D_{4}$ (as 4T3) $[2]$ $12.6232303792$
4.2.30056.1 $x^{4} - x^{3} - x^{2} - 10 x - 2$ $-\,2^{3}\cdot 13\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $10.9381373432$
4.2.30056.2 $x^{4} - x^{3} + 6 x^{2} - 22 x + 8$ $-\,2^{3}\cdot 13\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $26.5281055535$
4.4.30056.1 $x^{4} - 11 x^{2} + 26$ $2^{3}\cdot 13\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $32.4143701847$
4.4.30056.2 $x^{4} - x^{3} - 9 x^{2} - 6 x + 2$ $2^{3}\cdot 13\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $14.1622697187$
4.4.33813.1 $x^{4} - x^{3} - 13 x^{2} + 13 x + 16$ $3^{2}\cdot 13\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $25.385771591$
4.0.33813.2 $x^{4} - x^{3} - 29 x^{2} + 21 x + 237$ $3^{2}\cdot 13\cdot 17^{2}$ $D_{4}$ (as 4T3) $[2]$ $10.0740722038$
4.0.33813.3 $x^{4} - 2 x^{3} - 4 x^{2} + 5 x + 19$ $3^{2}\cdot 13\cdot 17^{2}$ $D_{4}$ (as 4T3) $[2]$ $2.8005138708$
4.0.34969.1 $x^{4} - 3 x^{2} + 49$ $11^{2}\cdot 17^{2}$ $C_2^2$ (as 4T2) trivial $4.18942509452$
4.2.36703.1 $x^{4} - x^{3} - 3 x^{2} + 25 x - 38$ $-\,17^{2}\cdot 127$ $D_{4}$ (as 4T3) trivial $46.0574482512$
4.0.41616.1 $x^{4} + 7 x^{2} + 25$ $2^{4}\cdot 3^{2}\cdot 17^{2}$ $C_2^2$ (as 4T2) $[4]$ $2.63391579385$
4.4.41616.1 $x^{4} - 2 x^{3} - 13 x^{2} + 14 x - 2$ $2^{4}\cdot 3^{2}\cdot 17^{2}$ $C_2^2$ (as 4T2) trivial $25.4075373607$
4.0.41616.3 $x^{4} - 17 x^{2} + 289$ $2^{4}\cdot 3^{2}\cdot 17^{2}$ $C_2^2$ (as 4T2) $[4]$ $9.21014034197$
4.2.43639.1 $x^{4} - 2 x^{3} + 7 x^{2} - 6 x - 8$ $-\,17^{2}\cdot 151$ $D_{4}$ (as 4T3) $[3]$ $17.2167853413$
4.0.49708.1 $x^{4} - x^{3} + 8 x^{2} + 11 x + 19$ $2^{2}\cdot 17^{2}\cdot 43$ $D_{4}$ (as 4T3) $[2]$ $4.18942509452$
4.4.49708.1 $x^{4} - x^{3} - 9 x^{2} + 11 x + 2$ $2^{2}\cdot 17^{2}\cdot 43$ $D_{4}$ (as 4T3) trivial $45.7744130361$
4.2.51731.1 $x^{4} - x^{3} - x^{2} - 27 x - 36$ $-\,17^{2}\cdot 179$ $D_{4}$ (as 4T3) trivial $24.8290794456$
4.0.54621.1 $x^{4} - x^{3} + 39 x^{2} - 13 x + 373$ $3^{3}\cdot 7\cdot 17^{2}$ $D_{4}$ (as 4T3) $[2]$ $10.8122672688$
4.2.56644.1 $x^{4} - x^{3} + 15 x - 13$ $-\,2^{2}\cdot 7^{2}\cdot 17^{2}$ $D_{4}$ (as 4T3) trivial $13.7911330547$
4.2.61268.1 $x^{4} - x^{3} - 13 x^{2} - 21 x - 18$ $-\,2^{2}\cdot 17^{2}\cdot 53$ $D_{4}$ (as 4T3) $[2]$ $20.6751882674$
4.2.61268.2 $x^{4} - x^{3} + 4 x^{2} - 21 x - 1$ $-\,2^{2}\cdot 17^{2}\cdot 53$ $D_{4}$ (as 4T3) $[2]$ $8.40492752203$
4.2.64447.1 $x^{4} - 2 x^{3} + 5 x^{2} - 4 x - 13$ $-\,17^{2}\cdot 223$ $D_{4}$ (as 4T3) trivial $9.04653794112$
4.0.65025.3 $x^{4} + 23 x^{2} + 196$ $3^{2}\cdot 5^{2}\cdot 17^{2}$ $C_2^2$ (as 4T2) $[12]$ $0.962423650119$
4.0.65025.4 $x^{4} - x^{3} + 22 x^{2} + 21 x + 441$ $3^{2}\cdot 5^{2}\cdot 17^{2}$ $C_2^2$ (as 4T2) $[12]$ $4.41869541723$
4.0.66181.1 $x^{4} - 2 x^{3} + 16 x^{2} - 15 x + 18$ $17^{2}\cdot 229$ $D_{4}$ (as 4T3) $[5]$ $4.18942509452$
4.0.68204.1 $x^{4} - x^{3} + 6 x^{2} - 5 x + 25$ $2^{2}\cdot 17^{2}\cdot 59$ $D_{4}$ (as 4T3) $[2]$ $4.18942509452$
4.4.68204.1 $x^{4} - x^{3} - 11 x^{2} - 5 x + 8$ $2^{2}\cdot 17^{2}\cdot 59$ $D_{4}$ (as 4T3) trivial $53.9172882552$
4.2.71383.1 $x^{4} - 2 x^{3} - x^{2} + 2 x - 16$ $-\,13\cdot 17^{2}\cdot 19$ $D_{4}$ (as 4T3) trivial $70.1173716711$
4.2.71383.2 $x^{4} - 2 x^{3} - 13 x^{2} + 14 x - 19$ $-\,13\cdot 17^{2}\cdot 19$ $D_{4}$ (as 4T3) trivial $8.71065666307$
4.0.74273.1 $x^{4} - 2 x^{3} + 13 x^{2} - 12 x + 19$ $17^{2}\cdot 257$ $D_{4}$ (as 4T3) trivial $4.18942509452$
4.2.76007.1 $x^{4} - 2 x^{3} + 3 x^{2} - 2 x - 16$ $-\,17^{2}\cdot 263$ $D_{4}$ (as 4T3) trivial $74.8574327661$
4.4.81209.1 $x^{4} - 2 x^{3} - 17 x^{2} + 18 x + 13$ $17^{2}\cdot 281$ $D_{4}$ (as 4T3) trivial $15.4177019463$
4.0.85833.2 $x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 52$ $3^{3}\cdot 11\cdot 17^{2}$ $D_{4}$ (as 4T3) $[2]$ $8.57614403166$
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