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Label Polynomial Discriminant Galois group Class group Regulator
4.4.4913.1 $x^{4} - x^{3} - 6 x^{2} + x + 1$ $17^{3}$ $C_4$ (as 4T1) trivial $3.46198873228$
4.2.19652.1 $x^{4} - 17$ $-\,2^{2}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2]$ $10.227465122$
4.0.63869.1 $x^{4} - 2 x^{3} + 10 x^{2} - 9 x + 16$ $13\cdot 17^{3}$ $D_{4}$ (as 4T3) $[4]$ $4.18942509452$
4.0.78608.1 $x^{4} + 17 x^{2} + 68$ $2^{4}\cdot 17^{3}$ $C_4$ (as 4T1) $[2, 2]$ $4.18942509452$
4.0.78608.2 $x^{4} - 2 x^{3} + 10 x^{2} + 8 x + 16$ $2^{4}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[8]$ $4.88251485167$
4.2.230911.1 $x^{4} - 2 x^{3} - 7 x^{2} + 8 x - 52$ $-\,17^{3}\cdot 47$ $D_{4}$ (as 4T3) $[2]$ $68.4497993353$
4.2.255476.1 $x^{4} - x^{3} - 6 x^{2} + 35 x - 67$ $-\,2^{2}\cdot 13\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2]$ $18.3401689211$
4.2.255476.2 $x^{4} - x^{3} + 11 x^{2} + 35 x - 50$ $-\,2^{2}\cdot 13\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2]$ $45.5378924018$
4.2.314432.1 $x^{4} - 68$ $-\,2^{6}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2]$ $29.3015153378$
4.4.314432.1 $x^{4} - 34 x^{2} + 272$ $2^{6}\cdot 17^{3}$ $C_4$ (as 4T1) $[2]$ $32.7121247887$
4.0.314432.2 $x^{4} + 34 x^{2} + 272$ $2^{6}\cdot 17^{3}$ $C_4$ (as 4T1) $[2, 2]$ $4.18942509452$
4.2.329171.1 $x^{4} - x^{3} - 6 x^{2} - 67 x - 271$ $-\,17^{3}\cdot 67$ $D_{4}$ (as 4T3) $[2]$ $33.7322801829$
4.2.353736.1 $x^{4} - x^{3} + 11 x^{2} - 50 x - 50$ $-\,2^{3}\cdot 3^{2}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2]$ $18.7470386186$
4.4.353736.1 $x^{4} - x^{3} - 40 x^{2} + 52 x + 256$ $2^{3}\cdot 3^{2}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2]$ $72.1948036488$
4.0.437257.1 $x^{4} - 2 x^{3} + 27 x^{2} - 26 x + 101$ $17^{3}\cdot 89$ $D_{4}$ (as 4T3) $[4]$ $4.18942509452$
4.0.496213.1 $x^{4} - 2 x^{3} + 44 x^{2} - 43 x + 118$ $17^{3}\cdot 101$ $D_{4}$ (as 4T3) $[16]$ $4.18942509452$
4.2.506039.1 $x^{4} - 2 x^{3} + 27 x^{2} - 26 x - 103$ $-\,17^{3}\cdot 103$ $D_{4}$ (as 4T3) $[2]$ $14.4482259079$
4.0.673081.1 $x^{4} - 2 x^{3} + 27 x^{2} - 26 x + 152$ $17^{3}\cdot 137$ $D_{4}$ (as 4T3) $[48]$ $4.18942509452$
4.4.732037.1 $x^{4} - 2 x^{3} - 24 x^{2} + 25 x + 152$ $17^{3}\cdot 149$ $D_{4}$ (as 4T3) $[2]$ $79.4810907877$
4.2.746776.1 $x^{4} - x^{3} - 6 x^{2} - 50 x - 152$ $-\,2^{3}\cdot 17^{3}\cdot 19$ $D_{4}$ (as 4T3) $[2]$ $76.8260155969$
4.2.746776.2 $x^{4} + 17 x^{2} - 646$ $-\,2^{3}\cdot 17^{3}\cdot 19$ $D_{4}$ (as 4T3) $[2]$ $16.7333528462$
4.0.746776.1 $x^{4} - x^{3} + 28 x^{2} + 18 x + 188$ $2^{3}\cdot 17^{3}\cdot 19$ $D_{4}$ (as 4T3) $[2, 14]$ $4.18942509452$
4.4.746776.1 $x^{4} - 51 x^{2} + 646$ $2^{3}\cdot 17^{3}\cdot 19$ $D_{4}$ (as 4T3) $[2]$ $37.9535626105$
4.4.771341.1 $x^{4} - x^{3} - 57 x^{2} + 69 x + 596$ $17^{3}\cdot 157$ $D_{4}$ (as 4T3) $[2]$ $66.6734617706$
4.0.830297.1 $x^{4} + 17 x^{2} + 17$ $13^{2}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2, 4]$ $5.40715166186$
4.4.830297.1 $x^{4} - x^{3} - 57 x^{2} + x + 664$ $13^{2}\cdot 17^{3}$ $C_4$ (as 4T1) $[2]$ $195.48693618$
4.2.840123.1 $x^{4} - 2 x^{3} - 24 x^{2} + 25 x - 188$ $-\,3^{2}\cdot 17^{3}\cdot 19$ $D_{4}$ (as 4T3) $[2]$ $53.4218772841$
4.2.879427.2 $x^{4} - x^{3} - 6 x^{2} + 18 x - 135$ $-\,17^{3}\cdot 179$ $S_4$ (as 4T5) $[4]$ $18.4970281926$
4.0.923644.1 $x^{4} - x^{3} + 28 x^{2} - 33 x + 239$ $2^{2}\cdot 17^{3}\cdot 47$ $D_{4}$ (as 4T3) $[2, 4]$ $4.18942509452$
4.4.923644.1 $x^{4} - x^{3} - 40 x^{2} - 33 x + 171$ $2^{2}\cdot 17^{3}\cdot 47$ $D_{4}$ (as 4T3) $[2]$ $51.2876032633$
4.2.938383.1 $x^{4} - x^{3} - 23 x^{2} + 137 x - 866$ $-\,17^{3}\cdot 191$ $D_{4}$ (as 4T3) $[4]$ $77.1594491964$
4.2.982600.1 $x^{4} - x^{3} - 23 x^{2} + 86 x - 254$ $-\,2^{3}\cdot 5^{2}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2, 2]$ $14.3162785409$
4.0.982600.1 $x^{4} - x^{3} + 62 x^{2} - 84 x + 936$ $2^{3}\cdot 5^{2}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2, 14]$ $4.18942509452$
4.2.997339.1 $x^{4} - 17 x + 17$ $-\,7\cdot 17^{3}\cdot 29$ $S_4$ (as 4T5) $[4]$ $7.08178620818$
4.4.1021904.1 $x^{4} - 34 x^{2} + 221$ $2^{4}\cdot 13\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2]$ $58.676263881$
4.0.1105425.1 $x^{4} - x^{3} + 62 x^{2} + x + 1021$ $3^{2}\cdot 5^{2}\cdot 17^{3}$ $C_4$ (as 4T1) $[2, 2]$ $4.18942509452$
4.2.1174207.1 $x^{4} - 2 x^{3} - 7 x^{2} + 8 x - 256$ $-\,17^{3}\cdot 239$ $D_{4}$ (as 4T3) $[4]$ $79.7779219572$
4.2.1233163.1 $x^{4} - 2 x^{3} + 44 x^{2} - 43 x - 256$ $-\,17^{3}\cdot 251$ $D_{4}$ (as 4T3) $[4]$ $23.597911336$
4.0.1257728.1 $x^{4} + 17$ $2^{8}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2, 8]$ $6.99416141276$
4.0.1316684.1 $x^{4} + 68 x^{2} + 1139$ $2^{2}\cdot 17^{3}\cdot 67$ $D_{4}$ (as 4T3) $[2, 4]$ $4.18942509452$
4.4.1316684.1 $x^{4} - 68 x^{2} + 1139$ $2^{2}\cdot 17^{3}\cdot 67$ $D_{4}$ (as 4T3) $[2]$ $137.426889776$
4.2.1331423.1 $x^{4} - x^{3} + 11 x^{2} + 137 x - 1172$ $-\,17^{3}\cdot 271$ $D_{4}$ (as 4T3) $[8]$ $49.1109241149$
4.0.1341249.1 $x^{4} + 17 x^{2} - 17 x + 272$ $3\cdot 7\cdot 13\cdot 17^{3}$ $S_4$ (as 4T5) $[4]$ $26.268343709$
4.0.1355988.1 $x^{4} - x^{3} + 11 x^{2} + x + 18$ $2^{2}\cdot 3\cdot 17^{3}\cdot 23$ $S_4$ (as 4T5) $[4]$ $71.9404132168$
4.2.1414944.1 $x^{4} + 51 x^{2} - 306$ $-\,2^{5}\cdot 3^{2}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2, 2]$ $24.4831255993$
4.0.1414944.1 $x^{4} + 51 x^{2} + 306$ $2^{5}\cdot 3^{2}\cdot 17^{3}$ $D_{4}$ (as 4T3) $[2, 2, 4]$ $4.18942509452$
4.4.1439509.1 $x^{4} - x^{3} - 74 x^{2} + 69 x + 1157$ $17^{3}\cdot 293$ $D_{4}$ (as 4T3) $[2]$ $112.311630961$
4.2.1493552.2 $x^{4} - 34 x - 17$ $-\,2^{4}\cdot 17^{3}\cdot 19$ $S_4$ (as 4T5) $[4]$ $28.5946836775$
4.2.1508291.1 $x^{4} - 2 x^{3} + 10 x^{2} - 9 x - 324$ $-\,17^{3}\cdot 307$ $D_{4}$ (as 4T3) $[8]$ $18.1854529665$
4.2.1690072.1 $x^{4} + 17 x^{2} - 1462$ $-\,2^{3}\cdot 17^{3}\cdot 43$ $D_{4}$ (as 4T3) $[2]$ $33.836701162$
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