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Label Polynomial Discriminant Galois group Class group Regulator
4.0.2197.1 $x^{4} - x^{3} + 2 x^{2} + 4 x + 3$ $13^{3}$ $C_4$ (as 4T1) trivial $2.38952643457$
4.4.19773.1 $x^{4} - x^{3} - 11 x^{2} - 9 x + 3$ $3^{2}\cdot 13^{3}$ $C_4$ (as 4T1) trivial $9.44732277257$
4.4.35152.1 $x^{4} - 13 x^{2} + 13$ $2^{4}\cdot 13^{3}$ $C_4$ (as 4T1) trivial $8.93062001005$
4.2.50531.1 $x^{4} - 2 x^{3} + 8 x^{2} - 7 x - 17$ $-\,13^{3}\cdot 23$ $D_{4}$ (as 4T3) trivial $5.45536139347$
4.4.63713.1 $x^{4} - x^{3} - 11 x^{2} + 4 x + 16$ $13^{3}\cdot 29$ $D_{4}$ (as 4T3) trivial $25.8341433054$
4.2.94471.1 $x^{4} - x^{3} - 11 x^{2} - 22 x - 36$ $-\,13^{3}\cdot 43$ $D_{4}$ (as 4T3) trivial $23.3447582997$
4.0.105456.1 $x^{4} + 13 x^{2} + 39$ $2^{4}\cdot 3\cdot 13^{3}$ $D_{4}$ (as 4T3) $[2, 2]$ $2.38952643457$
4.4.105456.1 $x^{4} - 13 x^{2} + 39$ $2^{4}\cdot 3\cdot 13^{3}$ $D_{4}$ (as 4T3) trivial $36.8710665742$
4.2.112047.1 $x^{4} - 2 x^{3} - 5 x^{2} + 6 x - 43$ $-\,3\cdot 13^{3}\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $9.31024114061$
4.2.112047.2 $x^{4} - x^{3} + 15 x^{2} + 30 x - 36$ $-\,3\cdot 13^{3}\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $16.4908377198$
4.0.116441.1 $x^{4} - 2 x^{3} + 21 x^{2} - 20 x + 48$ $13^{3}\cdot 53$ $D_{4}$ (as 4T3) $[8]$ $2.38952643457$
4.0.134017.1 $x^{4} - x^{3} + 15 x^{2} - 22 x + 68$ $13^{3}\cdot 61$ $D_{4}$ (as 4T3) $[4]$ $2.38952643457$
4.2.140608.1 $x^{4} - 52$ $-\,2^{6}\cdot 13^{3}$ $D_{4}$ (as 4T3) trivial $24.6378072219$
4.2.164775.1 $x^{4} - x^{3} + 15 x^{2} - 48 x - 36$ $-\,3\cdot 5^{2}\cdot 13^{3}$ $D_{4}$ (as 4T3) $[2]$ $20.6493211639$
4.2.202124.1 $x^{4} - 2 x^{3} + 8 x^{2} + 6 x - 4$ $-\,2^{2}\cdot 13^{3}\cdot 23$ $S_4$ (as 4T5) $[2]$ $31.0254430133$
4.2.208715.1 $x^{4} - 13 x + 13$ $-\,5\cdot 13^{3}\cdot 19$ $S_4$ (as 4T5) $[2]$ $11.7587433585$
4.2.226291.1 $x^{4} - x^{3} - 11 x^{2} + 43 x - 101$ $-\,13^{3}\cdot 103$ $D_{4}$ (as 4T3) trivial $27.9027111237$
4.0.237276.1 $x^{4} - x^{3} + 15 x^{2} + 17 x + 16$ $2^{2}\cdot 3^{3}\cdot 13^{3}$ $D_{4}$ (as 4T3) $[2, 4]$ $9.20933970133$
4.0.237276.2 $x^{4} + 39$ $2^{2}\cdot 3^{3}\cdot 13^{3}$ $D_{4}$ (as 4T3) $[2, 4]$ $6.30951472956$
4.4.248261.1 $x^{4} - 2 x^{3} - 18 x^{2} + 19 x + 87$ $13^{3}\cdot 113$ $D_{4}$ (as 4T3) trivial $38.1400276411$
4.2.279019.1 $x^{4} - x^{3} - 11 x^{2} - 35 x - 101$ $-\,13^{3}\cdot 127$ $D_{4}$ (as 4T3) $[3]$ $9.82816112783$
4.0.316368.2 $x^{4} + 39 x^{2} + 117$ $2^{4}\cdot 3^{2}\cdot 13^{3}$ $C_4$ (as 4T1) $[2, 2, 2]$ $2.38952643457$
4.2.322959.1 $x^{4} - x^{3} - 24 x^{2} + 69 x - 153$ $-\,3\cdot 7^{2}\cdot 13^{3}$ $D_{4}$ (as 4T3) $[2]$ $29.7816556869$
4.4.344929.1 $x^{4} - x^{3} - 24 x^{2} + 17 x + 107$ $13^{3}\cdot 157$ $D_{4}$ (as 4T3) trivial $40.6333360158$
4.2.393263.1 $x^{4} - x^{3} + 2 x^{2} + 43 x - 153$ $-\,13^{3}\cdot 179$ $D_{4}$ (as 4T3) trivial $91.9166714914$
4.2.421824.1 $x^{4} - 26 x^{2} - 156$ $-\,2^{6}\cdot 3\cdot 13^{3}$ $D_{4}$ (as 4T3) $[2]$ $13.7583411088$
4.2.421824.2 $x^{4} + 26 x^{2} - 156$ $-\,2^{6}\cdot 3\cdot 13^{3}$ $D_{4}$ (as 4T3) $[2]$ $27.4814481374$
4.2.437203.1 $x^{4} - x^{3} + 28 x^{2} + 56 x - 153$ $-\,13^{3}\cdot 199$ $D_{4}$ (as 4T3) trivial $33.3199608934$
4.2.454779.1 $x^{4} - 2 x^{3} - 18 x^{2} + 19 x - 173$ $-\,3^{2}\cdot 13^{3}\cdot 23$ $D_{4}$ (as 4T3) $[2, 2]$ $8.40482099894$
4.2.483340.1 $x^{4} - 26 x - 52$ $-\,2^{2}\cdot 5\cdot 11\cdot 13^{3}$ $S_4$ (as 4T5) $[2]$ $48.0676438985$
4.0.494325.1 $x^{4} - x^{3} - 11 x^{2} + 30 x + 120$ $3^{2}\cdot 5^{2}\cdot 13^{3}$ $D_{4}$ (as 4T3) $[2, 8]$ $8.64159561709$
4.0.520689.1 $x^{4} - 2 x^{3} + 47 x^{2} - 46 x + 204$ $3\cdot 13^{3}\cdot 79$ $D_{4}$ (as 4T3) $[2, 12]$ $2.38952643457$
4.4.520689.1 $x^{4} - x^{3} - 37 x^{2} - 22 x + 172$ $3\cdot 13^{3}\cdot 79$ $D_{4}$ (as 4T3) trivial $56.7773667534$
4.2.551447.1 $x^{4} - 13 x^{2} - 13 x + 13$ $-\,13^{3}\cdot 251$ $S_4$ (as 4T5) $[2]$ $29.9597319626$
4.2.551447.2 $x^{4} - 2 x^{3} - 31 x^{2} + 32 x - 212$ $-\,13^{3}\cdot 251$ $D_{4}$ (as 4T3) trivial $34.9608037836$
4.0.562432.1 $x^{4} + 13$ $2^{8}\cdot 13^{3}$ $D_{4}$ (as 4T3) $[4]$ $10.3107489691$
4.0.573417.1 $x^{4} - x^{3} + 28 x^{2} - 9 x + 237$ $3^{2}\cdot 13^{3}\cdot 29$ $D_{4}$ (as 4T3) $[2, 2, 4]$ $2.38952643457$
4.4.590993.1 $x^{4} - x^{3} - 50 x^{2} + 95 x + 159$ $13^{3}\cdot 269$ $D_{4}$ (as 4T3) trivial $92.3648049943$
4.2.597584.1 $x^{4} - 13 x^{2} - 221$ $-\,2^{4}\cdot 13^{3}\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $11.7300838898$
4.2.597584.2 $x^{4} + 13 x^{2} - 221$ $-\,2^{4}\cdot 13^{3}\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $48.7985223314$
4.2.621751.1 $x^{4} - 2 x^{3} + 21 x^{2} - 20 x - 225$ $-\,13^{3}\cdot 283$ $D_{4}$ (as 4T3) $[5]$ $13.8776503115$
4.0.634933.1 $x^{4} - x^{3} + 54 x^{2} + 56 x + 263$ $13^{3}\cdot 17^{2}$ $C_4$ (as 4T1) $[2, 2]$ $2.38952643457$
4.2.665691.1 $x^{4} - x^{3} + 2 x^{2} + 56 x - 257$ $-\,3\cdot 13^{3}\cdot 101$ $D_{4}$ (as 4T3) $[2]$ $16.0119364533$
4.2.665691.2 $x^{4} - x^{3} - 24 x^{2} + 82 x - 283$ $-\,3\cdot 13^{3}\cdot 101$ $D_{4}$ (as 4T3) $[2]$ $27.0933127313$
4.2.683267.1 $x^{4} - 2 x^{3} + 8 x^{2} - 7 x - 251$ $-\,13^{3}\cdot 311$ $D_{4}$ (as 4T3) trivial $18.2521350098$
4.4.687661.1 $x^{4} - 2 x^{3} - 44 x^{2} + 45 x + 243$ $13^{3}\cdot 313$ $D_{4}$ (as 4T3) trivial $117.693823642$
4.0.705237.1 $x^{4} - 2 x^{3} + 34 x^{2} - 33 x + 269$ $3\cdot 13^{3}\cdot 107$ $D_{4}$ (as 4T3) $[2, 4]$ $2.38952643457$
4.4.705237.1 $x^{4} - x^{3} - 37 x^{2} - 9 x + 237$ $3\cdot 13^{3}\cdot 107$ $D_{4}$ (as 4T3) trivial $38.1259568625$
4.0.790920.1 $x^{4} - x^{3} + 2 x^{2} - 35 x + 55$ $2^{3}\cdot 3^{2}\cdot 5\cdot 13^{3}$ $D_{4}$ (as 4T3) $[2, 8]$ $3.10714061537$
4.0.790920.4 $x^{4} - x^{3} + 15 x^{2} + 95 x + 250$ $2^{3}\cdot 3^{2}\cdot 5\cdot 13^{3}$ $D_{4}$ (as 4T3) $[2, 8]$ $9.50012732134$
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