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Label Polynomial Discriminant Galois group Class group Regulator
4.0.14336.1 $x^{4} + 8 x^{2} + 14$ $2^{11}\cdot 7$ $D_{4}$ (as 4T3) $[2]$ $1.76274717404$
4.4.14336.1 $x^{4} - 8 x^{2} + 14$ $2^{11}\cdot 7$ $D_{4}$ (as 4T3) trivial $9.01371174698$
4.2.18432.3 $x^{4} - 18$ $-\,2^{11}\cdot 3^{2}$ $D_{4}$ (as 4T3) trivial $7.43601643081$
4.0.47104.1 $x^{4} + 16 x^{2} + 46$ $2^{11}\cdot 23$ $D_{4}$ (as 4T3) $[6]$ $1.76274717404$
4.4.47104.1 $x^{4} - 16 x^{2} + 46$ $2^{11}\cdot 23$ $D_{4}$ (as 4T3) trivial $15.4151521533$
4.2.51200.1 $x^{4} + 4 x^{2} - 8 x + 2$ $-\,2^{11}\cdot 5^{2}$ $S_4$ (as 4T5) $[2]$ $9.83438807788$
4.2.51200.3 $x^{4} - 50$ $-\,2^{11}\cdot 5^{2}$ $D_{4}$ (as 4T3) $[2]$ $6.82915669795$
4.2.83968.1 $x^{4} - 8 x^{2} - 82$ $-\,2^{11}\cdot 41$ $D_{4}$ (as 4T3) $[2]$ $8.97915798253$
4.2.83968.2 $x^{4} + 8 x^{2} - 82$ $-\,2^{11}\cdot 41$ $D_{4}$ (as 4T3) $[2]$ $5.11128925853$
4.0.145408.2 $x^{4} - 4 x^{2} - 8 x + 18$ $2^{11}\cdot 71$ $S_4$ (as 4T5) $[2]$ $9.86465068566$
4.4.145408.2 $x^{4} - 24 x^{2} + 142$ $2^{11}\cdot 71$ $D_{4}$ (as 4T3) trivial $38.9202733523$
4.0.145408.3 $x^{4} + 24 x^{2} + 142$ $2^{11}\cdot 71$ $D_{4}$ (as 4T3) $[6]$ $1.76274717404$
4.2.149504.1 $x^{4} - 8 x^{2} - 146$ $-\,2^{11}\cdot 73$ $D_{4}$ (as 4T3) trivial $17.7457831194$
4.2.149504.2 $x^{4} + 8 x^{2} - 146$ $-\,2^{11}\cdot 73$ $D_{4}$ (as 4T3) trivial $28.1686213664$
4.2.182272.1 $x^{4} - 16 x^{2} - 178$ $-\,2^{11}\cdot 89$ $D_{4}$ (as 4T3) trivial $10.5001439408$
4.2.182272.2 $x^{4} + 16 x^{2} - 178$ $-\,2^{11}\cdot 89$ $D_{4}$ (as 4T3) trivial $26.0876710453$
4.0.210944.1 $x^{4} + 32 x^{2} + 206$ $2^{11}\cdot 103$ $D_{4}$ (as 4T3) $[6]$ $1.76274717404$
4.4.210944.1 $x^{4} - 32 x^{2} + 206$ $2^{11}\cdot 103$ $D_{4}$ (as 4T3) trivial $33.3528408081$
4.0.243712.1 $x^{4} + 32 x^{2} + 238$ $2^{11}\cdot 7\cdot 17$ $D_{4}$ (as 4T3) $[2, 4]$ $1.76274717404$
4.4.243712.1 $x^{4} - 32 x^{2} + 238$ $2^{11}\cdot 7\cdot 17$ $D_{4}$ (as 4T3) trivial $49.9319909232$
4.0.243712.2 $x^{4} + 40 x^{2} + 238$ $2^{11}\cdot 7\cdot 17$ $D_{4}$ (as 4T3) $[2, 6]$ $1.76274717404$
4.4.243712.2 $x^{4} - 40 x^{2} + 238$ $2^{11}\cdot 7\cdot 17$ $D_{4}$ (as 4T3) trivial $36.4464562873$
4.2.247808.3 $x^{4} - 242$ $-\,2^{11}\cdot 11^{2}$ $D_{4}$ (as 4T3) trivial $31.3415233334$
4.0.260096.5 $x^{4} + 16 x^{2} - 16 x + 78$ $2^{11}\cdot 127$ $S_4$ (as 4T5) $[2]$ $22.7747102314$
4.2.280576.3 $x^{4} - 16 x^{2} - 274$ $-\,2^{11}\cdot 137$ $D_{4}$ (as 4T3) $[2]$ $15.2687841034$
4.2.280576.4 $x^{4} + 16 x^{2} - 274$ $-\,2^{11}\cdot 137$ $D_{4}$ (as 4T3) $[2]$ $13.1129640247$
4.0.309248.1 $x^{4} + 40 x^{2} + 302$ $2^{11}\cdot 151$ $D_{4}$ (as 4T3) $[10]$ $1.76274717404$
4.4.309248.1 $x^{4} - 40 x^{2} + 302$ $2^{11}\cdot 151$ $D_{4}$ (as 4T3) trivial $29.2697374986$
4.2.313344.1 $x^{4} - 24 x^{2} - 306$ $-\,2^{11}\cdot 3^{2}\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $20.2912085301$
4.2.313344.2 $x^{4} + 24 x^{2} - 306$ $-\,2^{11}\cdot 3^{2}\cdot 17$ $D_{4}$ (as 4T3) $[2]$ $9.06187459621$
4.0.342016.1 $x^{4} + 48 x^{2} + 334$ $2^{11}\cdot 167$ $D_{4}$ (as 4T3) $[14]$ $1.76274717404$
4.4.342016.1 $x^{4} - 48 x^{2} + 334$ $2^{11}\cdot 167$ $D_{4}$ (as 4T3) trivial $50.9187348659$
4.2.346112.1 $x^{4} - 338$ $-\,2^{11}\cdot 13^{2}$ $D_{4}$ (as 4T3) $[2]$ $15.6090905476$
4.0.407552.1 $x^{4} + 40 x^{2} + 398$ $2^{11}\cdot 199$ $D_{4}$ (as 4T3) $[10]$ $1.76274717404$
4.4.407552.1 $x^{4} - 40 x^{2} + 398$ $2^{11}\cdot 199$ $D_{4}$ (as 4T3) trivial $46.872855375$
4.2.444416.1 $x^{4} - 32 x - 8$ $-\,2^{11}\cdot 7\cdot 31$ $S_4$ (as 4T5) $[2]$ $26.5823945707$
4.2.444416.3 $x^{4} - 8 x^{2} - 434$ $-\,2^{11}\cdot 7\cdot 31$ $D_{4}$ (as 4T3) $[2]$ $23.3930965265$
4.2.444416.4 $x^{4} + 8 x^{2} - 434$ $-\,2^{11}\cdot 7\cdot 31$ $D_{4}$ (as 4T3) $[2, 2]$ $10.2314078594$
4.2.444416.5 $x^{4} + 24 x^{2} - 434$ $-\,2^{11}\cdot 7\cdot 31$ $D_{4}$ (as 4T3) $[2]$ $22.1511049007$
4.2.444416.6 $x^{4} - 24 x^{2} - 434$ $-\,2^{11}\cdot 7\cdot 31$ $D_{4}$ (as 4T3) $[2]$ $14.3651767143$
4.2.477184.1 $x^{4} - 32 x^{2} - 466$ $-\,2^{11}\cdot 233$ $D_{4}$ (as 4T3) trivial $34.0815693871$
4.2.477184.2 $x^{4} + 32 x^{2} - 466$ $-\,2^{11}\cdot 233$ $D_{4}$ (as 4T3) trivial $32.9909958184$
4.0.538624.1 $x^{4} + 48 x^{2} + 526$ $2^{11}\cdot 263$ $D_{4}$ (as 4T3) $[10]$ $1.76274717404$
4.4.538624.1 $x^{4} - 48 x^{2} + 526$ $2^{11}\cdot 263$ $D_{4}$ (as 4T3) trivial $78.492632393$
4.2.559104.2 $x^{4} - 32 x - 114$ $-\,2^{11}\cdot 3\cdot 7\cdot 13$ $S_4$ (as 4T5) $[2]$ $62.1766618421$
4.0.571392.1 $x^{4} + 48 x^{2} + 558$ $2^{11}\cdot 3^{2}\cdot 31$ $D_{4}$ (as 4T3) $[2, 6]$ $1.76274717404$
4.4.571392.1 $x^{4} - 48 x^{2} + 558$ $2^{11}\cdot 3^{2}\cdot 31$ $D_{4}$ (as 4T3) trivial $62.0571421798$
4.2.575488.1 $x^{4} - 8 x^{2} - 562$ $-\,2^{11}\cdot 281$ $D_{4}$ (as 4T3) trivial $34.80664967$
4.2.575488.2 $x^{4} + 8 x^{2} - 562$ $-\,2^{11}\cdot 281$ $D_{4}$ (as 4T3) trivial $42.4297901901$
4.0.587776.5 $x^{4} - 4 x^{2} - 16 x + 60$ $2^{11}\cdot 7\cdot 41$ $S_4$ (as 4T5) $[2]$ $22.6273325609$
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