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Label Polynomial Discriminant Galois group Class group Regulator
5.1.609880344.1 $x^{5} - 71 x^{2} + 213 x - 1065$ $2^{3}\cdot 3\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $254.797572206$
5.5.2032934480.1 $x^{5} - x^{4} - 28 x^{3} + 34 x^{2} + 25 x - 1$ $2^{4}\cdot 5\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $527.704364604$
5.1.3176460125.2 $x^{5} - x^{4} - 28 x^{3} + 176 x^{2} - 472 x + 496$ $5^{3}\cdot 71^{4}$ $F_5$ (as 5T3) $[5]$ $382.315786668$
5.1.7725151024.1 $x^{5} - 2 x^{4} + 30 x^{3} - 12 x^{2} + 400 x - 600$ $2^{4}\cdot 19\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $1463.30862678$
5.3.8716206583.1 $x^{5} - 2 x^{4} + 30 x^{3} + 59 x^{2} - 1304 x - 387$ $-\,7^{3}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $413.092725823$
5.1.10977846192.2 $x^{5} - x^{4} - 28 x^{3} + 176 x^{2} + 451 x - 3551$ $2^{4}\cdot 3^{3}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $1024.80336052$
5.1.13036192353.1 $x^{5} - x^{4} + 43 x^{3} - 179 x^{2} + 380 x - 143$ $3^{3}\cdot 19\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $273.116538937$
5.1.14637128256.1 $x^{5} - x^{4} - 28 x^{3} + 34 x^{2} + 238 x - 498$ $2^{6}\cdot 3^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[15]$ $275.003234611$
5.1.16466769288.2 $x^{5} - 2 x^{4} - 41 x^{3} - 83 x^{2} - 26 x - 245$ $2^{3}\cdot 3^{4}\cdot 71^{4}$ $S_5$ (as 5T5) $[15]$ $768.702563683$
5.1.20329344800.1 $x^{5} - x^{4} - 28 x^{3} - 250 x^{2} - 1537 x - 3125$ $2^{5}\cdot 5^{2}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $2476.58341266$
5.1.21955692384.1 $x^{5} - 2 x^{4} + 30 x^{3} - 438 x^{2} + 3240 x - 6564$ $2^{5}\cdot 3^{3}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $3758.53178185$
5.1.24420625441.1 $x^{5} - 2 x^{4} + 30 x^{3} - 83 x^{2} + 258 x - 1097$ $31^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[15]$ $55.2940699259$
5.3.25208387552.1 $x^{5} - x^{4} - 28 x^{3} + 34 x^{2} + 96 x - 640$ $-\,2^{5}\cdot 31\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $5846.55568591$
5.3.28638964487.1 $x^{5} - x^{4} - 99 x^{3} - 37 x^{2} + 2652 x - 5113$ $-\,7^{2}\cdot 23\cdot 71^{4}$ $S_5$ (as 5T5) $[10]$ $277.803262761$
5.1.31129309225.1 $x^{5} + 142 x^{3} - 71 x^{2} + 852 x + 1136$ $5^{2}\cdot 7^{2}\cdot 71^{4}$ $D_{5}$ (as 5T2) $[5]$ $2540.65117047$
5.3.35576353400.1 $x^{5} - x^{4} - 99 x^{3} - 321 x^{2} - 46 x - 214$ $-\,2^{3}\cdot 5^{2}\cdot 7\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $1607.62824311$
5.1.43911384768.2 $x^{5} + 71 x^{3} - 1917 x - 3834$ $2^{6}\cdot 3^{3}\cdot 71^{4}$ $S_5$ (as 5T5) $[20]$ $789.596124276$
5.1.43911384768.3 $x^{5} - x^{4} + 43 x^{3} - 37 x^{2} + 25 x - 1$ $2^{6}\cdot 3^{3}\cdot 71^{4}$ $S_5$ (as 5T5) $[15]$ $724.397340683$
5.1.44826205284.1 $x^{5} + 71 x^{3} - 71 x^{2} + 1278 x - 2485$ $2^{2}\cdot 3^{2}\cdot 7^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[10]$ $2239.44964915$
5.1.49400307864.2 $x^{5} - 2 x^{4} + 30 x^{3} + 343 x^{2} - 1304 x + 1104$ $2^{3}\cdot 3^{5}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $7431.49642043$
5.1.51458654025.1 $x^{5} - 2 x^{4} + 101 x^{3} - 367 x^{2} + 2459 x - 14303$ $3^{4}\cdot 5^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[5]$ $714.301573838$
5.1.52043122688.3 $x^{5} - 2 x^{4} + 30 x^{3} + 272 x^{2} + 1465 x - 4150$ $2^{11}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $2124.83249357$
5.1.65867077152.1 $x^{5} - x^{4} + 43 x^{3} - 179 x^{2} - 3880 x - 8876$ $2^{5}\cdot 3^{4}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $2483.88622512$
5.1.76870335025.1 $x^{5} - x^{4} - 28 x^{3} - 889 x^{2} - 2957 x - 10509$ $5^{2}\cdot 11^{2}\cdot 71^{4}$ $D_{5}$ (as 5T2) $[5]$ $1834.33745599$
5.1.76870335025.2 $x^{5} - 2 x^{4} + 101 x^{3} - 12 x^{2} - 736 x - 4008$ $5^{2}\cdot 11^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[10]$ $2322.07826403$
5.1.79691031616.1 $x^{5} - x^{4} - 28 x^{3} - 250 x^{2} - 614 x - 782$ $2^{6}\cdot 7^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[5]$ $4385.20149513$
5.1.79691031616.2 $x^{5} - x^{4} - 28 x^{3} + 176 x^{2} - 756 x + 1348$ $2^{6}\cdot 7^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[15]$ $1164.78851492$
5.1.79691031616.3 $x^{5} - x^{4} - 28 x^{3} - 392 x^{2} + 3220 x - 4900$ $2^{6}\cdot 7^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[5]$ $5229.65878839$
5.1.85484894884.1 $x^{5} - x^{4} - 99 x^{3} + 602 x^{2} - 472 x + 212$ $2^{2}\cdot 29^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[5]$ $2343.52250337$
5.1.100858961889.2 $x^{5} - 2 x^{4} + 30 x^{3} - 367 x^{2} - 1162 x + 9411$ $3^{4}\cdot 7^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[5]$ $2202.44592889$
5.1.117097026048.1 $x^{5} - x^{4} - 28 x^{3} - 392 x^{2} + 2581 x - 1705$ $2^{9}\cdot 3^{2}\cdot 71^{4}$ $S_5$ (as 5T5) $[10]$ $1645.12750272$
5.1.123500769660.1 $x^{5} - x^{4} - 99 x^{3} + 318 x^{2} - 1182 x + 17820$ $2^{2}\cdot 3^{5}\cdot 5\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $13372.624383$
5.1.156129368064.1 $x^{5} - 2 x^{4} + 172 x^{3} - 296 x^{2} + 8068 x - 8552$ $2^{11}\cdot 3\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $4185.8510756$
5.5.164667692880.1 $x^{5} - x^{4} - 170 x^{3} + 602 x^{2} + 4285 x - 14485$ $2^{4}\cdot 3^{4}\cdot 5\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $26400.3204018$
5.1.196788057664.5 $x^{5} - x^{4} - 28 x^{3} - 108 x^{2} - 259 x - 569$ $2^{6}\cdot 11^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[5]$ $2477.0743046818857$
5.1.197601231456.2 $x^{5} - 2 x^{4} - 41 x^{3} + 414 x^{2} - 594 x + 252$ $2^{5}\cdot 3^{5}\cdot 71^{4}$ $S_5$ (as 5T5) $[15]$ $7796.96990674$
5.1.203293448000.1 $x^{5} - x^{4} + 114 x^{3} - 250 x^{2} + 2865 x - 7385$ $2^{6}\cdot 5^{3}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $5796.28104169$
5.3.214068000744.1 $x^{5} - x^{4} + 43 x^{3} - 250 x^{2} - 1466 x - 640$ $-\,2^{3}\cdot 3^{4}\cdot 13\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $23958.3000914$
5.1.239073094848.1 $x^{5} - x^{4} - 28 x^{3} + 176 x^{2} + 1303 x - 40187$ $2^{6}\cdot 3\cdot 7^{2}\cdot 71^{4}$ $S_5$ (as 5T5) $[10]$ $2708.60870202$
5.1.239073094848.2 $x^{5} - x^{4} - 28 x^{3} + 176 x^{2} + 1587 x - 711$ $2^{6}\cdot 3\cdot 7^{2}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $8939.51798005$
5.1.257293270125.1 $x^{5} - 5751$ $3^{4}\cdot 5^{3}\cdot 71^{4}$ $F_5$ (as 5T3) $[5, 5]$ $611.833525416$
5.1.268957231704.1 $x^{5} - x^{4} + 43 x^{3} + 1028 x^{2} + 4498 x + 5324$ $2^{3}\cdot 3^{3}\cdot 7^{2}\cdot 71^{4}$ $S_5$ (as 5T5) $[10]$ $8369.58974233$
5.1.274446154800.4 $x^{5} - x^{4} - 99 x^{3} + 1099 x^{2} + 13799 x + 34221$ $2^{4}\cdot 3^{3}\cdot 5^{2}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $9217.54776154$
5.1.274852741696.2 $x^{5} - 2 x^{4} + 30 x^{3} - 1148 x^{2} - 2440 x - 30704$ $2^{6}\cdot 13^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[5]$ $22066.3441077$
5.1.301916181961.1 $x^{5} - x^{4} + 43 x^{3} + 34 x^{2} + 25 x + 638$ $71^{4}\cdot 109^{2}$ $A_5$ (as 5T4) $[15]$ $1573.851846809876$
5.1.324481754689.1 $x^{5} - 2 x^{4} + 101 x^{3} - 83 x^{2} + 1607 x + 4725$ $71^{4}\cdot 113^{2}$ $A_5$ (as 5T4) $[15]$ $1164.74907604$
5.1.341736286088.1 $x^{5} - 2 x^{4} - 41 x^{3} + 272 x^{2} + 1678 x - 4008$ $2^{3}\cdot 41^{2}\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $63180.9358634$
5.3.360210578175.1 $x^{5} - 2 x^{4} + 30 x^{3} - 225 x^{2} - 3150 x + 4725$ $-\,3^{4}\cdot 5^{2}\cdot 7\cdot 71^{4}$ $S_5$ (as 5T5) $[10]$ $3810.09111895$
5.3.364301858816.1 $x^{5} - x^{4} - 170 x^{3} + 1170 x^{2} - 1537 x - 2415$ $-\,2^{11}\cdot 7\cdot 71^{4}$ $S_5$ (as 5T5) $[5]$ $17354.2612123$
5.1.365928206400.1 $x^{5} - x^{4} - 28 x^{3} - 392 x^{2} + 4711 x - 2131$ $2^{6}\cdot 3^{2}\cdot 5^{2}\cdot 71^{4}$ $A_5$ (as 5T4) $[15]$ $2024.59534867$
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