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Results (13 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
12.2.503...424.1 $x^{12} - 6 x^{10} - 4 x^{9} + 8 x^{8} + 18 x^{7} - 24 x^{6} - 16 x^{5} - 4 x^{4} + 26 x^{3} - 36 x^{2} + 72 x - 54$ $-\,2^{14}\cdot 11^{9}\cdot 19^{4}$ $S_3\times S_4$ (as 12T83) trivial $103041.24498711136$
12.2.283...376.1 $x^{12} - 6 x^{10} - 29 x^{9} + 8 x^{8} + 48 x^{7} + 9 x^{6} + 236 x^{5} + 238 x^{4} - 807 x^{3} - 3776 x^{2} + 8816 x - 5092$ $-\,2^{8}\cdot 11^{9}\cdot 19^{6}$ $S_3\times S_4$ (as 12T83) $[2]$ $288384.0579181684$
12.6.724...384.1 $x^{12} - 2 x^{11} - 10 x^{10} + 32 x^{9} - 20 x^{8} - 94 x^{7} + 76 x^{6} + 124 x^{5} + 44 x^{4} - 130 x^{3} - 12 x^{2} + 72 x - 54$ $-\,2^{14}\cdot 11^{9}\cdot 37^{4}$ $S_3\times S_4$ (as 12T83) trivial $685379.6015128667$
12.2.322...136.1 $x^{12} - 24 x^{10} - 34 x^{9} + 205 x^{8} + 1096 x^{7} - 1756 x^{6} - 8908 x^{5} + 9129 x^{4} + 27828 x^{3} - 17812 x^{2} - 11782 x - 34789$ $-\,2^{20}\cdot 11^{9}\cdot 19^{4}$ $C_2^6:S_3^2$ (as 12T239) trivial $638456.8358451137$
12.2.116...096.1 $x^{12} - 2 x^{11} + 32 x^{10} - 132 x^{9} + 322 x^{8} - 2340 x^{7} + 2848 x^{6} - 3740 x^{5} + 33440 x^{4} + 46168 x^{3} - 47792 x^{2} - 104792 x - 1000876$ $-\,2^{20}\cdot 11^{9}\cdot 19^{6}$ $C_2^6:S_3^2$ (as 12T239) $[2, 2, 2]$ $1782278.7579714607$
15.15.108...117.1 $x^{15} - 5 x^{14} - 42 x^{13} + 203 x^{12} + 595 x^{11} - 3150 x^{10} - 3122 x^{9} + 22950 x^{8} + 1310 x^{7} - 79947 x^{6} + 32585 x^{5} + 128275 x^{4} - 86317 x^{3} - 70917 x^{2} + 65258 x - 10429$ $7^{13}\cdot 11^{9}\cdot 41^{6}$ $S_5 \times C_3$ (as 15T24) trivial $22895742068.330822$
15.15.506...069.1 $x^{15} - 2 x^{14} - 123 x^{13} + 543 x^{12} + 4081 x^{11} - 30139 x^{10} + 2175 x^{9} + 450400 x^{8} - 1273256 x^{7} + 337628 x^{6} + 3724726 x^{5} - 5525825 x^{4} + 362639 x^{3} + 4758998 x^{2} - 3622511 x + 810473$ $7^{9}\cdot 11^{9}\cdot 41^{6}\cdot 257^{5}$ $S_5 \times S_3$ (as 15T29) trivial $1166366831487468.5$
16.4.366...896.1 $x^{16} - 8 x^{15} + 36 x^{14} - 12 x^{13} - 668 x^{12} + 3952 x^{11} - 3520 x^{10} + 2036 x^{9} + 79488 x^{8} - 218772 x^{7} + 497532 x^{6} - 191828 x^{5} - 2225530 x^{4} + 2806716 x^{3} + 307824 x^{2} - 929324 x - 250525$ $2^{36}\cdot 11^{12}\cdot 19^{8}$ $S_4^2$ (as 16T1033) $[2, 2]$ $15815486605.457214$
18.6.471...448.1 $x^{18} - 9 x^{16} + 78 x^{14} - 144 x^{13} - 99 x^{12} + 396 x^{11} + 153 x^{10} - 1224 x^{9} + 1143 x^{8} + 108 x^{7} - 591 x^{6} - 36 x^{5} + 270 x^{4} + 144 x^{3} - 216 x^{2} + 27$ $2^{18}\cdot 3^{27}\cdot 11^{9}$ $C_3\times S_5$ (as 18T144) trivial $22164984.3022$
18.4.928...496.1 $x^{18} - 4 x^{16} - 6 x^{15} + 4 x^{14} + 20 x^{13} + 15 x^{12} - 16 x^{11} - 43 x^{10} - 20 x^{9} + 24 x^{8} + 46 x^{7} + 18 x^{6} - 16 x^{5} - 23 x^{4} - 6 x^{3} + 4 x^{2} + 4 x + 1$ $-\,2^{18}\cdot 3^{12}\cdot 11^{9}\cdot 28255589$ $C_3^6.C_2\wr S_5$ (as 18T956) trivial $14100703.6716$
18.6.381...288.1 $x^{18} - 18 x^{16} - 2 x^{15} + 171 x^{14} - 102 x^{13} - 1078 x^{12} + 2808 x^{11} - 2610 x^{10} - 1206 x^{9} + 5292 x^{8} - 6804 x^{7} + 6903 x^{6} - 6372 x^{5} + 6354 x^{4} - 3672 x^{3} + 864 x^{2} - 216 x + 24$ $2^{18}\cdot 3^{31}\cdot 11^{9}$ $C_3^5:S_5$ (as 18T666) $[3]$ $40288341.9434$
18.0.514...472.1 $x^{18} - 5 x^{17} - 57 x^{16} + 427 x^{15} + 813 x^{14} - 13739 x^{13} + 16317 x^{12} + 199993 x^{11} - 677626 x^{10} - 879916 x^{9} + 8397984 x^{8} - 9904800 x^{7} - 36337276 x^{6} + 123262908 x^{5} - 69138500 x^{4} - 301503956 x^{3} + 710796136 x^{2} - 649730832 x + 231002432$ $-\,2^{39}\cdot 11^{9}\cdot 139^{2}\cdot 241^{2}\cdot 59497^{2}$ $C_3^6.C_2^5:S_5$ (as 18T950) $[3]$ $22153523613900$
18.0.235...392.1 $x^{18} - 7 x^{17} - 119 x^{16} + 505 x^{15} + 7875 x^{14} - 7533 x^{13} - 302141 x^{12} - 536517 x^{11} + 5804272 x^{10} + 26659928 x^{9} - 18979992 x^{8} - 416809088 x^{7} - 1022194812 x^{6} + 748973780 x^{5} + 9798499652 x^{4} + 25453815876 x^{3} + 34515633440 x^{2} + 25326612192 x + 8018664736$ $-\,2^{39}\cdot 11^{9}\cdot 61^{2}\cdot 2209983163^{2}$ $C_3^6.C_2^5:S_5$ (as 18T950) $[3]$ $2172168164960000$
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