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Results (1-50 of 66 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
12.0.383...000.1 $x^{12} - 2 x^{11} - 2655 x^{10} + 30626 x^{9} + 2794178 x^{8} - 61394206 x^{7} - 1056750713 x^{6} + 45388322884 x^{5} - 213614397622 x^{4} - 10475330498744 x^{3} + 202244606841425 x^{2} - 1487737800981192 x + 4119599974126711$ $2^{8}\cdot 5^{6}\cdot 1987^{10}$ $C_6\times S_3$ (as 12T18) $[14834954463]$ $81967.42179171897$
12.0.893...824.1 $x^{12} - 6 x^{11} - 801 x^{10} - 1628 x^{9} + 247491 x^{8} + 2273274 x^{7} - 16161863 x^{6} - 308901720 x^{5} - 198352728 x^{4} + 21876938040 x^{3} + 199543281444 x^{2} + 875308419936 x + 2128888301904$ $2^{12}\cdot 3^{18}\cdot 29^{6}\cdot 79^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 18, 208960164]$ $8250184.422474623$
12.0.385...296.1 $x^{12} - 6 x^{11} - 765 x^{10} - 1808 x^{9} + 235287 x^{8} + 2323170 x^{7} - 12666443 x^{6} - 290076780 x^{5} - 118924380 x^{4} + 24752961048 x^{3} + 248950587492 x^{2} + 1209430276272 x + 3360978639648$ $2^{12}\cdot 3^{18}\cdot 37^{6}\cdot 79^{10}$ $C_6\times S_3$ (as 12T18) $[6, 6494997168]$ $8250184.422474623$
12.0.499...000.1 $x^{12} - 6 x^{11} - 5085 x^{10} - 36008 x^{9} + 8900883 x^{8} + 164325474 x^{7} - 5031619979 x^{6} - 159936754188 x^{5} - 138170138040 x^{4} + 41530911642192 x^{3} + 579546450124308 x^{2} + 3133104053728896 x + 6273234061497936$ $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 7^{10}\cdot 61^{10}$ $C_6\times S_3$ (as 12T18) $[2, 2, 6, 6, 6, 14670192]$ $173074543.80287683$
12.0.649...856.1 $x^{12} - 6 x^{11} - 1881 x^{10} + 4244 x^{9} + 1169847 x^{8} + 1695114 x^{7} - 240423735 x^{6} - 1207471608 x^{5} + 14645360520 x^{4} + 153483145376 x^{3} + 826167439248 x^{2} + 2100940721280 x + 3477464646400$ $2^{18}\cdot 3^{18}\cdot 13^{6}\cdot 163^{10}$ $C_6\times S_3$ (as 12T18) $[2, 2, 6, 6, 6, 13203864]$ $393558993.55902886$
12.0.968...000.1 $x^{12} - 6 x^{11} - 3573 x^{10} + 15512 x^{9} + 4529943 x^{8} - 16948710 x^{7} - 2382150891 x^{6} + 11329780860 x^{5} + 465933975300 x^{4} - 3048952327456 x^{3} - 6665564400276 x^{2} + 35903666420064 x + 189576458461216$ $2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 7^{10}\cdot 43^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 60, 44756880]$ $49579467.01527228$
12.0.132...304.2 $x^{12} - 58016 x^{9} - 4568760 x^{8} + 142371264 x^{7} + 3151197056 x^{6} - 83304942336 x^{5} + 10009688364816 x^{4} - 574204138240768 x^{3} + 19662632149450752 x^{2} - 396387387773981184 x + 5607170138021374720$ $2^{18}\cdot 3^{18}\cdot 7^{8}\cdot 19^{6}\cdot 37^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 3, 3, 24, 24, 24, 12264]$ $1260818083.4671302$
12.0.284...456.1 $x^{12} - 6 x^{11} - 1341 x^{10} + 6252 x^{9} + 701541 x^{8} - 2755350 x^{7} - 151696773 x^{6} + 739644858 x^{5} + 11608749171 x^{4} - 75791485620 x^{3} + 775877026401 x^{2} - 2176281050814 x + 24414797670795$ $2^{18}\cdot 3^{18}\cdot 37^{6}\cdot 127^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 6, 1370793744]$ $34390723.52637186$
12.0.799...064.1 $x^{12} - 6 x^{11} - 1809 x^{10} + 3884 x^{9} + 1105911 x^{8} + 1953018 x^{7} - 209071983 x^{6} - 1245534912 x^{5} + 12663507384 x^{4} + 174619614560 x^{3} + 1472792946576 x^{2} + 4906832145408 x + 14660937611776$ $2^{18}\cdot 3^{18}\cdot 29^{6}\cdot 163^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 18, 18, 10782864]$ $393558993.55902886$
12.0.882...384.1 $x^{12} - 2 x^{11} + 711 x^{10} + 9762 x^{9} + 321972 x^{8} + 6143982 x^{7} + 162092137 x^{6} + 2828597864 x^{5} + 46230405160 x^{4} + 508914584780 x^{3} + 4647550627755 x^{2} + 24875822694688 x + 97843374679561$ $2^{8}\cdot 3^{6}\cdot 37^{6}\cdot 1063^{10}$ $C_6\times S_3$ (as 12T18) $[4, 4, 12, 48, 1872, 3744]$ $49457906.04128972$
12.0.115...784.1 $x^{12} + 2522 x^{10} + 2195101 x^{8} + 876073494 x^{6} + 164823916206 x^{4} + 11888984525876 x^{2} + 5655383391025$ $2^{24}\cdot 7^{6}\cdot 31^{10}\cdot 61^{10}$ $C_6\times S_3$ (as 12T18) $[6, 6, 6, 6, 8827440]$ $117702399.81026176$
12.0.242...000.1 $x^{12} - 6 x^{11} - 6237 x^{10} + 14504 x^{9} + 12671739 x^{8} - 8549118 x^{7} - 9083471619 x^{6} + 36419353308 x^{5} + 2499196023684 x^{4} - 19349215951360 x^{3} - 128826203869344 x^{2} + 742823917733376 x + 4705758207548416$ $2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 523^{10}$ $C_6\times S_3$ (as 12T18) $[2, 2, 2, 2, 2, 12, 84, 1643124]$ $366719060.6779844$
12.0.243...784.1 $x^{12} - 2928 x^{10} - 10868 x^{9} + 2801520 x^{8} + 21518640 x^{7} - 898126212 x^{6} - 11596590720 x^{5} + 56770726680 x^{4} + 1776082511632 x^{3} + 12798055612224 x^{2} + 41721272488896 x + 56386602696592$ $2^{22}\cdot 3^{18}\cdot 11^{6}\cdot 13^{10}\cdot 19^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 12, 75002184]$ $165821683.26346493$
12.0.286...000.1 $x^{12} - 4800 x^{10} - 8060 x^{9} + 7704288 x^{8} + 11606400 x^{7} - 4662407460 x^{6} + 12003919200 x^{5} + 1127848776696 x^{4} - 7694506049360 x^{3} - 48400609276800 x^{2} + 227148127065600 x + 1816016775043600$ $2^{22}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10}\cdot 31^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 12, 90862980]$ $237029660.10451075$
12.0.593...304.1 $x^{12} - 79310 x^{9} + 1408113 x^{8} - 28919310 x^{7} + 3089662366 x^{6} - 138859927920 x^{5} + 10480736892948 x^{4} - 325015634622840 x^{3} + 7319172918732696 x^{2} - 312222822290053920 x + 6606210679486824000$ $2^{12}\cdot 3^{18}\cdot 7^{8}\cdot 13^{6}\cdot 103^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 6, 18, 21608244]$ $12617106559.763407$
12.0.620...856.1 $x^{12} - 2 x^{11} - 4509 x^{10} + 65792 x^{9} + 6884543 x^{8} - 179824546 x^{7} - 3048549659 x^{6} + 145968008212 x^{5} - 703780876036 x^{4} - 32042482767464 x^{3} + 541531279966148 x^{2} - 3173042769163056 x + 6534516199010704$ $2^{18}\cdot 7^{6}\cdot 3391^{10}$ $C_6\times S_3$ (as 12T18) $[12719373696]$ $3767329824.5719085$
12.0.623...000.1 $x^{12} + 10452 x^{10} + 38144574 x^{8} + 57531852924 x^{6} + 32790995605017 x^{4} + 4052694227324184 x^{2} + 130563771381832464$ $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10}\cdot 67^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 6, 36, 27614772]$ $581866860.457979$
12.0.623...000.2 $x^{12} - 6968 x^{9} + 1835543658 x^{6} + 26867082872032 x^{3} + 218016120423040381$ $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10}\cdot 67^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 3, 6, 6, 18, 1240776]$ $581866860.457979$
12.0.623...000.3 $x^{12} + 5226 x^{10} - 95810 x^{9} + 11303838 x^{8} - 362616462 x^{7} + 28796618760 x^{6} - 505623605526 x^{5} + 35228673004473 x^{4} - 893459694470954 x^{3} + 32424680322296262 x^{2} - 410088604692849888 x + 6691773432069777376$ $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10}\cdot 67^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 6, 264, 5261256]$ $581866860.457979$
12.0.771...264.1 $x^{12} - 6 x^{11} - 5031 x^{10} - 36278 x^{9} + 8765370 x^{8} + 164869146 x^{7} - 4876060127 x^{6} - 159498881634 x^{5} - 184417059906 x^{4} + 42394910519910 x^{3} + 624398776281765 x^{2} + 3676234753830582 x + 8638874871129189$ $2^{12}\cdot 3^{18}\cdot 7^{10}\cdot 17^{6}\cdot 61^{10}$ $C_6\times S_3$ (as 12T18) $[2, 6, 6, 12, 18871992]$ $173074543.80287683$
12.0.847...456.1 $x^{12} + 9324 x^{10} + 27640998 x^{8} + 35082267948 x^{6} + 20134671862977 x^{4} + 4318749726113088 x^{2} + 2530077123216384$ $2^{24}\cdot 3^{18}\cdot 7^{8}\cdot 19^{6}\cdot 37^{10}$ $C_6\times S_3$ (as 12T18) $[6, 6, 6, 6, 11106060]$ $1260818083.4671302$
12.0.848...976.1 $x^{12} + 12324 x^{10} + 55957122 x^{8} + 111160682750 x^{6} + 82814111539653 x^{4} + 3025276210035846 x^{2} + 25811892335318401$ $2^{24}\cdot 3^{18}\cdot 13^{10}\cdot 79^{10}$ $C_6\times S_3$ (as 12T18) $[2, 6, 6, 6, 25501140]$ $180761757.40194216$
12.0.118...000.1 $x^{12} - 6 x^{11} - 7317 x^{10} + 12120 x^{9} + 17257671 x^{8} + 12621690 x^{7} - 13954910283 x^{6} + 27966528828 x^{5} + 4238397676116 x^{4} - 23200914438720 x^{3} - 254529144047700 x^{2} + 893278352383200 x + 7827500148170400$ $2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 613^{10}$ $C_6\times S_3$ (as 12T18) $[6, 6, 198, 4842684]$ $15521407057.37709$
12.0.131...024.1 $x^{12} - 2 x^{11} + 1263 x^{10} - 22974 x^{9} + 1331055 x^{8} - 18564858 x^{7} + 511858456 x^{6} - 5596752670 x^{5} + 127465182655 x^{4} - 1076870717548 x^{3} + 12553707679266 x^{2} - 8646114398180 x + 5655383391025$ $2^{18}\cdot 3^{6}\cdot 7^{6}\cdot 31^{10}\cdot 61^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 6, 6, 6, 6, 6, 484584]$ $117702399.81026176$
12.0.320...744.1 $x^{12} - 19838 x^{9} + 2017588692 x^{6} + 8157789819088 x^{3} + 31064563958430016$ $2^{8}\cdot 3^{18}\cdot 7^{10}\cdot 13^{6}\cdot 109^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 6, 6, 22260378]$ $1004170106.884998$
12.0.361...000.1 $x^{12} - 6 x^{11} - 7941 x^{10} - 4396 x^{9} + 20169945 x^{8} + 91749642 x^{7} - 17001722585 x^{6} - 25286054466 x^{5} + 5938928556417 x^{4} - 13710833977092 x^{3} - 664294421764629 x^{2} + 1191238534104390 x + 28418430999172635$ $2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 7^{10}\cdot 19^{8}\cdot 41^{6}$ $C_6\times S_3$ (as 12T18) $[3, 6, 6, 6, 12, 7468380]$ $178087482.40137187$
12.0.362...024.1 $x^{12} - 5088 x^{10} - 18788 x^{9} + 8232246 x^{8} + 53940348 x^{7} - 4316850390 x^{6} - 30851004492 x^{5} + 723540732993 x^{4} + 5193524642152 x^{3} + 7523384093478 x^{2} - 1070024603340 x + 167109861583225$ $2^{18}\cdot 3^{18}\cdot 7^{10}\cdot 11^{6}\cdot 61^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 12, 102008340]$ $1217745020.0914202$
12.0.362...024.2 $x^{12} - 9394 x^{9} + 366984723 x^{6} + 173401807502 x^{3} + 934953629947687$ $2^{18}\cdot 3^{18}\cdot 7^{10}\cdot 11^{6}\cdot 61^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 6, 18, 6802344]$ $1217745020.0914202$
12.0.434...000.1 $x^{12} - 6 x^{11} - 18693 x^{10} - 480928 x^{9} + 105424191 x^{8} + 5330863746 x^{7} - 87703352283 x^{6} - 7623998651844 x^{5} + 34449757742340 x^{4} + 4626659223759776 x^{3} - 23495534094161820 x^{2} - 1159275724519920768 x + 11018277107496691264$ $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 7^{8}\cdot 223^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 6, 6, 89904780]$ $4921550294.842649$
12.0.568...361.1 $x^{12} - 108919 x^{9} - 1223165573 x^{6} + 217293489631224 x^{3} + 8972097691689701568$ $3^{18}\cdot 19^{6}\cdot 43^{10}\cdot 229^{6}$ $C_6\times S_3$ (as 12T18) $[2, 6, 72, 23217696]$ $1376724985.5718458$
12.0.650...856.1 $x^{12} - 192584 x^{9} - 43845640548 x^{6} + 8348902202495500 x^{3} + 1495104251254056296875$ $2^{18}\cdot 3^{18}\cdot 19^{8}\cdot 181^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 3, 3, 3, 3, 18, 856386]$ $6715427797.665934$
12.0.707...696.1 $x^{12} - 3720 x^{10} - 16276 x^{9} + 4564080 x^{8} + 41894424 x^{7} - 1922523060 x^{6} - 30318672384 x^{5} + 148284803592 x^{4} + 6182148171056 x^{3} + 52683335143920 x^{2} + 197456226932640 x + 300062627652592$ $2^{22}\cdot 3^{18}\cdot 13^{6}\cdot 313^{10}$ $C_6\times S_3$ (as 12T18) $[2, 2, 2, 6, 6, 43694040]$ $2837358132.4665775$
12.0.114...000.2 $x^{12} - 9192 x^{10} - 6152 x^{9} + 30522150 x^{8} + 5204592 x^{7} - 43347086112 x^{6} + 79809483816 x^{5} + 23192753503113 x^{4} - 109710095912816 x^{3} - 940005732543048 x^{2} + 2512476976931520 x + 28408373535412864$ $2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 769^{10}$ $C_6\times S_3$ (as 12T18) $[6, 12, 153337548]$ $53461153843.88424$
12.0.115...000.2 $x^{12} - 410552 x^{9} + 63919939384 x^{6} - 2644937733143808 x^{3} + 292881411179278842816$ $2^{18}\cdot 3^{18}\cdot 5^{6}\cdot 19^{8}\cdot 73^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 6, 6, 18, 2117268]$ $1347645522.2133749$
12.0.120...024.1 $x^{12} + 16068 x^{10} + 89876358 x^{8} + 218488566660 x^{6} + 235539748495233 x^{4} + 112064835505551552 x^{2} + 19278048101121598464$ $2^{24}\cdot 3^{18}\cdot 13^{10}\cdot 103^{10}$ $C_6\times S_3$ (as 12T18) $[6, 6, 12, 36, 2082312]$ $2710748289.6994915$
12.0.120...000.1 $x^{12} - 6 x^{11} - 5733 x^{10} + 15252 x^{9} + 10788363 x^{8} - 14356170 x^{7} - 7299230841 x^{6} + 34567865370 x^{5} + 1903079879730 x^{4} - 16142865792966 x^{3} - 87529188362616 x^{2} + 591862482324144 x + 3387135357290556$ $2^{8}\cdot 3^{18}\cdot 5^{6}\cdot 7^{6}\cdot 13^{10}\cdot 37^{10}$ $C_6\times S_3$ (as 12T18) $[6, 6, 6, 12, 12695952]$ $308413535.4614734$
12.0.135...000.1 $x^{12} - 2 x^{11} + 1951 x^{10} + 45034 x^{9} + 3129235 x^{8} + 51135178 x^{7} + 1648598644 x^{6} + 20740012066 x^{5} + 562189453783 x^{4} + 5343787486908 x^{3} + 73935519644190 x^{2} + 1210714513092 x + 19802399841$ $2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 37^{10}\cdot 79^{10}$ $C_6\times S_3$ (as 12T18) $[2, 2, 6, 6, 18, 5109048]$ $2166670815.7545595$
12.0.190...216.1 $x^{12} - 2 x^{11} + 2275 x^{10} + 52522 x^{9} + 4191556 x^{8} + 70437010 x^{7} + 2643407173 x^{6} + 33815084632 x^{5} + 1090413287764 x^{4} + 10286208076320 x^{3} + 169827866087355 x^{2} - 253318914413100 x + 425254139699481$ $2^{8}\cdot 3^{6}\cdot 7^{10}\cdot 13^{6}\cdot 487^{10}$ $C_6\times S_3$ (as 12T18) $[2, 2, 2, 2, 6, 6, 6, 3106002]$ $39447000928.98204$
12.0.242...000.1 $x^{12} - 2 x^{11} + 2067 x^{10} + 44962 x^{9} + 3406357 x^{8} + 56852202 x^{7} + 2115269442 x^{6} + 30906927594 x^{5} + 895915741041 x^{4} + 9437171255100 x^{3} + 129347287850520 x^{2} + 39543723869364 x + 11834638902801$ $2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 19^{10}\cdot 163^{10}$ $C_6\times S_3$ (as 12T18) $[2, 6, 6, 6, 6, 6, 54, 16740]$ $19354601802.51896$
12.0.248...296.1 $x^{12} - 1760122 x^{9} + 763961492476 x^{6} + 42346850386289904 x^{3} + 584579870045421816384$ $2^{8}\cdot 3^{18}\cdot 7^{10}\cdot 11^{6}\cdot 13^{8}\cdot 19^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 3, 6, 6, 6, 6, 766416]$ $2310027851.9625864$
12.0.252...000.2 $x^{12} - 2522 x^{9} + 4311942843 x^{6} + 38219191103158 x^{3} + 3473555816436354181$ $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10}\cdot 97^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 6, 6, 18, 1023912]$ $5361686284.793181$
12.0.277...000.1 $x^{12} - 2 x^{11} + 2095 x^{10} - 52086 x^{9} + 3862715 x^{8} - 62710710 x^{7} + 1858506348 x^{6} - 9678896510 x^{5} + 384466050415 x^{4} - 554893381636 x^{3} + 67161706367670 x^{2} + 319224150926948 x + 2697908930077201$ $2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 43^{10}\cdot 73^{10}$ $C_6\times S_3$ (as 12T18) $[2, 2, 6, 6, 18, 9789264]$ $3274950554.487674$
12.0.528...384.1 $x^{12} + 28236 x^{10} + 222739686 x^{8} + 531513532212 x^{6} + 494851044738609 x^{4} + 172975826786743656 x^{2} + 18054803730002691600$ $2^{18}\cdot 3^{18}\cdot 13^{10}\cdot 181^{10}$ $C_6\times S_3$ (as 12T18) $[3, 6, 42, 120980328]$ $23926580867.466206$
12.0.689...000.1 $x^{12} - 7248 x^{10} - 48560 x^{9} + 17798994 x^{8} + 253483200 x^{7} - 15918966444 x^{6} - 393297977520 x^{5} + 2456841045969 x^{4} + 174017487226720 x^{3} + 2216702453857092 x^{2} + 11834963594620800 x + 24350667168606436$ $2^{24}\cdot 3^{18}\cdot 5^{6}\cdot 607^{10}$ $C_6\times S_3$ (as 12T18) $[2, 2, 6, 6, 137669532]$ $19195741270.829628$
12.0.695...216.1 $x^{12} - 241850 x^{9} + 460965074556 x^{6} + 65172724557564400 x^{3} + 2516368332996072097984$ $2^{8}\cdot 3^{18}\cdot 7^{10}\cdot 691^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 3, 6, 6, 6, 5460030]$ $8813235982.407635$
12.0.148...000.1 $x^{12} - 1000610 x^{9} + 512150301676 x^{6} + 21259664958776400 x^{3} + 222250329106580908224$ $2^{8}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10}\cdot 29^{6}\cdot 43^{8}$ $C_6\times S_3$ (as 12T18) $[3, 3, 6, 6, 84, 84, 31836]$ $3274905425.7253857$
12.0.177...000.1 $x^{12} - 702260 x^{9} + 272605761064 x^{6} + 11625426380449440 x^{3} + 290181165681237539904$ $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10}\cdot 23^{6}\cdot 37^{8}$ $C_6\times S_3$ (as 12T18) $[3, 3, 6, 6, 18, 2583036]$ $13286601776.666355$
12.0.218...096.1 $x^{12} - 33694 x^{9} + 4603357524 x^{6} + 5183580650960 x^{3} + 146539889709992128$ $2^{8}\cdot 3^{18}\cdot 17^{6}\cdot 991^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 3, 3, 3, 63615150]$ $11922820325.406708$
12.0.283...576.1 $x^{12} - 178126 x^{9} + 486266439828 x^{6} + 108847358231532752 x^{3} + 6465921864990854279104$ $2^{8}\cdot 3^{18}\cdot 11^{6}\cdot 13^{8}\cdot 17^{6}\cdot 31^{10}$ $C_6\times S_3$ (as 12T18) $[3, 3, 3, 3, 6, 6, 6, 3925056]$ $5842410029.8214$
12.0.373...000.1 $x^{12} - 52832 x^{9} + 19066702278 x^{6} + 453212521186048 x^{3} + 3631535238920302441$ $2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 13^{10}\cdot 127^{10}$ $C_6\times S_3$ (as 12T18) $[2, 2, 2, 2, 2, 6, 6, 6, 6, 1062828]$ $6532293221.223673$
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