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Label Polynomial Discriminant Galois group Class group Regulator
12.6.10513415548928.1 x122x11x10+4x911x8+20x712x6+8x44x3x22x+1x^{12} - 2 x^{11} - x^{10} + 4 x^{9} - 11 x^{8} + 20 x^{7} - 12 x^{6} + 8 x^{4} - 4 x^{3} - x^{2} - 2 x + 1 212672833-\,2^{12}\cdot 67^{2}\cdot 83^{3} C3S4C_3\wr S_4 (as 12T231) trivial 69.171151013469.1711510134
12.6.158072000000000.1 x124x95x8+6x6+10x5+5x44x35x2+1x^{12} - 4 x^{9} - 5 x^{8} + 6 x^{6} + 10 x^{5} + 5 x^{4} - 4 x^{3} - 5 x^{2} + 1 2125919759-\,2^{12}\cdot 5^{9}\cdot 19759 S3C4S_3\wr C_4 (as 12T264) trivial 356.187361644356.187361644
12.2.3792912694161408.1 x1211x618x3+1x^{12} - 11 x^{6} - 18 x^{3} + 1 21239196-\,2^{12}\cdot 3^{9}\cdot 19^{6} C33:S4C_3^3:S_4 (as 12T178) trivial 1280.935211471280.93521147
12.12.7340688973975552.1 x1213x10+65x8156x6+182x491x2+13x^{12} - 13 x^{10} + 65 x^{8} - 156 x^{6} + 182 x^{4} - 91 x^{2} + 13 21213112^{12}\cdot 13^{11} C12C_{12} (as 12T1) trivial 7070.232310147070.23231014
12.12.13086728000000000.1 x122x1115x10+36x9+62x8206x7+2x6+366x5298x4+28x3+38x212x+1x^{12} - 2 x^{11} - 15 x^{10} + 36 x^{9} + 62 x^{8} - 206 x^{7} + 2 x^{6} + 366 x^{5} - 298 x^{4} + 28 x^{3} + 38 x^{2} - 12 x + 1 21259127922^{12}\cdot 5^{9}\cdot 1279^{2} C3C4C_3\wr C_4 (as 12T131) trivial 9881.733140619881.73314061
12.12.46118408000000000.1 x124x1117x10+74x9+74x8412x723x6+734x5175x4324x3+90x2+22x+1x^{12} - 4 x^{11} - 17 x^{10} + 74 x^{9} + 74 x^{8} - 412 x^{7} - 23 x^{6} + 734 x^{5} - 175 x^{4} - 324 x^{3} + 90 x^{2} + 22 x + 1 21259782^{12}\cdot 5^{9}\cdot 7^{8} C12C_{12} (as 12T1) trivial 17863.721624217863.7216242
12.12.344...000.1 x1227x104x9+234x8+36x7737x6+72x5+795x4336x396x2+42x+1x^{12} - 27 x^{10} - 4 x^{9} + 234 x^{8} + 36 x^{7} - 737 x^{6} + 72 x^{5} + 795 x^{4} - 336 x^{3} - 96 x^{2} + 42 x + 1 212316592^{12}\cdot 3^{16}\cdot 5^{9} C12C_{12} (as 12T1) trivial 66792.577902466792.5779024
12.0.225...000.1 x12+35x10+455x8+2800x6+8575x4+12250x2+6125x^{12} + 35 x^{10} + 455 x^{8} + 2800 x^{6} + 8575 x^{4} + 12250 x^{2} + 6125 212597102^{12}\cdot 5^{9}\cdot 7^{10} C12C_{12} (as 12T1) [2,26][2, 26] 104.882003477104.882003477
12.0.309...000.1 x12+30x10+315x8+1500x6+3375x4+3375x2+1125x^{12} + 30 x^{10} + 315 x^{8} + 1500 x^{6} + 3375 x^{4} + 3375 x^{2} + 1125 212318592^{12}\cdot 3^{18}\cdot 5^{9} C12C_{12} (as 12T1) [10,10][10, 10] 201.000834787201.000834787
12.0.535...408.1 x12+39x10+585x8+4212x6+14742x4+22113x2+9477x^{12} + 39 x^{10} + 585 x^{8} + 4212 x^{6} + 14742 x^{4} + 22113 x^{2} + 9477 2123613112^{12}\cdot 3^{6}\cdot 13^{11} C12C_{12} (as 12T1) [2,2,26][2, 2, 26] 120.784031363120.784031363
12.12.652...000.1 x124x1125x10+90x9+206x8660x7511x6+2010x5219x42040x3+1290x254x79x^{12} - 4 x^{11} - 25 x^{10} + 90 x^{9} + 206 x^{8} - 660 x^{7} - 511 x^{6} + 2010 x^{5} - 219 x^{4} - 2040 x^{3} + 1290 x^{2} - 54 x - 79 212591382^{12}\cdot 5^{9}\cdot 13^{8} C12C_{12} (as 12T1) trivial 344057.048857344057.048857
12.4.652...000.1 x12+10x1025x8400x6525x4+1875x2+3125x^{12} + 10 x^{10} - 25 x^{8} - 400 x^{6} - 525 x^{4} + 1875 x^{2} + 3125 212591382^{12}\cdot 5^{9}\cdot 13^{8} C4×A4C_4\times A_4 (as 12T29) [2,2][2, 2] 19129.8821821961919129.88218219619
12.0.336...000.1 x124x11+43x10126x9+814x81852x7+8517x614386x5+51505x461084x3+200870x2138098x+354061x^{12} - 4 x^{11} + 43 x^{10} - 126 x^{9} + 814 x^{8} - 1852 x^{7} + 8517 x^{6} - 14386 x^{5} + 51505 x^{4} - 61084 x^{3} + 200870 x^{2} - 138098 x + 354061 2123659782^{12}\cdot 3^{6}\cdot 5^{9}\cdot 7^{8} C12C_{12} (as 12T1) [2,194][2, 194] 104.882003477104.882003477
12.12.114...000.1 x1265x10+1625x819500x6+113750x4284375x2+203125x^{12} - 65 x^{10} + 1625 x^{8} - 19500 x^{6} + 113750 x^{4} - 284375 x^{2} + 203125 2125613112^{12}\cdot 5^{6}\cdot 13^{11} C12C_{12} (as 12T1) [2][2] 398284.40925398284.40925
12.12.135...000.1 x124x1133x10+146x9+266x81508x7+x6+3766x5487x42748x338x2+418x19x^{12} - 4 x^{11} - 33 x^{10} + 146 x^{9} + 266 x^{8} - 1508 x^{7} + x^{6} + 3766 x^{5} - 487 x^{4} - 2748 x^{3} - 38 x^{2} + 418 x - 19 212591982^{12}\cdot 5^{9}\cdot 19^{8} C12C_{12} (as 12T1) trivial 805764.871501805764.871501
12.12.250...208.1 x124x1141x10+154x9+522x81820x72623x6+8286x5+5033x413524x32814x2+4646x+937x^{12} - 4 x^{11} - 41 x^{10} + 154 x^{9} + 522 x^{8} - 1820 x^{7} - 2623 x^{6} + 8286 x^{5} + 5033 x^{4} - 13524 x^{3} - 2814 x^{2} + 4646 x + 937 212781392^{12}\cdot 7^{8}\cdot 13^{9} C12C_{12} (as 12T1) trivial 2340092.997992340092.99799
12.12.728...648.1 x1237x10+407x81628x6+2035x4518x2+37x^{12} - 37 x^{10} + 407 x^{8} - 1628 x^{6} + 2035 x^{4} - 518 x^{2} + 37 21237112^{12}\cdot 37^{11} C12C_{12} (as 12T1) trivial 6018405.608636018405.60863
12.0.863...248.1 x12+91x10+3185x8+53508x6+436982x4+1529437x2+1529437x^{12} + 91 x^{10} + 3185 x^{8} + 53508 x^{6} + 436982 x^{4} + 1529437 x^{2} + 1529437 2127613112^{12}\cdot 7^{6}\cdot 13^{11} C12C_{12} (as 12T1) [10,130][10, 130] 120.784031363120.784031363
12.12.110...000.1 x1265x10+1235x89100x6+29575x442250x2+21125x^{12} - 65 x^{10} + 1235 x^{8} - 9100 x^{6} + 29575 x^{4} - 42250 x^{2} + 21125 2125913102^{12}\cdot 5^{9}\cdot 13^{10} C12C_{12} (as 12T1) [2][2] 3376001.195243376001.19524
12.12.164...000.1 x12105x10+4095x875600x6+694575x42976750x2+4465125x^{12} - 105 x^{10} + 4095 x^{8} - 75600 x^{6} + 694575 x^{4} - 2976750 x^{2} + 4465125 21236597102^{12}\cdot 3^{6}\cdot 5^{9}\cdot 7^{10} C12C_{12} (as 12T1) [2,2][2, 2] 1302741.024421302741.02442
12.12.186...568.1 x1251x104x9+834x8+36x75497x6264x5+14475x4+832x313128x2+714x+2809x^{12} - 51 x^{10} - 4 x^{9} + 834 x^{8} + 36 x^{7} - 5497 x^{6} - 264 x^{5} + 14475 x^{4} + 832 x^{3} - 13128 x^{2} + 714 x + 2809 2123161392^{12}\cdot 3^{16}\cdot 13^{9} C12C_{12} (as 12T1) trivial 4472033.791894472033.79189
12.0.475...000.1 x124x11+35x10110x9+706x81460x7+7389x612230x5+51061x430480x3+303670x2+57346x+710221x^{12} - 4 x^{11} + 35 x^{10} - 110 x^{9} + 706 x^{8} - 1460 x^{7} + 7389 x^{6} - 12230 x^{5} + 51061 x^{4} - 30480 x^{3} + 303670 x^{2} + 57346 x + 710221 21236591382^{12}\cdot 3^{6}\cdot 5^{9}\cdot 13^{8} C12C_{12} (as 12T1) [2,2,2,122][2, 2, 2, 122] 615.54450504615.54450504
12.0.122...192.1 x12+91x10+2639x8+28392x6+124215x4+215306x2+107653x^{12} + 91 x^{10} + 2639 x^{8} + 28392 x^{6} + 124215 x^{4} + 215306 x^{2} + 107653 2127101392^{12}\cdot 7^{10}\cdot 13^{9} C12C_{12} (as 12T1) [2,2,26,26][2, 2, 26, 26] 562.775330001562.775330001
12.0.130...672.1 x12+143x10+7865x8+207636x6+2664662x4+14655641x2+23030293x^{12} + 143 x^{10} + 7865 x^{8} + 207636 x^{6} + 2664662 x^{4} + 14655641 x^{2} + 23030293 21211613112^{12}\cdot 11^{6}\cdot 13^{11} C12C_{12} (as 12T1) [38,190][38, 190] 120.784031363120.784031363
12.0.168...112.1 x12+78x10+1755x8+14196x6+47151x4+59319x2+19773x^{12} + 78 x^{10} + 1755 x^{8} + 14196 x^{6} + 47151 x^{4} + 59319 x^{2} + 19773 2123181392^{12}\cdot 3^{18}\cdot 13^{9} C12C_{12} (as 12T1) [2,2,362][2, 2, 362] 1744.539506761744.53950676
12.12.280...000.1 x124x1157x10+146x9+1238x81388x711111x6+2146x5+36221x4+11712x319262x25282x+101x^{12} - 4 x^{11} - 57 x^{10} + 146 x^{9} + 1238 x^{8} - 1388 x^{7} - 11111 x^{6} + 2146 x^{5} + 36221 x^{4} + 11712 x^{3} - 19262 x^{2} - 5282 x + 101 212593782^{12}\cdot 5^{9}\cdot 37^{8} C12C_{12} (as 12T1) trivial 10882467.770610882467.7706
12.0.405...000.1 x12+93x104x9+3834x8+36x7+86663x6+3672x5+1136355x4+125824x3+8904264x2+1547082x+31597721x^{12} + 93 x^{10} - 4 x^{9} + 3834 x^{8} + 36 x^{7} + 86663 x^{6} + 3672 x^{5} + 1136355 x^{4} + 125824 x^{3} + 8904264 x^{2} + 1547082 x + 31597721 21231659762^{12}\cdot 3^{16}\cdot 5^{9}\cdot 7^{6} C12C_{12} (as 12T1) [2,2306][2, 2306] 201.000834787201.000834787
12.12.423...152.2 x1265x10+1365x810400x6+31486x436387x2+9477x^{12} - 65 x^{10} + 1365 x^{8} - 10400 x^{6} + 31486 x^{4} - 36387 x^{2} + 9477 2127813112^{12}\cdot 7^{8}\cdot 13^{11} C12C_{12} (as 12T1) [3][3] 9476244.817759476244.81775
12.0.490...000.1 x12+95x10+2375x8+19000x6+63175x4+90250x2+45125x^{12} + 95 x^{10} + 2375 x^{8} + 19000 x^{6} + 63175 x^{4} + 90250 x^{2} + 45125 2125919102^{12}\cdot 5^{9}\cdot 19^{10} C12C_{12} (as 12T1) [2,2,292][2, 2, 292] 1234.551632611234.55163261
12.0.817...000.1 x124x11+163x10526x9+10934x827772x7+382237x6724306x5+7349105x49390924x3+76289310x250833538x+338937061x^{12} - 4 x^{11} + 163 x^{10} - 526 x^{9} + 10934 x^{8} - 27772 x^{7} + 382237 x^{6} - 724306 x^{5} + 7349105 x^{4} - 9390924 x^{3} + 76289310 x^{2} - 50833538 x + 338937061 21259781162^{12}\cdot 5^{9}\cdot 7^{8}\cdot 11^{6} C12C_{12} (as 12T1) [2,2,4034][2, 2, 4034] 104.882003477104.882003477
12.0.836...000.1 x12+195x10+14625x8+526500x6+9213750x4+69103125x2+148078125x^{12} + 195 x^{10} + 14625 x^{8} + 526500 x^{6} + 9213750 x^{4} + 69103125 x^{2} + 148078125 212365613112^{12}\cdot 3^{6}\cdot 5^{6}\cdot 13^{11} C12C_{12} (as 12T1) [2,2,2,2,2,436][2, 2, 2, 2, 2, 436] 120.784031363120.784031363
12.0.990...000.1 x124x11+27x1054x9+526x81668x7+7901x611754x5+47433x4126788x3+653942x21181382x+1874521x^{12} - 4 x^{11} + 27 x^{10} - 54 x^{9} + 526 x^{8} - 1668 x^{7} + 7901 x^{6} - 11754 x^{5} + 47433 x^{4} - 126788 x^{3} + 653942 x^{2} - 1181382 x + 1874521 21236591982^{12}\cdot 3^{6}\cdot 5^{9}\cdot 19^{8} C12C_{12} (as 12T1) [6,582][6, 582] 1234.551632611234.55163261
12.12.177...088.1 x12221x10+18785x8766428x6+15200822x4129206987x2+313788397x^{12} - 221 x^{10} + 18785 x^{8} - 766428 x^{6} + 15200822 x^{4} - 129206987 x^{2} + 313788397 21213111762^{12}\cdot 13^{11}\cdot 17^{6} C12C_{12} (as 12T1) [2,2][2, 2] 13359911.871613359911.8716
12.12.178...456.1 x1261x10+915x85368x6+13603x414274x2+4941x^{12} - 61 x^{10} + 915 x^{8} - 5368 x^{6} + 13603 x^{4} - 14274 x^{2} + 4941 21261112^{12}\cdot 61^{11} C12C_{12} (as 12T1) trivial 3137114998.373137114998.37
12.0.182...632.1 x124x11+115x10366x9+4942x812220x7+89469x6159154x5+549577x4617452x3+2636654x21957730x+5710069x^{12} - 4 x^{11} + 115 x^{10} - 366 x^{9} + 4942 x^{8} - 12220 x^{7} + 89469 x^{6} - 159154 x^{5} + 549577 x^{4} - 617452 x^{3} + 2636654 x^{2} - 1957730 x + 5710069 21236781392^{12}\cdot 3^{6}\cdot 7^{8}\cdot 13^{9} C12C_{12} (as 12T1) [2,2,2,2,314][2, 2, 2, 2, 314] 562.775330001562.775330001
12.12.222...000.1 x124x11197x10+674x9+15134x842172x7579563x6+1221134x5+11583665x416161084x3112575690x2+75831982x+400281181x^{12} - 4 x^{11} - 197 x^{10} + 674 x^{9} + 15134 x^{8} - 42172 x^{7} - 579563 x^{6} + 1221134 x^{5} + 11583665 x^{4} - 16161084 x^{3} - 112575690 x^{2} + 75831982 x + 400281181 21259781362^{12}\cdot 5^{9}\cdot 7^{8}\cdot 13^{6} C12C_{12} (as 12T1) [2][2] 16251567.36116251567.361
12.12.315...992.2 x1278x10+1755x815496x6+55731x474529x2+31213x^{12} - 78 x^{10} + 1755 x^{8} - 15496 x^{6} + 55731 x^{4} - 74529 x^{2} + 31213 21231613112^{12}\cdot 3^{16}\cdot 13^{11} C12C_{12} (as 12T1) [3][3] 41837907.264241837907.2642
12.12.342...624.1 x124x1189x10+314x9+2570x87708x728175x6+69470x5+102233x4198132x353166x2+75334x+17401x^{12} - 4 x^{11} - 89 x^{10} + 314 x^{9} + 2570 x^{8} - 7708 x^{7} - 28175 x^{6} + 69470 x^{5} + 102233 x^{4} - 198132 x^{3} - 53166 x^{2} + 75334 x + 17401 212782992^{12}\cdot 7^{8}\cdot 29^{9} C12C_{12} (as 12T1) trivial 50981026.618550981026.6185
12.0.345...312.1 x12+247x10+23465x8+1070004x6+23718422x4+225325009x2+611596453x^{12} + 247 x^{10} + 23465 x^{8} + 1070004 x^{6} + 23718422 x^{4} + 225325009 x^{2} + 611596453 21213111962^{12}\cdot 13^{11}\cdot 19^{6} C12C_{12} (as 12T1) [170,170][170, 170] 120.784031363120.784031363
12.12.364...000.1 x12210x10+15435x8514500x6+8103375x456723625x2+132355125x^{12} - 210 x^{10} + 15435 x^{8} - 514500 x^{6} + 8103375 x^{4} - 56723625 x^{2} + 132355125 21231859762^{12}\cdot 3^{18}\cdot 5^{9}\cdot 7^{6} C12C_{12} (as 12T1) [2,2][2, 2] 10795763.948910795763.9489
12.0.531...392.1 x12+111x10+3663x8+43956x6+164835x4+125874x2+26973x^{12} + 111 x^{10} + 3663 x^{8} + 43956 x^{6} + 164835 x^{4} + 125874 x^{2} + 26973 2123637112^{12}\cdot 3^{6}\cdot 37^{11} C12C_{12} (as 12T1) [2,2,436][2, 2, 436] 2518.233240492518.23324049
12.0.610...000.1 x12+153x104x9+9954x8+36x7+346123x6+9792x5+6801015x4+478824x3+75200124x2+8319642x+367216741x^{12} + 153 x^{10} - 4 x^{9} + 9954 x^{8} + 36 x^{7} + 346123 x^{6} + 9792 x^{5} + 6801015 x^{4} + 478824 x^{3} + 75200124 x^{2} + 8319642 x + 367216741 212316591162^{12}\cdot 3^{16}\cdot 5^{9}\cdot 11^{6} C12C_{12} (as 12T1) [2,2,4394][2, 2, 4394] 201.000834787201.000834787
12.12.629...792.1 x12273x10+28665x81444716x6+35395542x4371653191x2+1114959573x^{12} - 273 x^{10} + 28665 x^{8} - 1444716 x^{6} + 35395542 x^{4} - 371653191 x^{2} + 1114959573 212367613112^{12}\cdot 3^{6}\cdot 7^{6}\cdot 13^{11} C12C_{12} (as 12T1) [2,2][2, 2] 13423777.93313423777.933
12.12.737...128.1 x124x1157x10+226x9+906x83428x75159x6+18006x5+10833x434220x34958x2+20914x3371x^{12} - 4 x^{11} - 57 x^{10} + 226 x^{9} + 906 x^{8} - 3428 x^{7} - 5159 x^{6} + 18006 x^{5} + 10833 x^{4} - 34220 x^{3} - 4958 x^{2} + 20914 x - 3371 2121391982^{12}\cdot 13^{9}\cdot 19^{8} C12C_{12} (as 12T1) trivial 59483998.23559483998.235
12.0.767...000.1 x124x11+95x10310x9+4086x89940x7+95129x6167270x5+1290821x41290920x3+10911490x22712134x+42149801x^{12} - 4 x^{11} + 95 x^{10} - 310 x^{9} + 4086 x^{8} - 9940 x^{7} + 95129 x^{6} - 167270 x^{5} + 1290821 x^{4} - 1290920 x^{3} + 10911490 x^{2} - 2712134 x + 42149801 21259761382^{12}\cdot 5^{9}\cdot 7^{6}\cdot 13^{8} C12C_{12} (as 12T1) [2,2,2,2402][2, 2, 2, 2402] 615.54450504615.54450504
12.0.803...000.1 x12+195x10+11115x8+245700x6+2395575x4+10266750x2+15400125x^{12} + 195 x^{10} + 11115 x^{8} + 245700 x^{6} + 2395575 x^{4} + 10266750 x^{2} + 15400125 212365913102^{12}\cdot 3^{6}\cdot 5^{9}\cdot 13^{10} C12C_{12} (as 12T1) [2,2,2,2,1570][2, 2, 2, 2, 1570] 615.54450504615.54450504
12.0.108...728.1 x12+299x10+34385x8+1898052x6+50931062x4+585707213x2+1924466557x^{12} + 299 x^{10} + 34385 x^{8} + 1898052 x^{6} + 50931062 x^{4} + 585707213 x^{2} + 1924466557 21213112362^{12}\cdot 13^{11}\cdot 23^{6} C12C_{12} (as 12T1) [2,4,4516][2, 4, 4516] 120.784031363120.784031363
12.12.111...000.1 x124x11257x10+874x9+25914x871452x71309383x6+2723614x5+34749905x447923684x3453217430x2+304232502x+2215713361x^{12} - 4 x^{11} - 257 x^{10} + 874 x^{9} + 25914 x^{8} - 71452 x^{7} - 1309383 x^{6} + 2723614 x^{5} + 34749905 x^{4} - 47923684 x^{3} - 453217430 x^{2} + 304232502 x + 2215713361 21259781762^{12}\cdot 5^{9}\cdot 7^{8}\cdot 17^{6} C12C_{12} (as 12T1) [2][2] 54495459.065754495459.0657
12.12.153...000.1 x124x1189x10+322x9+2678x88572x732455x6+88578x5+174741x4362144x3421366x2+465750x+396581x^{12} - 4 x^{11} - 89 x^{10} + 322 x^{9} + 2678 x^{8} - 8572 x^{7} - 32455 x^{6} + 88578 x^{5} + 174741 x^{4} - 362144 x^{3} - 421366 x^{2} + 465750 x + 396581 212596182^{12}\cdot 5^{9}\cdot 61^{8} C12C_{12} (as 12T1) trivial 104353287.037104353287.037
12.12.166...000.1 x12207x104x9+16434x8+36x7637037x6+16272x5+12549855x4755976x3115834236x2+10394682x+366872221x^{12} - 207 x^{10} - 4 x^{9} + 16434 x^{8} + 36 x^{7} - 637037 x^{6} + 16272 x^{5} + 12549855 x^{4} - 755976 x^{3} - 115834236 x^{2} + 10394682 x + 366872221 212316591362^{12}\cdot 3^{16}\cdot 5^{9}\cdot 13^{6} C12C_{12} (as 12T1) [2][2] 60912458.857760912458.8577
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