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Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

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Results (29 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
21.17.382...853.1 $x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 55 x^{16} - 897 x^{15} - 410 x^{14} + 2525 x^{13} + 1584 x^{12} - 4093 x^{11} - 3339 x^{10} + 3442 x^{9} + 3694 x^{8} - 1060 x^{7} - 1902 x^{6} - 106 x^{5} + 410 x^{4} + 98 x^{3} - 25 x^{2} - 11 x - 1$ $7^{14}\cdot 13\cdot 97\cdot 8914877\cdot 5021940620101$ $S_7\wr C_3$ (as 21T159) trivial $14921510518.5$
21.17.295...153.1 $x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 46 x^{16} - 906 x^{15} - 284 x^{14} + 2669 x^{13} + 927 x^{12} - 4945 x^{11} - 1794 x^{10} + 5773 x^{9} + 2182 x^{8} - 4063 x^{7} - 1665 x^{6} + 1511 x^{5} + 719 x^{4} - 184 x^{3} - 127 x^{2} - 20 x - 1$ $7^{14}\cdot 27427\cdot 15873511208841403811$ $S_7\wr C_3$ (as 21T159) trivial $42933689957.7$
21.17.380...957.1 $x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 49 x^{16} - 903 x^{15} - 326 x^{14} + 2621 x^{13} + 1146 x^{12} - 4667 x^{11} - 2321 x^{10} + 5032 x^{9} + 2776 x^{8} - 3086 x^{7} - 1910 x^{6} + 894 x^{5} + 670 x^{4} - 46 x^{3} - 87 x^{2} - 17 x - 1$ $7^{14}\cdot 757\cdot 1373\cdot 537599\cdot 1003457499787$ $S_7\wr C_3$ (as 21T159) trivial $56379445831.8$
21.17.139...064.1 $x^{21} - 18 x^{19} - 16 x^{18} + 36 x^{17} + 300 x^{16} + 1080 x^{15} - 990 x^{14} - 9240 x^{13} - 8424 x^{12} + 32616 x^{11} + 61062 x^{10} - 62433 x^{9} - 127386 x^{8} + 78735 x^{7} + 98312 x^{6} - 51048 x^{5} - 27456 x^{4} + 14400 x^{3} + 1728 x^{2} - 1344 x + 128$ $2^{14}\cdot 3^{21}\cdot 71^{3}\cdot 283583^{3}$ $C_3^7.(C_2^7.S_7)$ (as 21T152) trivial $71142558077.4$
21.17.124...168.1 $x^{21} - 3 x^{20} - 17 x^{19} + 52 x^{18} + 120 x^{17} - 368 x^{16} - 466 x^{15} + 1380 x^{14} + 1119 x^{13} - 2978 x^{12} - 1768 x^{11} + 3759 x^{10} + 1869 x^{9} - 2699 x^{8} - 1272 x^{7} + 1022 x^{6} + 510 x^{5} - 168 x^{4} - 104 x^{3} + 4 x^{2} + 8 x + 1$ $2^{8}\cdot 1009\cdot 81515745041\cdot 592110678165795251537$ $S_{21}$ (as 21T164) trivial $886636980208$
21.17.148...400.1 $x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 55 x^{16} - 897 x^{15} - 410 x^{14} + 2525 x^{13} + 1584 x^{12} - 4094 x^{11} - 3341 x^{10} + 3448 x^{9} + 3709 x^{8} - 1064 x^{7} - 1931 x^{6} - 123 x^{5} + 415 x^{4} + 104 x^{3} - 24 x^{2} - 11 x - 1$ $2^{14}\cdot 5^{2}\cdot 37^{7}\cdot 381413904556105579993$ $S_7\wr C_3.C_2$ (as 21T162) trivial $362502333654$
21.17.693...621.1 $x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 54 x^{16} - 898 x^{15} - 396 x^{14} + 2541 x^{13} + 1511 x^{12} - 4192 x^{11} - 3176 x^{10} + 3727 x^{9} + 3591 x^{8} - 1411 x^{7} - 1998 x^{6} + 10 x^{5} + 476 x^{4} + 96 x^{3} - 32 x^{2} - 12 x - 1$ $229^{7}\cdot 45112649\cdot 465666337416281$ $S_7\wr C_3.C_2$ (as 21T162) trivial $2958187891910$
21.17.740...856.1 $x^{21} - 24 x^{19} - 16 x^{18} + 117 x^{17} + 156 x^{16} + 889 x^{15} + 1674 x^{14} - 8037 x^{13} - 24160 x^{12} + 135 x^{11} + 70962 x^{10} + 105085 x^{9} + 63972 x^{8} - 40641 x^{7} - 244466 x^{6} - 475956 x^{5} - 523368 x^{4} - 347952 x^{3} - 139104 x^{2} - 30912 x - 2944$ $2^{14}\cdot 3^{21}\cdot 23^{2}\cdot 71^{3}\cdot 283583^{3}$ $C_3^7.(C_2^7.S_7)$ (as 21T152) trivial $1856015308900$
21.17.185...661.1 $x^{21} - 21 x^{19} - 3 x^{18} + 186 x^{17} + 51 x^{16} - 901 x^{15} - 354 x^{14} + 2589 x^{13} + 1292 x^{12} - 4480 x^{11} - 2669 x^{10} + 4528 x^{9} + 3147 x^{8} - 2428 x^{7} - 2028 x^{6} + 502 x^{5} + 620 x^{4} + 33 x^{3} - 62 x^{2} - 15 x - 1$ $67\cdot 229^{7}\cdot 4447\cdot 13291\cdot 2106919\cdot 6747049$ $S_7\wr C_3.C_2$ (as 21T162) trivial $5933753579790$
21.17.272...269.1 $x^{21} - 2 x^{20} - 19 x^{19} + 34 x^{18} + 151 x^{17} - 233 x^{16} - 653 x^{15} + 831 x^{14} + 1676 x^{13} - 1665 x^{12} - 2626 x^{11} + 1895 x^{10} + 2517 x^{9} - 1184 x^{8} - 1458 x^{7} + 363 x^{6} + 489 x^{5} - 33 x^{4} - 86 x^{3} - 6 x^{2} + 6 x + 1$ $3\cdot 683\cdot 1240271\cdot 39356833\cdot 49784320121\cdot 547454828827$ $S_{21}$ (as 21T164) trivial $5743982678470$
21.17.700...848.1 $x^{21} - 21 x^{19} - 44 x^{18} + 189 x^{17} + 792 x^{16} - 833 x^{15} - 5940 x^{14} + 1155 x^{13} + 23916 x^{12} + 4977 x^{11} - 55332 x^{10} - 26001 x^{9} + 72576 x^{8} + 50949 x^{7} - 47772 x^{6} - 50544 x^{5} + 5724 x^{4} + 22688 x^{3} + 10368 x^{2} + 1920 x + 128$ $2^{34}\cdot 3^{21}\cdot 139\cdot 809^{6}$ $C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) trivial $168464474581000$
21.17.143...488.1 $x^{21} - 21 x^{19} - 23 x^{18} + 189 x^{17} + 414 x^{16} - 813 x^{15} - 3105 x^{14} + 855 x^{13} + 12212 x^{12} + 6777 x^{11} - 25449 x^{10} - 30665 x^{9} + 22302 x^{8} + 52425 x^{7} + 6305 x^{6} - 35532 x^{5} - 20496 x^{4} + 2944 x^{3} + 5472 x^{2} + 1536 x + 128$ $2^{36}\cdot 3^{21}\cdot 71\cdot 809^{6}$ $C_3^7.(C_2^7.\GL(3,2))$ (as 21T147) trivial $29375371000300$
21.17.151...592.1 $x^{21} - 48 x^{19} - 32 x^{18} + 927 x^{17} + 1236 x^{16} - 8795 x^{15} - 18414 x^{14} + 37539 x^{13} + 130112 x^{12} - 10044 x^{11} - 417240 x^{10} - 431286 x^{9} + 352296 x^{8} + 1057599 x^{7} + 691446 x^{6} - 303156 x^{5} - 822024 x^{4} - 633136 x^{3} - 260064 x^{2} - 57792 x - 5504$ $2^{14}\cdot 3^{25}\cdot 43^{2}\cdot 8388019^{3}$ $C_3^7.(C_2^6.S_7)$ (as 21T149) trivial $13575529467400$
21.17.439...789.1 $x^{21} - 8 x^{20} - x^{19} + 83 x^{18} + 31 x^{17} - 219 x^{16} - 433 x^{15} - 960 x^{14} - 206 x^{13} + 2604 x^{12} + 2808 x^{11} + 2203 x^{10} + 1933 x^{9} - 7087 x^{8} - 12004 x^{7} + 1523 x^{6} + 9926 x^{5} + 2591 x^{4} - 2172 x^{3} - 923 x^{2} - 78 x - 1$ $29^{18}\cdot 389\cdot 463^{2}\cdot 1583^{2}$ $C_3^7:C_2\wr C_7$ (as 21T123) trivial $22031081472200$
21.17.330...344.1 $x^{21} - 48 x^{19} - 32 x^{18} + 909 x^{17} + 1212 x^{16} - 8209 x^{15} - 17226 x^{14} + 31284 x^{13} + 111496 x^{12} + 7614 x^{11} - 304092 x^{10} - 350139 x^{9} + 142452 x^{8} + 622908 x^{7} + 500928 x^{6} + 12528 x^{5} - 272448 x^{4} - 231872 x^{3} - 96768 x^{2} - 21504 x - 2048$ $2^{15}\cdot 3^{21}\cdot 149^{6}\cdot 211^{6}$ $C_3^7.(C_2^7.A_7)$ (as 21T151) trivial $339181484466000$
21.17.780...096.1 $x^{21} - 21 x^{19} - 41 x^{18} + 189 x^{17} + 738 x^{16} - 1010 x^{15} - 5535 x^{14} + 3810 x^{13} + 22384 x^{12} - 10953 x^{11} - 52743 x^{10} + 23361 x^{9} + 72954 x^{8} - 34884 x^{7} - 55577 x^{6} + 34911 x^{5} + 15780 x^{4} - 18860 x^{3} + 5976 x^{2} - 768 x + 32$ $2^{7}\cdot 3^{21}\cdot 2029^{9}$ $C_3^7:C_2\wr D_7$ (as 21T131) trivial $698797737095000$
21.17.102...848.1 $x^{21} - 42 x^{19} - 28 x^{18} + 684 x^{17} + 912 x^{16} - 5150 x^{15} - 10908 x^{14} + 14760 x^{13} + 57136 x^{12} + 17442 x^{11} - 111588 x^{10} - 154462 x^{9} - 23256 x^{8} + 128814 x^{7} + 161852 x^{6} + 114264 x^{5} + 64944 x^{4} + 32416 x^{3} + 12096 x^{2} + 2688 x + 256$ $2^{32}\cdot 3^{21}\cdot 73^{12}$ $C_3^7.C_2\wr C_7:C_3$ (as 21T137) trivial $289968592086000$
21.17.143...392.1 $x^{21} - 48 x^{19} - 32 x^{18} + 909 x^{17} + 1212 x^{16} - 8236 x^{15} - 17280 x^{14} + 31653 x^{13} + 112568 x^{12} + 8208 x^{11} - 305232 x^{10} - 359509 x^{9} + 111852 x^{8} + 580389 x^{7} + 488282 x^{6} + 52164 x^{5} - 210168 x^{4} - 187152 x^{3} - 78624 x^{2} - 17472 x - 1664$ $2^{14}\cdot 3^{21}\cdot 7\cdot 13^{2}\cdot 577^{9}$ $C_3^7:C_2\wr D_7$ (as 21T131) trivial $101941065977000$
21.17.297...000.1 $x^{21} - 42 x^{19} - 28 x^{18} + 639 x^{17} + 852 x^{16} - 3955 x^{15} - 8478 x^{14} + 5445 x^{13} + 28336 x^{12} + 28863 x^{11} + 10722 x^{10} - 26563 x^{9} - 104220 x^{8} - 181755 x^{7} - 202326 x^{6} - 177660 x^{5} - 133560 x^{4} - 77840 x^{3} - 30240 x^{2} - 6720 x - 640$ $2^{14}\cdot 3^{21}\cdot 5^{9}\cdot 6679^{6}$ $C_3^7.(C_2^7.A_7)$ (as 21T151) trivial $655194099396000$
21.17.514...400.1 $x^{21} - 63 x^{19} - 42 x^{18} + 1413 x^{17} + 1884 x^{16} - 12359 x^{15} - 25974 x^{14} + 15327 x^{13} + 83200 x^{12} + 223371 x^{11} + 493098 x^{10} + 63391 x^{9} - 1791828 x^{8} - 3514005 x^{7} - 3183978 x^{6} - 1524420 x^{5} - 320328 x^{4} + 27408 x^{3} + 30240 x^{2} + 6720 x + 640$ $2^{33}\cdot 3^{21}\cdot 5^{2}\cdot 73^{12}$ $C_3^7.C_2\wr C_7:C_3$ (as 21T137) trivial $2744894558830000$
21.17.103...944.1 $x^{21} - 45 x^{19} - 30 x^{18} + 756 x^{17} + 1008 x^{16} - 5415 x^{15} - 11502 x^{14} + 9504 x^{13} + 44088 x^{12} + 54054 x^{11} + 47892 x^{10} - 77257 x^{9} - 444996 x^{8} - 684633 x^{7} - 275986 x^{6} + 489132 x^{5} + 837144 x^{4} + 609616 x^{3} + 247968 x^{2} + 55104 x + 5248$ $2^{14}\cdot 3^{21}\cdot 17\cdot 29^{18}\cdot 41^{2}$ $C_3^7:C_2\wr C_7$ (as 21T123) trivial $2510830150440000$
21.17.224...336.1 $x^{21} - 30 x^{19} - 20 x^{18} + 261 x^{17} + 348 x^{16} + 386 x^{15} + 540 x^{14} - 14058 x^{13} - 38368 x^{12} + 21573 x^{11} + 182982 x^{10} + 238397 x^{9} + 75780 x^{8} - 257349 x^{7} - 827098 x^{6} - 1443204 x^{5} - 1539720 x^{4} - 1015280 x^{3} - 405216 x^{2} - 90048 x - 8576$ $2^{14}\cdot 3^{40}\cdot 29^{6}\cdot 59^{6}\cdot 67^{2}$ $C_3^7.C_2^6:A_7$ (as 21T148) trivial $22138474101600000$
21.17.190...728.1 $x^{21} - 45 x^{19} - 30 x^{18} + 756 x^{17} + 1008 x^{16} - 5361 x^{15} - 11394 x^{14} + 9009 x^{13} + 42592 x^{12} + 48168 x^{11} + 32640 x^{10} - 38489 x^{9} - 224676 x^{8} - 426999 x^{7} - 522910 x^{6} - 521964 x^{5} - 432216 x^{4} - 262224 x^{3} - 102816 x^{2} - 22848 x - 2176$ $2^{15}\cdot 3^{21}\cdot 7^{12}\cdot 17^{2}\cdot 173^{9}$ $C_3^7.C_2\wr F_7$ (as 21T142) trivial $203677761128000000$
21.17.210...208.1 $x^{21} - 93 x^{19} - 62 x^{18} + 3186 x^{17} + 4248 x^{16} - 45699 x^{15} - 94230 x^{14} + 151668 x^{13} + 558008 x^{12} + 1909683 x^{11} + 4713258 x^{10} - 6558322 x^{9} - 46220760 x^{8} - 64186983 x^{7} + 10446906 x^{6} + 132062292 x^{5} + 178126920 x^{4} + 124258480 x^{3} + 50143968 x^{2} + 11143104 x + 1061248$ $2^{14}\cdot 3^{28}\cdot 71^{3}\cdot 8291^{2}\cdot 283583^{3}$ $C_3^7.(C_2^6.S_7)$ (as 21T149) trivial $38671611908100000$
21.17.889...552.1 $x^{21} - 21 x^{19} - 63 x^{18} + 189 x^{17} + 1134 x^{16} - 825 x^{15} - 8505 x^{14} + 1035 x^{13} + 34584 x^{12} + 5697 x^{11} - 83313 x^{10} - 29457 x^{9} + 122310 x^{8} + 65853 x^{7} - 104151 x^{6} - 87480 x^{5} + 29556 x^{4} + 56976 x^{3} + 24192 x^{2} + 4032 x + 192$ $2^{33}\cdot 3^{39}\cdot 13^{15}\cdot 499$ $C_3^7.C_2\wr F_7$ (as 21T142) trivial $250555206234000000$
21.17.136...064.1 $x^{21} - 48 x^{19} - 32 x^{18} + 891 x^{17} + 1188 x^{16} - 7596 x^{15} - 15984 x^{14} + 24498 x^{13} + 91376 x^{12} + 26676 x^{11} - 181896 x^{10} - 255415 x^{9} - 55836 x^{8} + 176274 x^{7} + 223260 x^{6} + 146664 x^{5} + 73584 x^{4} + 33376 x^{3} + 12096 x^{2} + 2688 x + 256$ $2^{41}\cdot 3^{40}\cdot 13^{15}$ $C_3^7.C_2^6:F_7$ (as 21T133) trivial $713272843731000000$
21.17.103...376.1 $x^{21} - 48 x^{19} - 32 x^{18} + 846 x^{17} + 1128 x^{16} - 5726 x^{15} - 12204 x^{14} - 3924 x^{13} + 9424 x^{12} + 186678 x^{11} + 589812 x^{10} - 71609 x^{9} - 2888964 x^{8} - 4329267 x^{7} + 474058 x^{6} + 8477028 x^{5} + 11551176 x^{4} + 8074864 x^{3} + 3259872 x^{2} + 724416 x + 68992$ $2^{14}\cdot 3^{22}\cdot 7^{4}\cdot 11^{2}\cdot 1601^{9}$ $C_3^7:(C_2^6:D_7)$ (as 21T122) trivial $523529356224000000$
21.17.437...424.1 $x^{21} - 48 x^{19} - 32 x^{18} + 846 x^{17} + 1128 x^{16} - 6536 x^{15} - 13824 x^{14} + 16542 x^{13} + 66640 x^{12} + 42444 x^{11} - 56952 x^{10} - 180078 x^{9} - 351864 x^{8} - 355914 x^{7} + 182412 x^{6} + 980856 x^{5} + 1261296 x^{4} + 870944 x^{3} + 350784 x^{2} + 77952 x + 7424$ $2^{32}\cdot 3^{22}\cdot 29^{2}\cdot 199^{12}$ $C_3^7.C_2^3:F_8:C_3$ (as 21T127) trivial $10071419774400000000$
21.17.497...344.1 $x^{21} - 84 x^{19} - 56 x^{18} + 2376 x^{17} + 3168 x^{16} - 22002 x^{15} - 46116 x^{14} - 63144 x^{13} - 93232 x^{12} + 1201014 x^{11} + 4252980 x^{10} + 3168314 x^{9} - 6373944 x^{8} - 22213458 x^{7} - 45277188 x^{6} - 68252328 x^{5} - 69462864 x^{4} - 45190496 x^{3} - 17986752 x^{2} - 3997056 x - 380672$ $2^{32}\cdot 3^{28}\cdot 73^{12}\cdot 1487^{2}$ $C_3^7.C_2^3:F_8:C_3$ (as 21T127) trivial $26957491730500000000$
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