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Label Polynomial Discriminant Galois group Class group Regulator
18.0.118...699.1 $x^{18} - 5 x^{17} + 16 x^{16} - 39 x^{15} + 80 x^{14} - 141 x^{13} + 221 x^{12} - 312 x^{11} + 400 x^{10} - 465 x^{9} + 489 x^{8} - 463 x^{7} + 395 x^{6} - 300 x^{5} + 195 x^{4} - 101 x^{3} + 38 x^{2} - 9 x + 1$ $-\,7^{4}\cdot 139\cdot 1373^{4}$ $C_2^9.A_9$ (as 18T966) trivial $22.1660529321$
18.0.820...051.1 $x^{18} - 2 x^{17} - 2 x^{16} + 9 x^{15} - 18 x^{13} + 10 x^{12} + 24 x^{11} - 20 x^{10} - 17 x^{9} + 12 x^{8} + 19 x^{7} + 18 x^{6} - 4 x^{5} + 8 x^{4} + 12 x^{3} + 5 x^{2} + 3 x + 1$ $-\,7^{5}\cdot 1373^{5}$ $C_2^9.A_9$ (as 18T966) trivial $302.434508105$
18.0.317...471.1 $x^{18} - 3 x^{16} - 3 x^{15} + 8 x^{14} + 13 x^{13} + 3 x^{12} - 9 x^{11} + x^{10} + 9 x^{9} + x^{8} - 9 x^{7} + 3 x^{6} + 13 x^{5} + 8 x^{4} - 3 x^{3} - 3 x^{2} + 1$ $-\,11^{4}\cdot 31\cdot 37^{4}\cdot 139^{4}$ $C_2^9.A_9$ (as 18T966) trivial $977.467803568$
18.6.378...917.1 $x^{18} - 3 x^{17} + 2 x^{16} - 5 x^{15} + 4 x^{14} + 29 x^{13} - 5 x^{12} - 83 x^{11} + 7 x^{10} + 105 x^{9} + 7 x^{8} - 83 x^{7} - 5 x^{6} + 29 x^{5} + 4 x^{4} - 5 x^{3} + 2 x^{2} - 3 x + 1$ $11^{4}\cdot 37^{5}\cdot 139^{4}$ $C_2^9.A_9$ (as 18T966) trivial $1568.66869653$
18.4.113...751.1 $x^{18} - 5 x^{17} + 10 x^{16} - 12 x^{15} + 41 x^{13} - 90 x^{12} + 125 x^{11} - 171 x^{10} + 201 x^{9} - 171 x^{8} + 125 x^{7} - 90 x^{6} + 41 x^{5} - 12 x^{3} + 10 x^{2} - 5 x + 1$ $-\,3\cdot 11^{4}\cdot 37^{5}\cdot 139^{4}$ $C_2^9.A_9$ (as 18T966) trivial $2637.81846478$
18.6.144...981.1 $x^{18} - x^{17} + 4 x^{16} + 4 x^{15} - 2 x^{14} + 12 x^{13} - 8 x^{12} - 12 x^{11} - 29 x^{10} - 52 x^{9} - 36 x^{8} - 46 x^{7} - 21 x^{6} - 2 x^{5} + 5 x^{4} + 11 x^{3} + 3 x^{2} + x + 1$ $3\cdot 11^{4}\cdot 37^{4}\cdot 47\cdot 139^{4}$ $C_2^9.A_9$ (as 18T966) trivial $4227.82306897$
18.4.154...391.1 $x^{18} - 8 x^{16} - 5 x^{15} + 27 x^{14} + 36 x^{13} - 49 x^{12} - 95 x^{11} + 31 x^{10} + 147 x^{9} + 7 x^{8} - 126 x^{7} - 35 x^{6} + 76 x^{5} + 17 x^{4} - 24 x^{3} - 3 x^{2} + 5 x - 1$ $-\,11^{4}\cdot 37^{4}\cdot 139^{4}\cdot 151$ $C_2^9.A_9$ (as 18T966) trivial $4246.06379679$
18.2.164...221.1 $x^{18} - 4 x^{17} + 11 x^{16} - 35 x^{15} + 73 x^{14} - 142 x^{13} + 262 x^{12} - 387 x^{11} + 541 x^{10} - 687 x^{9} + 732 x^{8} - 722 x^{7} + 624 x^{6} - 446 x^{5} + 270 x^{4} - 136 x^{3} + 50 x^{2} - 11 x + 1$ $11^{4}\cdot 13\cdot 337\cdot 2251^{4}$ $C_2^9.A_9$ (as 18T966) trivial $2495.26810301$
18.2.185...621.1 $x^{18} - 5 x^{17} + 11 x^{16} - 15 x^{15} + 11 x^{14} - 3 x^{13} - x^{12} - 9 x^{11} + 21 x^{10} - 31 x^{9} + 21 x^{8} - 9 x^{7} - x^{6} - 3 x^{5} + 11 x^{4} - 15 x^{3} + 11 x^{2} - 5 x + 1$ $11^{4}\cdot 37^{4}\cdot 139^{4}\cdot 181$ $C_2^9.A_9$ (as 18T966) trivial $1962.65121962$
18.2.201...477.1 $x^{18} - 4 x^{17} + 8 x^{16} - 11 x^{15} + 12 x^{14} - 11 x^{13} + 14 x^{12} - 19 x^{11} + 12 x^{10} + 14 x^{9} - 40 x^{8} + 49 x^{7} - 24 x^{6} - 16 x^{5} + 26 x^{4} - 11 x^{3} - 4 x^{2} + 8 x - 3$ $11^{4}\cdot 37^{4}\cdot 139^{4}\cdot 197$ $C_2^9.A_9$ (as 18T966) trivial $3465.90589736$
18.2.156...328.1 $x^{18} + x^{16} + x^{14} + x^{12} - 3 x^{8} - 9 x^{6} - 14 x^{4} - 14 x^{2} - 7$ $2^{18}\cdot 7^{5}\cdot 1373^{4}$ $C_2^9.A_9$ (as 18T966) trivial $7160.20318105$
18.8.668...375.1 $x^{18} - 3 x^{17} + x^{15} + 3 x^{14} + 3 x^{13} + 3 x^{12} + 6 x^{11} - 15 x^{10} - 3 x^{9} - 15 x^{8} + 6 x^{7} + 3 x^{6} + 3 x^{5} + 3 x^{4} + x^{3} - 3 x + 1$ $-\,3^{15}\cdot 5^{9}\cdot 13^{4}\cdot 17^{4}$ $C_2^9.A_9$ (as 18T966) trivial $46678.2467071$
18.8.194...131.1 $x^{18} - 5 x^{17} + 14 x^{16} - 18 x^{15} - x^{14} + 64 x^{13} - 144 x^{12} + 143 x^{11} + 46 x^{10} - 300 x^{9} + 345 x^{8} - 100 x^{7} - 300 x^{6} + 215 x^{5} + 133 x^{4} - 26 x^{3} - 69 x^{2} + 2 x + 9$ $-\,11^{4}\cdot 37^{6}\cdot 139^{5}$ $C_2^9.A_9$ (as 18T966) trivial $419992.659206$
18.0.268...704.2 $x^{18} + 4 x^{16} - x^{14} - 12 x^{12} - 12 x^{10} - 5 x^{8} + 19 x^{6} + 26 x^{4} + 10 x^{2} + 1$ $-\,2^{18}\cdot 11^{4}\cdot 37^{4}\cdot 139^{4}$ $C_2^9.A_9$ (as 18T966) trivial $47368.0680883$
18.10.273...125.1 $x^{18} - 6 x^{17} + 7 x^{16} + 25 x^{15} - 78 x^{14} + 53 x^{13} + 112 x^{12} - 204 x^{11} - 206 x^{10} + 631 x^{9} + 183 x^{8} - 1128 x^{7} + 281 x^{6} + 627 x^{5} - 124 x^{4} - 225 x^{3} + 65 x - 13$ $3^{12}\cdot 5^{10}\cdot 13^{5}\cdot 17^{5}$ $C_2^9.A_9$ (as 18T966) trivial $445391.922114$
18.10.136...625.1 $x^{18} - 5 x^{17} - x^{16} + 51 x^{15} - 81 x^{14} - 142 x^{13} + 416 x^{12} + 126 x^{11} - 916 x^{10} - 74 x^{9} + 1382 x^{8} + 195 x^{7} - 1530 x^{6} - 329 x^{5} + 941 x^{4} + 311 x^{3} - 220 x^{2} - 117 x - 13$ $3^{12}\cdot 5^{11}\cdot 13^{5}\cdot 17^{5}$ $C_2^9.A_9$ (as 18T966) trivial $1093656.11823$
18.12.110...768.1 $x^{18} - 6 x^{17} + x^{16} + 50 x^{15} - 67 x^{14} - 60 x^{13} + 27 x^{12} - 3 x^{11} + 983 x^{10} - 1488 x^{9} - 766 x^{8} + 2645 x^{7} - 1088 x^{6} - 647 x^{5} + 439 x^{4} - 21 x^{3} + 7 x^{2} - 6 x - 2$ $-\,2^{3}\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $31529557.5303$
18.8.110...768.1 $x^{18} - 10 x^{16} - 56 x^{14} + 42 x^{12} + 230 x^{10} + 59 x^{8} - 171 x^{6} - 77 x^{4} + 11 x^{2} + 2$ $-\,2^{3}\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $13882713.55$
18.10.178...373.1 $x^{18} - x^{17} - 13 x^{16} + 15 x^{15} + 52 x^{14} - 70 x^{13} - 74 x^{12} + 140 x^{11} + 31 x^{10} - 161 x^{9} + 31 x^{8} + 140 x^{7} - 74 x^{6} - 70 x^{5} + 52 x^{4} + 15 x^{3} - 13 x^{2} - x + 1$ $13\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $18888755.1345$
18.6.178...373.1 $x^{18} - 9 x^{17} + 55 x^{16} - 236 x^{15} + 772 x^{14} - 1988 x^{13} + 3957 x^{12} - 5984 x^{11} + 5741 x^{10} - 402 x^{9} - 11848 x^{8} + 27842 x^{7} - 40700 x^{6} + 43097 x^{5} - 34016 x^{4} + 19612 x^{3} - 7623 x^{2} + 1729 x - 169$ $13\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $4951882.99755$
18.10.178...373.2 $x^{18} - 8 x^{17} + 19 x^{16} - 5 x^{15} - 102 x^{14} + 281 x^{13} - 253 x^{12} - 265 x^{11} + 1047 x^{10} - 1096 x^{9} + 278 x^{8} + 491 x^{7} - 936 x^{6} + 881 x^{5} - 540 x^{4} + 225 x^{3} - 41 x^{2} - 5 x + 2$ $13\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $44487758.0374$
18.6.178...373.2 $x^{18} + 5 x^{16} - 45 x^{14} - 193 x^{12} + 482 x^{10} + 1366 x^{8} - 960 x^{6} - 2924 x^{4} - 1083 x^{2} - 52$ $13\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $24409129.0912$
18.12.261...699.1 $x^{18} - 7 x^{17} + 18 x^{16} - 40 x^{15} + 68 x^{14} + 82 x^{13} - 352 x^{12} + 235 x^{11} - 341 x^{10} + 311 x^{9} + 972 x^{8} + 494 x^{7} - 2963 x^{6} - 119 x^{5} + 2375 x^{4} - 477 x^{3} - 364 x^{2} + 139 x - 13$ $-\,19\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $41157694.9045$
18.4.261...699.1 $x^{18} - 9 x^{17} + 51 x^{16} - 204 x^{15} + 533 x^{14} - 875 x^{13} + 616 x^{12} + 1049 x^{11} - 3880 x^{10} + 5947 x^{9} - 4860 x^{8} + 549 x^{7} + 4078 x^{6} - 5941 x^{5} + 4708 x^{4} - 2394 x^{3} + 781 x^{2} - 150 x + 13$ $-\,19\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $5875164.13322$
18.8.261...699.1 $x^{18} - 2 x^{17} - 12 x^{16} + 32 x^{15} + 3 x^{14} - 34 x^{13} + 86 x^{12} - 338 x^{11} + 706 x^{10} - 301 x^{9} - 2833 x^{8} + 3354 x^{7} - 325 x^{6} - 4030 x^{5} + 2156 x^{4} + x^{3} - 547 x^{2} - 92 x - 4$ $-\,19\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $29735870.0582$
18.4.426...351.1 $x^{18} - x^{17} - 18 x^{16} - 5 x^{15} + 159 x^{14} + 82 x^{13} - 777 x^{12} - 517 x^{11} + 1884 x^{10} + 793 x^{9} - 3070 x^{8} - 246 x^{7} + 2754 x^{6} - 765 x^{5} - 925 x^{4} + 689 x^{3} + 19 x^{2} - 3 x - 4$ $-\,31\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) $[2]$ $12356456.4944$
18.0.143...984.1 $x^{18} - 3 x^{17} + 10 x^{16} - 17 x^{15} + 66 x^{14} - 99 x^{13} + 410 x^{12} - 286 x^{11} + 1264 x^{10} - 1653 x^{9} + 3829 x^{8} - 4955 x^{7} + 2704 x^{6} + 291 x^{5} - 3670 x^{4} + 2589 x^{3} + 739 x^{2} - 805 x + 193$ $-\,2^{3}\cdot 13\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) $[2, 2]$ $1815716.26646$
18.16.225...244.1 $x^{18} - 27 x^{16} + 190 x^{14} - 305 x^{12} - 1406 x^{10} + 6214 x^{8} - 8812 x^{6} + 4829 x^{4} - 853 x^{2} + 41$ $-\,2^{2}\cdot 37^{4}\cdot 41\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $319257414.847$
18.14.236...012.1 $x^{18} - 3 x^{17} - 10 x^{16} + 49 x^{15} - 54 x^{14} - 174 x^{13} + 839 x^{12} - 648 x^{11} - 2289 x^{10} + 4469 x^{9} - 1755 x^{8} - 4579 x^{7} + 13237 x^{6} - 9659 x^{5} - 11639 x^{4} + 16371 x^{3} - 1163 x^{2} - 2668 x - 341$ $2^{2}\cdot 37^{4}\cdot 43\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $217449720.188$
18.2.265...153.1 $x^{18} - 9 x^{17} + 56 x^{16} - 244 x^{15} + 820 x^{14} - 2184 x^{13} + 4481 x^{12} - 6944 x^{11} + 6182 x^{10} + 2475 x^{9} - 23693 x^{8} + 53692 x^{7} - 80879 x^{6} + 89214 x^{5} - 73660 x^{4} + 44488 x^{3} - 18745 x^{2} + 4949 x - 626$ $37^{4}\cdot 151^{4}\cdot 193\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) $[2]$ $15943950.5641$
18.16.563...216.1 $x^{18} - 16 x^{16} + 91 x^{14} - 228 x^{12} + 234 x^{10} - 181 x^{6} + 135 x^{4} - 39 x^{2} + 4$ $-\,2^{12}\cdot 37^{4}\cdot 151^{4}\cdot 613^{4}$ $C_2^9.A_9$ (as 18T966) trivial $1522893441.27$
18.14.270...712.1 $x^{18} - 12 x^{16} + 2 x^{14} + 388 x^{12} - 1217 x^{10} - 904 x^{8} + 8226 x^{6} - 9732 x^{4} + 2097 x^{2} - 108$ $2^{46}\cdot 3^{5}\cdot 3547^{4}$ $C_2^9.A_9$ (as 18T966) trivial $3254286297.51$
18.2.270...712.1 $x^{18} + 37 x^{16} + 564 x^{14} + 4564 x^{12} + 21044 x^{10} + 55148 x^{8} + 77424 x^{6} + 50784 x^{4} + 10224 x^{2} - 432$ $2^{46}\cdot 3^{5}\cdot 3547^{4}$ $C_2^9.A_9$ (as 18T966) $[2]$ $147428820.884$
18.0.173...568.1 $x^{18} + 31 x^{16} + 354 x^{14} + 1898 x^{12} + 5215 x^{10} + 7345 x^{8} + 4896 x^{6} + 1300 x^{4} + 129 x^{2} + 3$ $-\,2^{52}\cdot 3^{5}\cdot 3547^{4}$ $C_2^9.A_9$ (as 18T966) $[166]$ $5284504.97814$
18.18.173...568.1 $x^{18} - 32 x^{16} + 390 x^{14} - 2288 x^{12} + 6784 x^{10} - 10052 x^{8} + 7742 x^{6} - 3016 x^{4} + 495 x^{2} - 12$ $2^{52}\cdot 3^{5}\cdot 3547^{4}$ $C_2^9.A_9$ (as 18T966) trivial $99097381440.0$
18.18.692...272.1 $x^{18} - 31 x^{16} + 354 x^{14} - 1898 x^{12} + 5215 x^{10} - 7345 x^{8} + 4896 x^{6} - 1300 x^{4} + 129 x^{2} - 3$ $2^{54}\cdot 3^{5}\cdot 3547^{4}$ $C_2^9.A_9$ (as 18T966) trivial $300783583945$
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