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Label Polynomial Discriminant Galois group Class group Regulator
18.0.295...643.1 $x^{18} - x^{9} + 1$ $-\,3^{45}$ $C_{18}$ (as 18T1) trivial $40934.0329443$
18.0.548...939.1 $x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ $-\,19^{17}$ $C_{18}$ (as 18T1) trivial $22305.8950792$
18.0.567...123.1 $x^{18} - x^{17} + 9 x^{16} - 6 x^{15} + 50 x^{14} - 29 x^{13} + 162 x^{12} - 63 x^{11} + 361 x^{10} - 118 x^{9} + 494 x^{8} - 77 x^{7} + 431 x^{6} - 71 x^{5} + 185 x^{4} + 10 x^{3} + 35 x^{2} - 5 x + 1$ $-\,3^{9}\cdot 19^{16}$ $C_{18}$ (as 18T1) $[9]$ $22305.8950792$
18.0.756...064.1 $x^{18} + 17 x^{16} + 120 x^{14} + 455 x^{12} + 1001 x^{10} + 1287 x^{8} + 924 x^{6} + 330 x^{4} + 45 x^{2} + 1$ $-\,2^{18}\cdot 19^{16}$ $C_{18}$ (as 18T1) $[19]$ $22305.8950792$
18.18.107...337.1 $x^{18} - x^{17} - 18 x^{16} + 18 x^{15} + 134 x^{14} - 134 x^{13} - 531 x^{12} + 531 x^{11} + 1198 x^{10} - 1198 x^{9} - 1519 x^{8} + 1519 x^{7} + 989 x^{6} - 989 x^{5} - 265 x^{4} + 265 x^{3} + 20 x^{2} - 20 x + 1$ $3^{9}\cdot 19^{17}$ $C_{18}$ (as 18T1) trivial $10972846.7711$
18.0.258...864.7 $x^{18} + 18 x^{16} + 135 x^{14} + 546 x^{12} + 1287 x^{10} + 1782 x^{8} + 1386 x^{6} + 540 x^{4} + 81 x^{2} + 1$ $-\,2^{18}\cdot 3^{44}$ $C_{18}$ (as 18T1) $[19]$ $40934.0329443$
18.18.456...917.1 $x^{18} - x^{17} - 17 x^{16} + 16 x^{15} + 120 x^{14} - 105 x^{13} - 455 x^{12} + 364 x^{11} + 1001 x^{10} - 715 x^{9} - 1287 x^{8} + 792 x^{7} + 924 x^{6} - 462 x^{5} - 330 x^{4} + 120 x^{3} + 45 x^{2} - 9 x - 1$ $37^{17}$ $C_{18}$ (as 18T1) trivial $24199468.4506$
18.18.563...125.1 $x^{18} - x^{17} - 25 x^{16} + 20 x^{15} + 232 x^{14} - 137 x^{13} - 1018 x^{12} + 403 x^{11} + 2291 x^{10} - 566 x^{9} - 2742 x^{8} + 387 x^{7} + 1711 x^{6} - 131 x^{5} - 505 x^{4} + 30 x^{3} + 55 x^{2} - 5 x - 1$ $5^{9}\cdot 19^{16}$ $C_{18}$ (as 18T1) trivial $26179751.3516$
18.18.774...592.1 $x^{18} - 18 x^{16} + 135 x^{14} - 546 x^{12} + 1287 x^{10} - 1782 x^{8} + 1386 x^{6} - 540 x^{4} + 81 x^{2} - 3$ $2^{18}\cdot 3^{45}$ $C_{18}$ (as 18T1) trivial $43670324.6529$
18.18.143...216.1 $x^{18} - 19 x^{16} + 152 x^{14} - 665 x^{12} + 1729 x^{10} - 2717 x^{8} + 2508 x^{6} - 1254 x^{4} + 285 x^{2} - 19$ $2^{18}\cdot 19^{17}$ $C_{18}$ (as 18T1) trivial $39601653.8367$
18.18.192...125.1 $x^{18} - 27 x^{16} + 270 x^{14} - 1269 x^{12} + 3042 x^{10} - 76 x^{9} - 3888 x^{8} + 261 x^{7} + 2601 x^{6} - 297 x^{5} - 810 x^{4} + 120 x^{3} + 81 x^{2} - 9 x - 1$ $3^{44}\cdot 5^{9}$ $C_{18}$ (as 18T1) trivial $49974435.7673$
18.0.577...375.1 $x^{18} + 18 x^{16} + 135 x^{14} + 546 x^{12} + 1287 x^{10} - 76 x^{9} + 1782 x^{8} - 684 x^{7} + 1386 x^{6} - 2052 x^{5} + 540 x^{4} - 2280 x^{3} + 81 x^{2} - 684 x + 5779$ $-\,3^{45}\cdot 5^{9}$ $C_{18}$ (as 18T1) $[74]$ $40934.0329443$
18.0.107...375.1 $x^{18} - x^{17} + 20 x^{16} - 20 x^{15} + 172 x^{14} - 172 x^{13} + 837 x^{12} - 837 x^{11} + 2566 x^{10} - 2566 x^{9} + 5283 x^{8} - 5283 x^{7} + 7791 x^{6} - 7791 x^{5} + 9045 x^{4} - 9045 x^{3} + 9330 x^{2} - 9330 x + 9349$ $-\,5^{9}\cdot 19^{17}$ $C_{18}$ (as 18T1) $[152]$ $22305.8950792$
18.0.116...367.1 $x^{18} - x^{17} + 26 x^{16} - 19 x^{15} + 319 x^{14} - 179 x^{13} + 2258 x^{12} - 914 x^{11} + 9881 x^{10} - 2825 x^{9} + 26418 x^{8} - 4536 x^{7} + 41176 x^{6} - 4496 x^{5} + 32480 x^{4} + 10240 x^{2} - 1280 x + 512$ $-\,7^{9}\cdot 19^{16}$ $C_{18}$ (as 18T1) $[2, 74]$ $22305.8950792$
18.0.387...768.1 $x^{18} + 34 x^{16} + 480 x^{14} + 3640 x^{12} + 16016 x^{10} + 41184 x^{8} + 59136 x^{6} + 42240 x^{4} + 11520 x^{2} + 512$ $-\,2^{27}\cdot 19^{16}$ $C_{18}$ (as 18T1) $[171]$ $22305.8950792$
18.18.387...768.1 $x^{18} - 34 x^{16} + 480 x^{14} - 3640 x^{12} + 16016 x^{10} - 41184 x^{8} + 59136 x^{6} - 42240 x^{4} + 11520 x^{2} - 512$ $2^{27}\cdot 19^{16}$ $C_{18}$ (as 18T1) trivial $214558784.635$
18.0.397...767.1 $x^{18} + 27 x^{16} + 351 x^{14} + 2646 x^{12} + 12465 x^{10} - 5 x^{9} + 35964 x^{8} + 468 x^{7} + 61488 x^{6} + 4752 x^{5} + 51840 x^{4} + 9600 x^{3} + 20736 x^{2} + 2304 x + 512$ $-\,3^{44}\cdot 7^{9}$ $C_{18}$ (as 18T1) $[163]$ $40934.0329443$
18.18.119...301.1 $x^{18} - 36 x^{16} + 540 x^{14} - 4368 x^{12} + 20592 x^{10} - 5 x^{9} - 57024 x^{8} + 90 x^{7} + 88704 x^{6} - 540 x^{5} - 69120 x^{4} + 1200 x^{3} + 20736 x^{2} - 720 x - 1511$ $3^{45}\cdot 7^{9}$ $C_{18}$ (as 18T1) trivial $550518949.413$
18.0.132...368.2 $x^{18} + 36 x^{16} + 540 x^{14} + 4368 x^{12} + 20592 x^{10} + 57024 x^{8} + 88704 x^{6} + 69120 x^{4} + 20736 x^{2} + 512$ $-\,2^{27}\cdot 3^{44}$ $C_{18}$ (as 18T1) $[333]$ $40934.0329443$
18.18.132...368.1 $x^{18} - 36 x^{16} + 540 x^{14} - 4368 x^{12} + 20592 x^{10} - 57024 x^{8} + 88704 x^{6} - 69120 x^{4} + 20736 x^{2} - 512$ $2^{27}\cdot 3^{44}$ $C_{18}$ (as 18T1) trivial $336692032.456$
18.18.221...973.1 $x^{18} - x^{17} - 37 x^{16} + 37 x^{15} + 571 x^{14} - 571 x^{13} - 4749 x^{12} + 4749 x^{11} + 22915 x^{10} - 22915 x^{9} - 64029 x^{8} + 64029 x^{7} + 96483 x^{6} - 96483 x^{5} - 64029 x^{4} + 64029 x^{3} + 8931 x^{2} - 8931 x - 797$ $7^{9}\cdot 19^{17}$ $C_{18}$ (as 18T1) trivial $428418281.929$
18.0.242...603.1 $x^{18} - x^{17} + 17 x^{16} - 6 x^{15} + 201 x^{14} - 76 x^{13} + 999 x^{12} - 218 x^{11} + 3519 x^{10} - 623 x^{9} + 5540 x^{8} + 1505 x^{7} + 5069 x^{6} - 129 x^{5} + 528 x^{4} - 97 x^{3} + 56 x^{2} - 7 x + 1$ $-\,3^{9}\cdot 37^{16}$ $C_{18}$ (as 18T1) $[171]$ $409151.310213$
18.0.396...104.1 $x^{18} + 36 x^{16} + 540 x^{14} + 4368 x^{12} + 20592 x^{10} + 57024 x^{8} + 88704 x^{6} + 69120 x^{4} + 20736 x^{2} + 1536$ $-\,2^{27}\cdot 3^{45}$ $C_{18}$ (as 18T1) $[542]$ $40934.0329443$
18.18.396...104.1 $x^{18} - 36 x^{16} + 540 x^{14} - 4368 x^{12} + 20592 x^{10} - 57024 x^{8} + 88704 x^{6} - 69120 x^{4} + 20736 x^{2} - 1536$ $2^{27}\cdot 3^{45}$ $C_{18}$ (as 18T1) trivial $1186002844.94$
18.0.680...571.1 $x^{18} - 7 x^{17} + 31 x^{16} - 98 x^{15} + 331 x^{14} - 957 x^{13} + 2693 x^{12} - 6227 x^{11} + 15226 x^{10} - 30674 x^{9} + 66392 x^{8} - 111391 x^{7} + 216508 x^{6} - 293668 x^{5} + 517517 x^{4} - 511304 x^{3} + 833369 x^{2} - 453934 x + 713641$ $-\,11^{9}\cdot 19^{16}$ $C_{18}$ (as 18T1) $[2, 542]$ $22305.8950792$
18.0.735...592.1 $x^{18} + 38 x^{16} + 608 x^{14} + 5320 x^{12} + 27664 x^{10} + 86944 x^{8} + 160512 x^{6} + 160512 x^{4} + 72960 x^{2} + 9728$ $-\,2^{27}\cdot 19^{17}$ $C_{18}$ (as 18T1) $[1026]$ $22305.8950792$
18.18.735...592.1 $x^{18} - 38 x^{16} + 608 x^{14} - 5320 x^{12} + 27664 x^{10} - 86944 x^{8} + 160512 x^{6} - 160512 x^{4} + 72960 x^{2} - 9728$ $2^{27}\cdot 19^{17}$ $C_{18}$ (as 18T1) trivial $1274691143.44$
18.18.148...712.1 $x^{18} - 2 x^{17} - 42 x^{16} + 78 x^{15} + 680 x^{14} - 1150 x^{13} - 5337 x^{12} + 7992 x^{11} + 20953 x^{10} - 26642 x^{9} - 38251 x^{8} + 38696 x^{7} + 26450 x^{6} - 19276 x^{5} - 4165 x^{4} + 2054 x^{3} + 53 x^{2} - 40 x + 1$ $2^{18}\cdot 3^{9}\cdot 19^{16}$ $C_{18}$ (as 18T1) trivial $1824767825.56$
18.0.232...771.2 $x^{18} - 9 x^{17} + 45 x^{16} - 156 x^{15} + 504 x^{14} - 1512 x^{13} + 4272 x^{12} - 10422 x^{11} + 24552 x^{10} - 51962 x^{9} + 108099 x^{8} - 193914 x^{7} + 351249 x^{6} - 518733 x^{5} + 814050 x^{4} - 933768 x^{3} + 1272483 x^{2} - 860841 x + 992091$ $-\,3^{44}\cdot 11^{9}$ $C_{18}$ (as 18T1) $[1791]$ $40934.0329443$
18.18.305...013.1 $x^{18} - 7 x^{17} - 23 x^{16} + 238 x^{15} + 67 x^{14} - 3057 x^{13} + 2147 x^{12} + 18205 x^{11} - 22172 x^{10} - 48410 x^{9} + 80696 x^{8} + 38369 x^{7} - 112670 x^{6} + 27104 x^{5} + 41513 x^{4} - 25352 x^{3} + 2633 x^{2} + 1022 x - 191$ $13^{9}\cdot 19^{16}$ $C_{18}$ (as 18T1) trivial $1710187464.86$
18.0.323...704.1 $x^{18} + 33 x^{16} + 410 x^{14} + 2443 x^{12} + 7424 x^{10} + 11040 x^{8} + 6723 x^{6} + 1135 x^{4} + 63 x^{2} + 1$ $-\,2^{18}\cdot 37^{16}$ $C_{18}$ (as 18T1) $[171]$ $409151.310213$
18.18.696...313.1 $x^{18} - 54 x^{16} + 1215 x^{14} - 14742 x^{12} + 104247 x^{10} - 136 x^{9} - 433026 x^{8} + 3672 x^{7} + 1010394 x^{6} - 33048 x^{5} - 1180980 x^{4} + 110160 x^{3} + 531441 x^{2} - 99144 x - 40553$ $3^{45}\cdot 11^{9}$ $C_{18}$ (as 18T1) trivial $4187524895.96$
18.0.898...311.1 $x^{18} - x^{17} + 20 x^{16} - 21 x^{15} + 120 x^{14} - 142 x^{13} + 174 x^{12} - 302 x^{11} - 405 x^{10} - 1196 x^{9} + 785 x^{8} - 6238 x^{7} + 9767 x^{6} + 981 x^{5} - 3327 x^{4} + 13403 x^{3} + 21875 x^{2} + 620 x + 22717$ $-\,3^{9}\cdot 37^{17}$ $C_{18}$ (as 18T1) $[152]$ $409151.310213$
18.18.104...613.1 $x^{18} - 9 x^{17} - 9 x^{16} + 276 x^{15} - 360 x^{14} - 3024 x^{13} + 6864 x^{12} + 13338 x^{11} - 44460 x^{10} - 12218 x^{9} + 118251 x^{8} - 56754 x^{7} - 104295 x^{6} + 107991 x^{5} - 10584 x^{4} - 23004 x^{3} + 8559 x^{2} - 297 x - 159$ $3^{44}\cdot 13^{9}$ $C_{18}$ (as 18T1) trivial $9384873349.02$
18.0.110...375.2 $x^{18} - 7 x^{17} + 40 x^{16} - 154 x^{15} + 627 x^{14} - 1979 x^{13} + 6508 x^{12} - 16865 x^{11} + 47380 x^{10} - 103535 x^{9} + 254065 x^{8} - 459765 x^{7} + 999805 x^{6} - 1439914 x^{5} + 2800752 x^{4} - 2907231 x^{3} + 5123532 x^{2} - 2913750 x + 4775041$ $-\,3^{9}\cdot 5^{9}\cdot 19^{16}$ $C_{18}$ (as 18T1) $[3258]$ $22305.8950792$
18.18.129...849.1 $x^{18} - x^{17} - 56 x^{16} + 56 x^{15} + 1312 x^{14} - 1312 x^{13} - 16643 x^{12} + 16643 x^{11} + 123406 x^{10} - 123406 x^{9} - 536825 x^{8} + 536825 x^{7} + 1291507 x^{6} - 1291507 x^{5} - 1450991 x^{4} + 1450991 x^{3} + 418894 x^{2} - 418894 x + 44917$ $11^{9}\cdot 19^{17}$ $C_{18}$ (as 18T1) trivial $3961676166.05$
18.18.240...125.1 $x^{18} - 7 x^{17} - 21 x^{16} + 230 x^{15} - 39 x^{14} - 2523 x^{13} + 2827 x^{12} + 12069 x^{11} - 19596 x^{10} - 25476 x^{9} + 52436 x^{8} + 21175 x^{7} - 56437 x^{6} - 10039 x^{5} + 24080 x^{4} + 4861 x^{3} - 1984 x^{2} - 565 x - 31$ $5^{9}\cdot 37^{16}$ $C_{18}$ (as 18T1) trivial $8441875446.42$
18.0.282...528.1 $x^{18} + 57 x^{16} + 1368 x^{14} + 17955 x^{12} + 140049 x^{10} + 660231 x^{8} + 1828332 x^{6} + 2742498 x^{4} + 1869885 x^{2} + 373977$ $-\,2^{18}\cdot 3^{9}\cdot 19^{17}$ $C_{18}$ (as 18T1) $[2, 2786]$ $22305.8950792$
18.0.313...839.1 $x^{18} + 54 x^{16} + 1215 x^{14} + 14742 x^{12} + 104247 x^{10} - 1810 x^{9} + 433026 x^{8} - 48870 x^{7} + 1010394 x^{6} - 439830 x^{5} + 1180980 x^{4} - 1466100 x^{3} + 531441 x^{2} - 1319490 x + 3335149$ $-\,3^{45}\cdot 13^{9}$ $C_{18}$ (as 18T1) $[2524]$ $40934.0329443$
18.18.342...457.1 $x^{18} - 7 x^{17} - 32 x^{16} + 294 x^{15} + 275 x^{14} - 4779 x^{13} + 1076 x^{12} + 37663 x^{11} - 29140 x^{10} - 146783 x^{9} + 161417 x^{8} + 251979 x^{7} - 350891 x^{6} - 118682 x^{5} + 269024 x^{4} - 41471 x^{3} - 43388 x^{2} + 12154 x - 191$ $17^{9}\cdot 19^{16}$ $C_{18}$ (as 18T1) trivial $6552525312.42$
18.0.408...243.1 $x^{18} - 12691 x^{9} + 40353607$ $-\,3^{45}\cdot 7^{12}$ $C_{18}$ (as 18T1) $[543]$ $4392158.29124$
18.0.408...243.2 $x^{18} - 5831 x^{9} + 40353607$ $-\,3^{45}\cdot 7^{12}$ $C_{18}$ (as 18T1) $[327]$ $10392888.2142$
18.18.474...953.1 $x^{18} - x^{17} - 34 x^{16} + 29 x^{15} + 435 x^{14} - 311 x^{13} - 2671 x^{12} + 1551 x^{11} + 8348 x^{10} - 3867 x^{9} - 13016 x^{8} + 4608 x^{7} + 9365 x^{6} - 1994 x^{5} - 2859 x^{4} + 250 x^{3} + 224 x^{2} - 32 x + 1$ $73^{17}$ $C_{18}$ (as 18T1) trivial $7147727796.24$
18.0.581...247.1 $x^{18} - x^{17} + 58 x^{16} - 58 x^{15} + 1426 x^{14} - 1426 x^{13} + 19381 x^{12} - 19381 x^{11} + 159430 x^{10} - 159430 x^{9} + 819661 x^{8} - 819661 x^{7} + 2647993 x^{6} - 2647993 x^{5} + 5390491 x^{4} - 5390491 x^{3} + 7260376 x^{2} - 7260376 x + 7634353$ $-\,13^{9}\cdot 19^{17}$ $C_{18}$ (as 18T1) $[9774]$ $22305.8950792$
18.0.758...739.1 $x^{18} - x^{17} + x^{16} - 39 x^{15} + 39 x^{14} - 39 x^{13} + 476 x^{12} + 1177 x^{11} + 951 x^{10} - 1673 x^{9} - 14857 x^{8} - 2167 x^{7} + 23181 x^{6} + 3723 x^{5} + 245519 x^{4} - 597570 x^{3} + 418761 x^{2} - 77749 x + 32263$ $-\,7^{12}\cdot 19^{17}$ $C_{18}$ (as 18T1) $[3, 3, 3, 3, 3]$ $7595459.56275$
18.0.758...739.2 $x^{18} - x^{17} + x^{16} - 39 x^{15} + 39 x^{14} - 39 x^{13} + 476 x^{12} - 818 x^{11} + 5739 x^{10} - 10185 x^{9} + 13605 x^{8} - 52973 x^{7} + 10679 x^{6} - 11572 x^{5} + 80200 x^{4} + 256689 x^{3} + 421421 x^{2} + 316197 x + 116851$ $-\,7^{12}\cdot 19^{17}$ $C_{18}$ (as 18T1) $[3, 3, 3, 3]$ $4369063.34801$
18.18.116...857.1 $x^{18} - 9 x^{17} - 18 x^{16} + 348 x^{15} - 252 x^{14} - 5040 x^{13} + 8472 x^{12} + 33174 x^{11} - 76374 x^{10} - 91106 x^{9} + 292437 x^{8} + 35910 x^{7} - 455655 x^{6} + 186741 x^{5} + 192555 x^{4} - 131820 x^{3} - 2259 x^{2} + 14355 x - 2161$ $3^{44}\cdot 17^{9}$ $C_{18}$ (as 18T1) trivial $13605878233.0$
18.0.119...048.1 $x^{18} + 37 x^{16} + 518 x^{14} + 3515 x^{12} + 12284 x^{10} + 22200 x^{8} + 20683 x^{6} + 9287 x^{4} + 1591 x^{2} + 37$ $-\,2^{18}\cdot 37^{17}$ $C_{18}$ (as 18T1) $[1526]$ $409151.310213$
18.0.147...000.1 $x^{18} - 2 x^{17} + 30 x^{16} - 50 x^{15} + 552 x^{14} - 814 x^{13} + 6983 x^{12} - 8936 x^{11} + 65641 x^{10} - 72082 x^{9} + 465597 x^{8} - 424984 x^{7} + 2471666 x^{6} - 1778572 x^{5} + 9429355 x^{4} - 4814010 x^{3} + 23461605 x^{2} - 6474360 x + 29134601$ $-\,2^{18}\cdot 5^{9}\cdot 19^{16}$ $C_{18}$ (as 18T1) $[8582]$ $22305.8950792$
18.18.210...125.1 $x^{18} - x^{17} - 75 x^{16} + 75 x^{15} + 2357 x^{14} - 2357 x^{13} - 40203 x^{12} + 40203 x^{11} + 402421 x^{10} - 402421 x^{9} - 2379787 x^{8} + 2379787 x^{7} + 7892981 x^{6} - 7892981 x^{5} - 12652555 x^{4} + 12652555 x^{3} + 6025205 x^{2} - 6025205 x + 1044469$ $3^{9}\cdot 5^{9}\cdot 19^{17}$ $C_{18}$ (as 18T1) $[2]$ $9738921681.01$
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