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Label Polynomial Discriminant Galois group Class group Regulator
18.2.483...741.1 $x^{18} - 3 x^{17} + 2 x^{16} - 5 x^{15} + 15 x^{14} - 6 x^{13} + 2 x^{12} - 29 x^{11} + 17 x^{10} + 11 x^{9} + 17 x^{8} - 29 x^{7} + 2 x^{6} - 6 x^{5} + 15 x^{4} - 5 x^{3} + 2 x^{2} - 3 x + 1$ $23^{6}\cdot 59^{2}\cdot 149\cdot 251^{2}$ $C_2\times S_4^3.S_4$ (as 18T912) trivial $67.155663406$
18.2.642...321.1 $x^{18} - 2 x^{17} - x^{16} + 6 x^{15} - 4 x^{14} - 10 x^{13} + 11 x^{12} + 9 x^{11} - 16 x^{10} - 5 x^{9} + 16 x^{8} + 5 x^{7} - 15 x^{6} - 5 x^{5} + 12 x^{4} + x^{3} - 5 x^{2} + 1$ $23^{6}\cdot 208333^{2}$ $A_4^3.(C_2\times S_4)$ (as 18T776) trivial $79.1741198129$
18.2.718...137.1 $x^{18} - 5 x^{17} + 12 x^{16} - 22 x^{15} + 39 x^{14} - 63 x^{13} + 85 x^{12} - 97 x^{11} + 99 x^{10} - 98 x^{9} + 91 x^{8} - 71 x^{7} + 53 x^{6} - 44 x^{5} + 29 x^{4} - 15 x^{3} + 10 x^{2} - 4 x + 1$ $7^{12}\cdot 113\cdot 2143^{2}$ $C_2\times S_4^3.A_4$ (as 18T879) trivial $84.7255286435$
18.2.867...481.1 $x^{18} - x^{17} + 2 x^{16} - 5 x^{15} + x^{14} - 6 x^{13} + 2 x^{12} + 4 x^{10} + 3 x^{9} + 4 x^{8} + 2 x^{6} - 6 x^{5} + x^{4} - 5 x^{3} + 2 x^{2} - x + 1$ $41^{3}\cdot 11221481^{2}$ $C_2^9.S_9$ (as 18T968) trivial $93.6283865561$
18.2.897...489.1 $x^{18} - x^{17} + 3 x^{15} - x^{14} + x^{13} + 7 x^{12} + 2 x^{11} + 3 x^{10} + 11 x^{9} + 3 x^{8} + 2 x^{7} + 7 x^{6} + x^{5} - x^{4} + 3 x^{3} - x + 1$ $7^{12}\cdot 41^{3}\cdot 97^{2}$ $D_6\wr C_3$ (as 18T472) trivial $95.2465332123$
18.2.109...009.1 $x^{18} - 2 x^{17} + 4 x^{15} - 7 x^{14} + x^{13} + 7 x^{12} + 2 x^{11} - 10 x^{10} + x^{9} + 20 x^{8} - 22 x^{7} - 2 x^{6} + 7 x^{5} + 2 x^{4} - 10 x^{3} + 11 x^{2} - 5 x + 1$ $43^{2}\cdot 83\cdot 107\cdot 311^{2}\cdot 2621^{2}$ $C_2^9.S_9$ (as 18T968) trivial $106.811954559$
18.2.109...837.1 $x^{18} - x^{17} + 3 x^{16} - 5 x^{15} + 4 x^{14} - 6 x^{13} - 5 x^{12} - 2 x^{11} - 16 x^{10} + x^{9} - 16 x^{8} - 2 x^{7} - 5 x^{6} - 6 x^{5} + 4 x^{4} - 5 x^{3} + 3 x^{2} - x + 1$ $53\cdot 453771377^{2}$ $C_2^9.S_9$ (as 18T968) trivial $106.041791279$
18.2.109...889.1 $x^{18} - x^{16} - 4 x^{15} - x^{14} + 3 x^{13} + 9 x^{12} + x^{11} - 2 x^{10} - 13 x^{9} - 2 x^{8} + x^{7} + 9 x^{6} + 3 x^{5} - x^{4} - 4 x^{3} - x^{2} + 1$ $23^{6}\cdot 379^{2}\cdot 719^{2}$ $A_4^3.(C_2\times S_4)$ (as 18T776) trivial $107.172918917$
18.2.116...689.1 $x^{18} - 4 x^{17} + 4 x^{16} + 9 x^{15} - 27 x^{14} + 17 x^{13} + 26 x^{12} - 46 x^{11} + 12 x^{10} + 20 x^{9} - 12 x^{8} + 15 x^{7} - 48 x^{6} + 48 x^{5} - x^{4} - 29 x^{3} + 20 x^{2} - 5 x + 1$ $5881\cdot 44555813^{2}$ $C_2^9.S_9$ (as 18T968) trivial $111.7260845$
18.2.153...696.1 $x^{18} + 5 x^{16} + 5 x^{14} - 8 x^{12} - 8 x^{10} + 17 x^{8} + 19 x^{6} + x^{4} - 2 x^{2} - 1$ $2^{18}\cdot 37^{6}\cdot 151^{2}$ $S_3^3:S_4$ (as 18T483) trivial $139.095050977$
18.2.184...177.1 $x^{18} - 2 x^{17} + 4 x^{15} - 5 x^{14} - 6 x^{13} + 18 x^{12} - x^{11} - 18 x^{10} + 9 x^{9} + 13 x^{8} - 25 x^{7} - 6 x^{6} + 23 x^{5} + 10 x^{4} - 11 x^{3} - 5 x^{2} + x + 1$ $7^{4}\cdot 23^{6}\cdot 83^{2}\cdot 7537$ $C_2\times S_4^3.S_4$ (as 18T912) trivial $146.457400567$
18.2.210...728.1 $x^{18} - 5 x^{17} + 6 x^{16} + 9 x^{15} - 20 x^{14} - 15 x^{13} + 52 x^{12} - 6 x^{11} - 57 x^{10} + 25 x^{9} + 37 x^{8} - 29 x^{7} - 14 x^{6} + 24 x^{5} + x^{4} - 13 x^{3} + 4 x + 1$ $2^{12}\cdot 7^{12}\cdot 13^{5}$ $C_6^3:C_6$ (as 18T282) trivial $159.599072679$
18.2.212...913.1 $x^{18} - 3 x^{17} + 5 x^{16} - 6 x^{15} + 5 x^{14} + x^{13} - 9 x^{12} + 18 x^{11} - 26 x^{10} + 29 x^{9} - 26 x^{8} + 18 x^{7} - 9 x^{6} + x^{5} + 5 x^{4} - 6 x^{3} + 5 x^{2} - 3 x + 1$ $7^{12}\cdot 41^{2}\cdot 97^{3}$ $D_6\wr C_3$ (as 18T472) trivial $158.336114215$
18.2.246...625.1 $x^{18} - 2 x^{17} + 4 x^{16} - 7 x^{15} + 7 x^{14} - 10 x^{13} + 15 x^{12} - 23 x^{11} + 21 x^{10} - 13 x^{9} + 21 x^{8} - 23 x^{7} + 15 x^{6} - 10 x^{5} + 7 x^{4} - 7 x^{3} + 4 x^{2} - 2 x + 1$ $5^{8}\cdot 83^{6}\cdot 193$ $C_2^4:A_4^2.D_6$ (as 18T662) trivial $174.087268526$
18.2.299...000.1 $x^{18} - 5 x^{17} + 14 x^{16} - 25 x^{15} + 23 x^{14} + 21 x^{13} - 137 x^{12} + 330 x^{11} - 559 x^{10} + 747 x^{9} - 826 x^{8} + 768 x^{7} - 606 x^{6} + 405 x^{5} - 226 x^{4} + 102 x^{3} - 35 x^{2} + 8 x - 1$ $2^{12}\cdot 5^{3}\cdot 37^{6}\cdot 151^{2}$ $D_6\wr S_3$ (as 18T556) trivial $193.593644649$
18.2.308...216.1 $x^{18} - 2 x^{17} + 3 x^{16} - 2 x^{15} + 6 x^{14} - 12 x^{13} + 14 x^{12} + 2 x^{11} - 24 x^{10} + 36 x^{9} - 24 x^{8} + 2 x^{7} + 14 x^{6} - 12 x^{5} + 6 x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$ $2^{20}\cdot 37^{6}\cdot 107^{2}$ $S_3^3:S_4$ (as 18T483) trivial $333.51149291$
18.2.350...173.1 $x^{18} + x^{16} - 2 x^{15} + 4 x^{13} + 5 x^{12} - 25 x^{11} + x^{10} + 27 x^{9} + 41 x^{8} - 93 x^{7} + 10 x^{6} + 54 x^{5} - 9 x^{4} - 21 x^{3} + 2 x^{2} + 4 x - 1$ $11^{7}\cdot 23^{9}$ $C_2\times C_3^3:S_4$ (as 18T301) trivial $213.366849664$
18.2.380...000.1 $x^{18} - 2 x^{17} + 2 x^{16} - 3 x^{15} + 2 x^{14} - 4 x^{13} + 2 x^{12} - 10 x^{11} + 2 x^{10} - 3 x^{9} - 2 x^{8} - 10 x^{7} - 2 x^{6} - 4 x^{5} - 2 x^{4} - 3 x^{3} - 2 x^{2} - 2 x - 1$ $2^{12}\cdot 5^{9}\cdot 41^{6}$ $\SOPlus(4,2)$ (as 18T34) trivial $225.62524734$
18.2.433...096.1 $x^{18} - x^{15} - 8 x^{12} + 17 x^{9} - 8 x^{6} - x^{3} + 1$ $2^{12}\cdot 3^{6}\cdot 29^{9}$ $S_3\times D_6$ (as 18T29) trivial $230.414214587$
18.2.440...413.1 $x^{18} - 5 x^{17} + 14 x^{16} - 27 x^{15} + 44 x^{14} - 68 x^{13} + 98 x^{12} - 117 x^{11} + 102 x^{10} - 50 x^{9} - 18 x^{8} + 74 x^{7} - 101 x^{6} + 95 x^{5} - 69 x^{4} + 39 x^{3} - 17 x^{2} + 5 x - 1$ $23^{7}\cdot 59^{3}\cdot 251^{2}$ $C_2\times S_4^3.S_4$ (as 18T912) trivial $226.057810023$
18.2.625...168.1 $x^{18} + 2 x^{16} - x^{15} + 2 x^{14} - 2 x^{13} + 2 x^{12} - 4 x^{11} + 2 x^{10} - 5 x^{9} + 2 x^{8} - 4 x^{7} + 2 x^{6} - 2 x^{5} + 2 x^{4} - x^{3} + 2 x^{2} + 1$ $2^{12}\cdot 37^{7}\cdot 401^{2}$ $S_4^3.S_4$ (as 18T884) trivial $294.2519764$
18.2.631...281.1 $x^{18} - x^{17} + 2 x^{16} - 4 x^{15} + 6 x^{14} - 20 x^{13} + 22 x^{12} - 27 x^{11} + 19 x^{10} - 11 x^{9} + 16 x^{8} - 5 x^{7} + 2 x^{6} - 5 x^{5} - 9 x^{4} - 7 x^{3} - x^{2} + 2 x + 1$ $23^{7}\cdot 2647^{3}$ $S_4^3.S_4$ (as 18T880) trivial $291.939159084$
18.2.645...809.1 $x^{18} - x^{17} + x^{16} - x^{15} + 9 x^{13} - 17 x^{12} + 12 x^{11} - x^{10} - 15 x^{9} + 47 x^{8} - 76 x^{7} + 56 x^{6} + 14 x^{5} - 70 x^{4} + 68 x^{3} - 34 x^{2} + 9 x - 1$ $19\cdot 31^{2}\cdot 59\cdot 7742417^{2}$ $C_2^9.S_9$ (as 18T968) trivial $308.996338318$
18.2.733...089.1 $x^{18} - 5 x^{16} - 7 x^{15} + 10 x^{14} + 25 x^{13} + x^{12} - 36 x^{11} - 15 x^{10} + 36 x^{9} + 20 x^{8} - 40 x^{7} - 43 x^{6} + 7 x^{5} + 28 x^{4} + 8 x^{3} - 7 x^{2} - 5 x - 1$ $11^{6}\cdot 23^{10}$ $A_4^3:S_4$ (as 18T713) trivial $305.528305053$
18.2.785...649.1 $x^{18} - 3 x^{17} + 4 x^{16} - 2 x^{15} - 9 x^{14} + 22 x^{13} - 21 x^{12} + 9 x^{11} + 15 x^{10} - 31 x^{9} + 15 x^{8} + 9 x^{7} - 21 x^{6} + 22 x^{5} - 9 x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 1$ $7^{14}\cdot 41^{5}$ $C_6^3:C_6$ (as 18T282) trivial $355.232713744$
18.2.791...504.1 $x^{18} - 3 x^{16} + x^{14} + 8 x^{12} - 20 x^{10} + 25 x^{8} - 17 x^{6} + 5 x^{4} + 2 x^{2} - 1$ $2^{18}\cdot 7^{6}\cdot 37^{6}$ $C_6^2:D_6$ (as 18T154) trivial $351.495037427$
18.2.802...089.1 $x^{18} - x^{17} + 4 x^{16} - x^{15} + 6 x^{14} - 4 x^{13} + 10 x^{12} - 6 x^{11} + x^{10} - 3 x^{9} + 2 x^{8} - 7 x^{7} - 10 x^{6} + x^{5} - 9 x^{4} - 4 x^{2} - 2 x - 1$ $31^{6}\cdot 67^{6}$ $A_4^3.S_4$ (as 18T711) trivial $326.952777148$
18.2.844...312.1 $x^{18} + 3 x^{16} - 4 x^{15} + 12 x^{14} + 6 x^{13} + 47 x^{12} - 6 x^{11} + 24 x^{10} - 88 x^{9} - 21 x^{8} - 120 x^{7} - 40 x^{6} - 60 x^{5} - 27 x^{4} - 10 x^{3} - 9 x^{2} - 1$ $2^{6}\cdot 3^{18}\cdot 23^{7}$ $C_2^7.C_6^2:D_6$ (as 18T734) trivial $385.83435797$
18.2.859...768.1 $x^{18} - 8 x^{17} + 32 x^{16} - 83 x^{15} + 154 x^{14} - 216 x^{13} + 232 x^{12} - 192 x^{11} + 130 x^{10} - 101 x^{9} + 130 x^{8} - 192 x^{7} + 232 x^{6} - 216 x^{5} + 154 x^{4} - 83 x^{3} + 32 x^{2} - 8 x + 1$ $2^{12}\cdot 13^{3}\cdot 37^{6}\cdot 61^{2}$ $D_6\wr S_3$ (as 18T556) trivial $365.762580816$
18.2.103...441.1 $x^{18} - 4 x^{16} - 2 x^{15} + 6 x^{14} + x^{13} - 6 x^{12} - 8 x^{11} - 3 x^{10} - x^{9} - 2 x^{8} - 10 x^{7} - 3 x^{6} - 5 x^{5} - 12 x^{4} - 6 x^{3} - 3 x^{2} - 3 x - 1$ $23^{6}\cdot 101^{2}\cdot 8263^{2}$ $A_4^3.(C_2\times S_4)$ (as 18T776) trivial $432.085458037$
18.2.104...408.1 $x^{18} + 2 x^{16} - 6 x^{15} + 2 x^{14} - 10 x^{13} + 15 x^{12} - 8 x^{11} + 19 x^{10} - 20 x^{9} + 10 x^{8} - 18 x^{7} + 14 x^{6} - 6 x^{5} + 9 x^{4} - 6 x^{3} + 2 x^{2} - 2 x + 1$ $2^{18}\cdot 11\cdot 43\cdot 587^{3}\cdot 4153$ $C_3^6.(C_2^6.S_6)$ (as 18T962) trivial $410.045077467$
18.2.107...649.1 $x^{18} - 2 x^{17} + 4 x^{16} - 9 x^{15} + 15 x^{14} - 22 x^{13} + 35 x^{12} - 47 x^{11} + 53 x^{10} - 67 x^{9} + 66 x^{8} - 59 x^{7} + 56 x^{6} - 39 x^{5} + 26 x^{4} - 17 x^{3} + 7 x^{2} - 3 x + 1$ $23^{6}\cdot 317^{2}\cdot 2687^{2}$ $A_4^3.(C_2\times S_4)$ (as 18T776) trivial $414.56387322$
18.2.108...696.1 $x^{18} + 5 x^{16} + x^{14} - 36 x^{12} - 88 x^{10} - 99 x^{8} - 69 x^{6} - 35 x^{4} - 10 x^{2} - 1$ $2^{18}\cdot 37^{6}\cdot 401^{2}$ $S_3^3:S_4$ (as 18T483) trivial $417.015615194$
18.2.111...312.1 $x^{18} - 4 x^{17} + 8 x^{16} - 8 x^{15} + x^{14} + 8 x^{13} - 10 x^{12} + 2 x^{11} + 6 x^{10} - 4 x^{9} - 4 x^{8} + 10 x^{7} - 6 x^{6} + 4 x^{5} + x^{4} + 2 x^{2} + 1$ $2^{27}\cdot 97^{6}$ $\SOPlus(4,2)$ (as 18T34) trivial $473.705580838$
18.2.131...961.1 $x^{18} - 5 x^{16} - 3 x^{15} + 8 x^{14} + 10 x^{13} + 4 x^{12} - 4 x^{11} - 21 x^{10} - 15 x^{9} + 15 x^{8} + 7 x^{7} - 8 x^{6} + 8 x^{5} + 5 x^{4} - 3 x^{3} + x^{2} + 1$ $3^{12}\cdot 23^{4}\cdot 31^{6}$ $A_4^3:S_4$ (as 18T718) trivial $505.71690915$
18.2.139...829.1 $x^{18} - 7 x^{17} + 21 x^{16} - 35 x^{15} + 41 x^{14} - 54 x^{13} + 81 x^{12} - 80 x^{11} + 28 x^{10} + 12 x^{9} + 7 x^{8} - 14 x^{7} - 33 x^{6} + 46 x^{5} - 3 x^{4} - 27 x^{3} + 21 x^{2} - 7 x + 1$ $3^{6}\cdot 29\cdot 433^{6}$ $C_2^4.S_4^2:C_2^2$ (as 18T691) trivial $511.222708619$
18.2.145...272.1 $x^{18} + 4 x^{16} + 3 x^{14} - 12 x^{12} + 7 x^{10} + 6 x^{8} - 11 x^{6} + 4 x^{4} + 4 x^{2} - 2$ $2^{33}\cdot 19^{8}$ $S_3^2$ (as 18T9) trivial $965.073685258$
18.2.169...264.1 $x^{18} - x^{14} - 3 x^{12} - 9 x^{10} + 2 x^{8} - 24 x^{6} + 9 x^{4} - x^{2} - 1$ $2^{24}\cdot 3^{6}\cdot 7^{12}$ $S_3\times A_4$ (as 18T31) trivial $522.985932438$
18.2.215...493.1 $x^{18} + 6 x^{16} - 7 x^{15} + 15 x^{14} - 35 x^{13} + 39 x^{12} - 70 x^{11} + 91 x^{10} - 95 x^{9} + 120 x^{8} - 110 x^{7} + 92 x^{6} - 82 x^{5} + 49 x^{4} - 28 x^{3} + 15 x^{2} - 3 x + 1$ $257^{6}\cdot 749557$ $C_3^6.C_2\wr A_4.C_2$ (as 18T930) trivial $627.643142925$
18.2.219...856.1 $x^{18} + x^{16} - 5 x^{14} - 5 x^{12} + 7 x^{10} - 2 x^{8} - 26 x^{6} - 23 x^{4} - 8 x^{2} - 1$ $2^{18}\cdot 307^{6}$ $C_2^2:A_4^2:S_3$ (as 18T437) trivial $730.001621669$
18.2.227...125.1 $x^{18} - 2 x^{17} - x^{16} + 6 x^{15} - 9 x^{14} + 6 x^{13} + 13 x^{11} - 52 x^{10} + 77 x^{9} - 52 x^{8} + 13 x^{7} + 6 x^{5} - 9 x^{4} + 6 x^{3} - x^{2} - 2 x + 1$ $5^{9}\cdot 13^{6}\cdot 17^{6}$ $S_3^2:C_2^2$ (as 18T63) trivial $715.911525302$
18.2.228...384.1 $x^{18} - 3 x^{16} + 6 x^{14} - 8 x^{12} + 8 x^{10} - 5 x^{8} + 3 x^{6} - x^{4} + x^{2} - 1$ $2^{18}\cdot 101^{2}\cdot 292181^{2}$ $C_2^8.S_9$ (as 18T964) trivial $571.6445084$
18.2.228...384.2 $x^{18} + 2 x^{16} + 2 x^{14} - 3 x^{10} - 7 x^{8} - 8 x^{6} - 6 x^{4} - 3 x^{2} - 1$ $2^{18}\cdot 101^{2}\cdot 292181^{2}$ $C_2^8.S_9$ (as 18T964) trivial $585.079655294$
18.2.234...216.1 $x^{18} + 9 x^{16} + 36 x^{14} + 84 x^{12} + 126 x^{10} + 126 x^{8} + 83 x^{6} + 33 x^{4} + 6 x^{2} - 1$ $2^{12}\cdot 3^{18}\cdot 23^{6}$ $C_2^2:A_4^2:D_6$ (as 18T520) trivial $573.045111995$
18.2.254...009.1 $x^{18} - 5 x^{17} + 16 x^{16} - 35 x^{15} + 59 x^{14} - 73 x^{13} + 59 x^{12} - 5 x^{11} - 79 x^{10} + 163 x^{9} - 224 x^{8} + 229 x^{7} - 192 x^{6} + 127 x^{5} - 59 x^{4} + 24 x^{3} - 4 x - 1$ $7^{12}\cdot 97^{2}\cdot 1399^{2}$ $S_4^3.A_4$ (as 18T838) trivial $661.987726773$
18.2.271...744.1 $x^{18} + x^{16} - 2 x^{12} + 5 x^{8} + 8 x^{6} + 6 x^{4} + x^{2} - 1$ $2^{18}\cdot 23^{6}\cdot 2647^{2}$ $S_3^3:S_4$ (as 18T483) trivial $636.303906811$
18.2.271...744.2 $x^{18} - 3 x^{16} + 8 x^{14} - 12 x^{12} + 11 x^{10} - 5 x^{8} - 2 x^{6} + 2 x^{4} - 1$ $2^{18}\cdot 23^{6}\cdot 2647^{2}$ $S_4^3.S_4$ (as 18T883) trivial $656.67762437$
18.2.271...744.3 $x^{18} - 5 x^{16} + 11 x^{14} - 15 x^{12} + 19 x^{10} - 20 x^{8} + 14 x^{6} - 10 x^{4} + 5 x^{2} - 1$ $2^{18}\cdot 23^{6}\cdot 2647^{2}$ $S_4^3.S_4$ (as 18T883) trivial $608.086604501$
18.2.297...352.1 $x^{18} - 3 x^{17} + 2 x^{16} + 10 x^{14} - 23 x^{13} + 6 x^{12} + 20 x^{11} - 11 x^{10} + 7 x^{9} - 65 x^{8} + 106 x^{7} - 43 x^{6} - 60 x^{5} + 101 x^{4} - 69 x^{3} + 28 x^{2} - 7 x + 1$ $2^{6}\cdot 3^{6}\cdot 23^{7}\cdot 37^{4}$ $A_4^3.(C_2^2\times S_4)$ (as 18T835) trivial $695.730594256$
18.2.297...352.2 $x^{18} - 4 x^{17} + 10 x^{16} - 27 x^{15} + 57 x^{14} - 83 x^{13} + 97 x^{12} - 102 x^{11} + 82 x^{10} - 36 x^{9} + 13 x^{8} - 34 x^{7} + 37 x^{6} - 5 x^{5} - 2 x^{4} - 15 x^{3} + 16 x^{2} - 7 x + 1$ $2^{6}\cdot 3^{6}\cdot 23^{7}\cdot 37^{4}$ $A_4^3.(C_2^2\times S_4)$ (as 18T835) trivial $940.892214705$
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