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Results (displaying matches 1-50 of at least 1000) Next
| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.14478127324240404768365927869710336.1 | x18 + 114x16 + 5472x14 + 143640x12 + 2240784x10 + 21127392x8 + 117013248x6 + 351039744x4 + 478690560x2 + 191476224 | \( -\,2^{27}\cdot 3^{9}\cdot 19^{17} \) | $C_{18}$ (as 18T1) | $[2, 91252]$ (GRH) |
| 18.0.22733694229750493213828467513671875.1 | x18 - 7x17 + 85x16 - 434x15 + 3187x14 - 12969x13 + 71783x12 - 239315x11 + 1080280x10 - 2959970x9 + 11308280x8 - 25028575x7 + 82531870x6 - 141089824x5 + 405966017x4 - 485008616x3 + 1225758137x2 - 780172810x + 1741936681 | \( -\,5^{9}\cdot 7^{9}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[2, 4, 15124]$ (GRH) |
| 18.0.31252066838841568420795791520825344.1 | x18 + 126x16 + 6615x14 + 187278x12 + 3090087x10 + 29950074x8 + 163061514x6 + 444713220x4 + 466948881x2 + 121060821 | \( -\,2^{18}\cdot 3^{45}\cdot 7^{9} \) | $C_{18}$ (as 18T1) | $[2, 65786]$ (GRH) |
| 18.0.42858645692297580966155834896045767.1 | x18 + 126x16 + 6615x14 + 187278x12 + 3090087x10 - 33286x9 + 29950074x8 - 2097018x7 + 163061514x6 - 44037378x5 + 444713220x4 - 342512940x3 + 466948881x2 - 719277174x + 1229018617 | \( -\,3^{45}\cdot 29^{9} \) | $C_{18}$ (as 18T1) | $[111834]$ (GRH) |
| 18.0.57974030982712602914750026736730112.1 | x18 + 133x16 + 7448x14 + 228095x12 + 4151329x10 + 45664619x8 + 295063692x6 + 1032722922x4 + 1642968285x2 + 766718533 | \( -\,2^{18}\cdot 7^{9}\cdot 19^{17} \) | $C_{18}$ (as 18T1) | $[2, 2, 4, 10804]$ (GRH) |
| 18.0.60205903544285399375543269800867879.1 | x18 - 7x17 + 94x16 - 490x15 + 3915x14 - 16343x13 + 97606x12 - 334121x11 + 1618870x10 - 4550063x9 + 18591955x8 - 42122997x7 + 148181983x6 - 258570274x5 + 792133944x4 - 962623287x3 + 2585263350x2 - 1667313198x + 3945435121 | \( -\,3^{9}\cdot 13^{9}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[143164]$ (GRH) |
| 18.0.75613185918270483380568064000000000.2 | x18 - 2x17 + 75x16 - 130x15 + 2812x14 - 4244x13 + 67463x12 - 87766x11 + 1128241x10 - 1240582x9 + 13547997x8 - 12178574x7 + 116358536x6 - 80761652x5 + 687949530x4 - 330301660x3 + 2540118205x2 - 638418210x + 4468927451 | \( -\,2^{27}\cdot 5^{9}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[324558]$ (GRH) |
| 18.0.77615347601079862368096390169921875.2 | x18 - 9x17 + 99x16 - 588x15 + 3960x14 - 18144x13 + 92400x12 - 342630x11 + 1416780x10 - 4312778x9 + 14929371x8 - 36981954x7 + 108462921x6 - 210931569x5 + 524296044x4 - 733296564x3 + 1530279351x2 - 1193424489x + 2049933909 | \( -\,3^{44}\cdot 5^{9}\cdot 7^{9} \) | $C_{18}$ (as 18T1) | $[9, 27558]$ (GRH) |
| 18.0.79504772150118146627331158545105991.1 | x18 - x17 + 134x16 - 134x15 + 7582x14 - 7582x13 + 235677x12 - 235677x11 + 4387006x10 - 4387006x9 + 50051625x8 - 50051625x7 + 345115317x6 - 345115317x5 + 1377838239x4 - 1377838239x3 + 3020806524x2 - 3020806524x + 3787525057 | \( -\,19^{17}\cdot 29^{9} \) | $C_{18}$ (as 18T1) | $[376922]$ (GRH) |
| 18.0.85364764011113444925996300478214031.3 | x18 + 108x16 - x15 + 4482x14 - 111x13 + 93702x12 - 9351x11 + 1098684x10 - 328269x9 + 7734366x8 - 5411529x7 + 35788472x6 - 38234673x5 + 133520847x4 - 101345687x3 + 428074110x2 - 56209332x + 843884056 | \( -\,3^{27}\cdot 7^{15}\cdot 11^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 6, 18, 1026]$ (GRH) |
| 18.0.103357462359885242066848874838225951.6 | x18 - 9x17 + 78x16 - 412x15 + 2424x14 - 10500x13 + 52678x12 - 200712x11 + 869706x10 - 2838208x9 + 10478436x8 - 28265604x7 + 87960240x6 - 186727650x5 + 478893783x4 - 727075369x3 + 1476438822x2 - 1247429208x + 1875384008 | \( -\,3^{24}\cdot 7^{12}\cdot 31^{9} \) | $C_6 \times C_3$ (as 18T2) | $[3, 6, 13338]$ (GRH) |
| 18.0.144968523435705866934593522684771083.1 | x18 - 7x17 + 103x16 - 546x15 + 4715x14 - 20109x13 + 128861x12 - 451187x11 + 2334770x10 - 6708098x9 + 29183672x8 - 67479711x7 + 252196324x6 - 448042532x5 + 1455886589x4 - 1795886216x3 + 5108474617x2 - 3332816606x + 8337560089 | \( -\,19^{16}\cdot 43^{9} \) | $C_{18}$ (as 18T1) | $[228253]$ (GRH) |
| 18.0.159008743546498260206901265688807751.4 | x18 - 3x17 + 72x16 - 208x15 + 2574x14 - 7524x13 + 58932x12 - 170670x11 + 946242x10 - 2591186x9 + 10996740x8 - 25819998x7 + 87289860x6 - 156514464x5 + 432944661x4 - 534000599x3 + 1263575190x2 - 999364212x + 2115047096 | \( -\,3^{24}\cdot 7^{15}\cdot 17^{9} \) | $C_6 \times C_3$ (as 18T2) | $[2, 18, 8190]$ (GRH) |
| 18.0.254352889166747560743047516520738867.1 | x18 - x17 + 153x16 - 153x15 + 9881x14 - 9881x13 + 350361x12 - 350361x11 + 7432345x10 - 7432345x9 + 96463001x8 - 96463001x7 + 753920153x6 - 753920153x5 + 3383748761x4 - 3383748761x3 + 8165255321x2 - 8165255321x + 10715392153 | \( -\,3^{9}\cdot 11^{9}\cdot 19^{17} \) | $C_{18}$ (as 18T1) | $[2, 2, 4, 25708]$ (GRH) |
| 18.0.258151783382020583032356864000000000.2 | x18 + 72x16 + 2655x14 + 63384x12 + 1064547x10 - 2x9 + 12937608x8 + 738x7 + 113290266x6 - 29034x5 + 688088160x4 + 236460x3 + 2631789081x2 - 334818x + 4843960811 | \( -\,2^{27}\cdot 3^{44}\cdot 5^{9} \) | $C_{18}$ (as 18T1) | $[256298]$ (GRH) |
| 18.0.322803575628362753619753567652073327.1 | x18 - 7x17 + 112x16 - 602x15 + 5587x14 - 24267x13 + 166052x12 - 592865x11 + 3262588x10 - 9555455x9 + 44088281x8 - 103781941x7 + 410585125x6 - 741082426x5 + 2545728128x4 - 3182071487x3 + 9558403988x2 - 6299768998x + 16620397249 | \( -\,19^{16}\cdot 47^{9} \) | $C_{18}$ (as 18T1) | $[638885]$ (GRH) |
| 18.0.383947619242049123161763424792980511.1 | x18 + 162x16 + 10935x14 + 398034x12 + 8444007x10 - 83188x9 + 105225318x8 - 6738228x7 + 736577226x6 - 181932156x5 + 2582803260x4 - 1819321560x3 + 3486784401x2 - 4912168212x + 8082504811 | \( -\,3^{45}\cdot 37^{9} \) | $C_{18}$ (as 18T1) | $[2, 2, 79496]$ (GRH) |
| 18.0.474625342823745253277656048537109375.1 | x18 - x17 + 103x16 - 108x15 + 3454x14 - 3989x13 + 46893x12 - 69879x11 + 359244x10 - 608429x9 + 2260520x8 - 2195492x7 + 11950469x6 + 3825443x5 + 41497328x4 + 36129351x3 + 104448324x2 + 69234848x + 190444864 | \( -\,5^{9}\cdot 7^{15}\cdot 13^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 2, 4810]$ (GRH) |
| 18.0.479635217269575679584198692398854144.3 | x18 - 9x17 + 132x16 - 828x15 + 6498x14 - 31242x13 + 164170x12 - 670416x11 + 2543787x10 - 9052937x9 + 25552602x8 - 61654620x7 + 140163682x6 - 24671388x5 + 749479584x4 + 932445416x3 + 6255389784x2 + 2047765272x + 7031654056 | \( -\,2^{12}\cdot 3^{21}\cdot 7^{15}\cdot 11^{9} \) | $S_3 \times C_6$ (as 18T6) | $[6, 6, 3618]$ (GRH) |
| 18.0.494938579887862497256991740536934683.2 | x18 - 9x17 + 117x16 - 732x15 + 5688x14 - 27720x13 + 160752x12 - 634806x11 + 2965176x10 - 9587546x9 + 37297827x8 - 97660890x7 + 320905905x6 - 655191549x5 + 1822549050x4 - 2651158680x3 + 6197190291x2 - 4966452585x + 9587714579 | \( -\,3^{44}\cdot 43^{9} \) | $C_{18}$ (as 18T1) | $[7, 7, 11557]$ (GRH) |
| 18.0.580827582411592412573117020901351303.1 | x18 - 3x17 + 16x16 - 48x15 + 490x14 - 914x13 + 8852x12 - 12672x11 + 127488x10 - 130764x9 + 1475240x8 - 834166x7 + 12750158x6 - 3226096x5 + 76232667x4 - 10655757x3 + 281458960x2 - 20839308x + 478852184 | \( -\,7^{12}\cdot 13^{12}\cdot 23^{9} \) | $C_6 \times C_3$ (as 18T2) | $[3, 6, 13338]$ (GRH) |
| 18.0.581652040856250348581103942808504447.1 | x18 - x17 + 4x16 - 20x15 + 110x14 - 638x13 + 3828x12 - 10452x11 + 27225x10 - 60665x9 + 120032x8 - 195632x7 + 494368x6 - 886384x5 + 698944x4 + 424704x3 - 566272x2 - 573440x + 1048576 | \( -\,127^{17} \) | $C_{18}$ (as 18T1) | $[200135]$ (GRH) |
| 18.0.673269902026520824357188276050914131.2 | x18 - 7x17 + 121x16 - 658x15 + 6531x14 - 28817x13 + 209683x12 - 761507x11 + 4439956x10 - 13225274x9 + 64493752x8 - 154238751x7 + 643876978x6 - 1178657248x5 + 4267526217x4 - 5397548424x3 + 17074629129x2 - 11355872994x + 31522065121 | \( -\,3^{9}\cdot 17^{9}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[784854]$ (GRH) |
| 18.0.712240610787788121582600955510822303.1 | x18 - x17 + 172x16 - 172x15 + 12484x14 - 12484x13 + 497269x12 - 497269x11 + 11841238x10 - 11841238x9 + 172277371x8 - 172277371x7 + 1505131399x6 - 1505131399x5 + 7502974525x4 - 7502974525x3 + 19771290010x2 - 19771290010x + 27132279301 | \( -\,19^{17}\cdot 37^{9} \) | $C_{18}$ (as 18T1) | $[2, 2, 2, 2, 2, 2, 2, 14, 518]$ (GRH) |
| 18.0.774455350146061749097070592000000000.1 | x18 + 180x16 + 13500x14 + 546000x12 + 12870000x10 + 178200000x8 + 1386000000x6 + 5400000000x4 + 8100000000x2 + 3000000000 | \( -\,2^{27}\cdot 3^{45}\cdot 5^{9} \) | $C_{18}$ (as 18T1) | $[2, 244454]$ (GRH) |
| 18.0.801839982660831770253640955071823872.2 | x18 - 2x17 + 102x16 - 178x15 + 5032x14 - 7646x13 + 155495x12 - 203272x11 + 3292921x10 - 3626002x9 + 49341285x8 - 44214104x7 + 521749394x6 - 358900172x5 + 3749466651x4 - 1771316602x3 + 16612972693x2 - 4071582408x + 34608450449 | \( -\,2^{18}\cdot 13^{9}\cdot 19^{16} \) | $C_{18}$ (as 18T1) | $[9, 88578]$ (GRH) |
| 18.0.851918174186670722606904836351852544.4 | x18 + 14x16 - 16x15 + 462x14 + 124x13 + 9178x12 + 6384x11 + 146137x10 + 123252x9 + 1740052x8 + 1558324x7 + 15348721x6 + 12244424x5 + 93696170x4 + 51485984x3 + 356716588x2 + 95100288x + 652602712 | \( -\,2^{27}\cdot 3^{9}\cdot 7^{12}\cdot 13^{12} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 36, 468]$ (GRH) |
| 18.0.882021844557535515255288446111186944.2 | x18 + 101x16 + 4109x14 + 87716x12 + 1065692x10 + 7439224x8 + 28481283x6 + 52334795x4 + 31866025x2 + 1274641 | \( -\,2^{18}\cdot 1129^{10} \) | 18T548 | $[2, 53644]$ (GRH) |
| 18.0.967188608675270393759591510313094923.1 | x18 + 180x16 + 13500x14 + 546000x12 + 12870000x10 - 122791x9 + 178200000x8 - 11051190x7 + 1386000000x6 - 331535700x5 + 5400000000x4 - 3683730000x3 + 8100000000x2 - 11051190000x + 18077629681 | \( -\,3^{45}\cdot 41^{9} \) | $C_{18}$ (as 18T1) | $[19, 42446]$ (GRH) |
| 18.0.1024770265180753855691096064000000000.1 | x18 + 60x16 - 8x15 + 2133x14 - 96x13 + 54990x12 + 7350x11 + 1056552x10 + 290492x9 + 15135612x8 + 4958358x7 + 157769068x6 + 47240316x5 + 1124100009x4 + 248935216x3 + 4850734998x2 + 576974412x + 9505772641 | \( -\,2^{27}\cdot 3^{24}\cdot 5^{9}\cdot 7^{12} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 252, 252]$ (GRH) |
| 18.0.1418619440298203088067262326207274631.1 | x18 - x17 + 84x16 - 83x15 + 2190x14 - 2100x13 + 20098x12 + 32172x11 + 32703x10 + 186817x9 + 143808x8 + 341949x7 + 2032311x6 - 1063041x5 + 10119676x4 - 10269721x3 + 19805226x2 - 17042844x + 31109176 | \( -\,3^{9}\cdot 7^{15}\cdot 19^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 2, 3416]$ (GRH) |
| 18.0.1436650532447139184230793216000000000.1 | x18 + 190x16 + 15200x14 + 665000x12 + 17290000x10 + 271700000x8 + 2508000000x6 + 12540000000x4 + 28500000000x2 + 19000000000 | \( -\,2^{27}\cdot 5^{9}\cdot 19^{17} \) | $C_{18}$ (as 18T1) | $[38, 23978]$ (GRH) |
| 18.0.1531201474666953640931762831258280303.1 | x18 - 6x17 + 129x16 - 560x15 + 6714x14 - 20664x13 + 184456x12 - 363096x11 + 3000297x10 - 2959990x9 + 33312717x8 - 10998372x7 + 286497301x6 - 48374466x5 + 1803174465x4 - 405210528x3 + 6188670615x2 - 814254078x + 10029275353 | \( -\,3^{27}\cdot 7^{12}\cdot 29^{9} \) | $C_6 \times C_3$ (as 18T2) | $[6, 6, 23058]$ (GRH) |
| 18.0.1794179650728830182319895880000714379.1 | x18 - x17 + 191x16 - 191x15 + 15391x14 - 15391x13 + 680391x12 - 680391x11 + 17970391x10 - 17970391x9 + 289670391x8 - 289670391x7 + 2797670391x6 - 2797670391x5 + 15337670391x4 - 15337670391x3 + 43837670391x2 - 43837670391x + 62837670391 | \( -\,19^{17}\cdot 41^{9} \) | $C_{18}$ (as 18T1) | $[934990]$ (GRH) |
| 18.0.1826125204659502814026858937270403072.1 | x18 + 198x16 + 16335x14 + 726726x12 + 18842967x10 + 286992882x8 + 2455383546x6 + 10523072340x4 + 17363069361x2 + 7073843073 | \( -\,2^{18}\cdot 3^{45}\cdot 11^{9} \) | $C_{18}$ (as 18T1) | $[2, 347282]$ (GRH) |
| 18.0.1938499160566797308196011628480688128.1 | x18 - 9x17 + 54x16 - 212x15 + 1032x14 - 4572x13 + 20478x12 - 67602x11 + 236595x10 - 726875x9 + 2543820x8 - 6888426x7 + 19295616x6 - 41853396x5 + 109772868x4 - 221288668x3 + 489750240x2 - 607457328x + 728867672 | \( -\,2^{12}\cdot 3^{18}\cdot 7^{14}\cdot 23^{9} \) | $S_3 \times C_6$ (as 18T6) | $[3, 9, 9, 1026]$ (GRH) |
| 18.0.3220475320686797629881417736272539648.1 | x18 - x17 + 65x16 - 382x15 + 2176x14 - 14219x13 + 66249x12 - 203491x11 + 732082x10 - 2078441x9 + 4599882x8 - 10931026x7 + 19106088x6 - 32206984x5 + 67169500x4 - 46835020x3 + 118790560x2 - 86126792x + 92027224 | \( -\,2^{12}\cdot 11^{9}\cdot 37^{15} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 8, 24, 144]$ (GRH) |
| 18.0.3368994499603041762677432832000000000.1 | x18 - 6x17 + 18x16 - 44x15 + 402x14 - 1464x13 + 7930x12 - 22524x11 + 104349x10 - 243054x9 + 1196652x8 - 2104020x7 + 10180097x6 - 12952074x5 + 57659838x4 - 51315152x3 + 191003796x2 - 91799112x + 265747256 | \( -\,2^{18}\cdot 3^{24}\cdot 5^{9}\cdot 13^{12} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 36, 468]$ (GRH) |
| 18.0.3446030759610882930198241186568024064.1 | x18 - 9x17 + 123x16 - 716x15 + 5532x14 - 21096x13 + 106762x12 - 286986x11 + 813441x10 - 1769347x9 + 2206947x8 - 3211662x7 + 8452852x6 - 9702642x5 + 284543364x4 - 552590982x3 + 2252365185x2 - 3133190175x + 3038757625 | \( -\,2^{12}\cdot 3^{21}\cdot 7^{14}\cdot 17^{9} \) | $S_3 \times C_6$ (as 18T6) | $[2, 36, 3276]$ (GRH) |
| 18.0.3981163315919720752483315106924610739.1 | x18 - 7x17 + 33x16 - 106x15 + 513x14 - 1911x13 + 8905x12 - 28707x11 + 113286x10 - 312000x9 + 1072652x8 - 2391737x7 + 6978401x6 - 11975323x5 + 30556226x4 - 38411315x3 + 83255438x2 - 59181109x + 96478091 | \( -\,19^{9}\cdot 37^{16} \) | $C_{18}$ (as 18T1) | $[145669]$ (GRH) |
| 18.0.4408339576964120838747979776000000000.1 | x18 + 54x16 - 16x15 + 1980x14 + 49888x12 + 4800x11 + 940608x10 + 298064x9 + 13801632x8 + 6632928x7 + 151261200x6 + 90910848x5 + 1241215776x4 + 885349568x3 + 6833853696x2 + 3796985088x + 17040056384 | \( -\,2^{33}\cdot 3^{18}\cdot 5^{9}\cdot 7^{14} \) | $S_3 \times C_6$ (as 18T6) | $[6, 6, 11322]$ (GRH) |
| 18.0.4535231005796548759010580522990234375.1 | x18 - 9x17 + 144x16 - 948x15 + 8820x14 - 45864x13 + 313680x12 - 1326330x11 + 7239870x10 - 25028738x9 + 113150061x8 - 315334674x7 + 1200620121x6 - 2590431399x5 + 8346151809x4 - 12699762504x3 + 34466899041x2 - 28501566129x + 64264721489 | \( -\,3^{44}\cdot 5^{9}\cdot 11^{9} \) | $C_{18}$ (as 18T1) | $[846748]$ (GRH) |
| 18.0.5132921777297808355912172232996877887.1 | x18 - 6x17 + 51x16 + 42x15 - 1611x14 + 15876x13 - 67656x12 + 114906x11 + 769713x10 - 7444440x9 + 36860769x8 - 126914076x7 + 339321753x6 - 715801902x5 + 1239478116x4 - 1811464128x3 + 2278390032x2 - 2293113888x + 2010480704 | \( -\,3^{30}\cdot 7^{12}\cdot 23^{9} \) | $S_3 \times C_6$ (as 18T6) | $[3, 6, 9198]$ (GRH) |
| 18.0.6316806100079189177484411392000000000.1 | x18 - 2x17 + 14x16 - 26x15 + 346x14 - 498x13 + 5677x12 - 6174x11 + 71998x10 - 56440x9 + 707615x8 - 471728x7 + 5120273x6 - 2764682x5 + 26177811x4 - 8570496x3 + 82523855x2 - 10820664x + 116015941 | \( -\,2^{18}\cdot 5^{9}\cdot 37^{16} \) | $C_{18}$ (as 18T1) | $[146978]$ (GRH) |
| 18.0.8374216152942811568456908683240234375.1 | x18 - 3x17 + 48x16 - 4x15 + 684x14 + 2712x13 + 4202x12 + 25530x11 + 50940x10 - 150228x9 + 260676x8 + 1689372x7 + 4385648x6 + 5730762x5 + 11848893x4 + 12429935x3 + 18187044x2 + 4539660x + 22373704 | \( -\,3^{24}\cdot 5^{9}\cdot 19^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 18, 936]$ (GRH) |
| 18.0.11833920810399528639829186240681437183.1 | x18 - 9x17 - 12x16 + 286x15 - 165x14 - 3807x13 + 6441x12 + 12183x11 - 22956x10 - 34024x9 + 232287x8 - 295545x7 + 764284x6 - 997932x5 + 3322872x4 - 4412288x3 + 8997792x2 - 5924352x + 7562752 | \( -\,3^{18}\cdot 7^{9}\cdot 31^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 140378]$ (GRH) |
| 18.0.11911501053328835794135616273165234176.1 | x18 - 7x17 + 39x16 - 122x15 + 519x14 - 1965x13 + 9993x12 - 37201x11 + 143358x10 - 436376x9 + 1381097x8 - 3591517x7 + 9385751x6 - 19663227x5 + 40163743x4 - 61821841x3 + 90274691x2 - 80448578x + 66363211 | \( -\,2^{12}\cdot 19^{9}\cdot 37^{14} \) | $S_3 \times C_6$ (as 18T6) | $[2, 2, 37386]$ (GRH) |
| 18.0.15464650229059143166953879566724609375.1 | x18 - 9x17 + 6x16 + 142x15 - 21x14 - 2379x13 + 8007x12 - 18729x11 + 69558x10 - 212016x9 + 1087623x8 - 2223417x7 + 9310034x6 - 14204472x5 + 51935352x4 - 61439152x3 + 173788800x2 - 114413568x + 232459264 | \( -\,3^{21}\cdot 5^{9}\cdot 31^{14} \) | $S_3 \times C_6$ (as 18T6) | $[9, 126, 378]$ (GRH) |
| 18.0.17548929959529003835585593295529296875.1 | x18 - x17 + 131x16 - 132x15 + 6336x14 - 6469x13 + 143253x12 - 140828x11 + 1562253x10 - 1571735x9 + 8052725x8 - 14267296x7 + 27823148x6 - 81796806x5 + 58201854x4 - 165861112x3 + 190294745x2 - 40222117x + 639840259 | \( -\,3^{9}\cdot 5^{9}\cdot 37^{17} \) | $C_{18}$ (as 18T1) | $[38, 6878]$ (GRH) |
| 18.0.18893592163670789529965168685732855808.1 | x18 + 133x16 + 5852x14 + 104937x12 + 902139x10 + 4121537x8 + 10383443x6 + 14115822x4 + 9410548x2 + 2352637 | \( -\,2^{18}\cdot 7^{15}\cdot 19^{15} \) | $C_6 \times C_3$ (as 18T2) | $[2, 2, 4, 4, 4, 868]$ (GRH) |
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