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Label Polynomial Discriminant Galois group Class group
18.0.1844362878529525198848.1 x18 + 45x12 + 27x6 + 27 \( -\,2^{12}\cdot 3^{37} \) $C_3^2 : C_2$ (as 18T4) Trivial
18.0.10460353203000000000000.1 x18 + 49x12 + 67x6 + 27 \( -\,2^{12}\cdot 3^{21}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3]$
18.0.593038347905528851673088.4 x18 + 37x12 - 29x6 + 27 \( -\,2^{12}\cdot 3^{21}\cdot 7^{12} \) $C_3^2 : C_2$ (as 18T4) $[3]$
18.0.2727747884710191986159616.4 x18 + 3x16 - 12x15 + 18x14 - 24x13 + 155x12 - 198x11 + 198x10 - 382x9 + 1305x8 - 1326x7 + 1667x6 - 2772x5 + 5418x4 - 4584x3 + 3528x2 - 2340x + 676 \( -\,2^{12}\cdot 3^{24}\cdot 11^{9} \) $C_3^2 : C_2$ (as 18T4) $[3]$ (GRH)
18.0.5080969518089676267073536.1 x18 - 9x17 + 39x16 - 108x15 + 240x14 - 504x13 + 988x12 - 1638x11 + 2775x10 - 5295x9 + 8883x8 - 11094x7 + 10882x6 - 9186x5 + 6900x4 - 4230x3 + 1815x2 - 459x + 51 \( -\,2^{12}\cdot 3^{21}\cdot 17^{9} \) $C_3^2 : C_2$ (as 18T4) $[6]$
18.0.18294428062468623673667584.4 x18 - 8x17 + 33x16 - 114x15 + 383x14 - 1156x13 + 3191x12 - 8326x11 + 19412x10 - 39456x9 + 73892x8 - 130472x7 + 201816x6 - 249352x5 + 231552x4 - 154816x3 + 70784x2 - 20064x + 2736 \( -\,2^{12}\cdot 7^{12}\cdot 19^{9} \) $C_3^2 : C_2$ (as 18T4) $[3]$
18.0.45639710758676856201171875.1 x18 - 3x17 + 12x16 - 35x15 + 109x14 - 232x13 + 465x12 - 905x11 + 1933x10 - 4064x9 + 7485x8 - 11437x7 + 14084x6 - 13785x5 + 11517x4 - 8290x3 + 5868x2 - 3024x + 1728 \( -\,5^{12}\cdot 83^{9} \) $C_3^2 : C_2$ (as 18T4) $[3, 3]$
18.0.99221394673320004142313472.1 x18 - 2x16 + 15x14 - 108x12 + 103x10 + 610x8 + 1929x6 - 576x4 + 400x2 + 1228 \( -\,2^{12}\cdot 307^{9} \) $C_3^2 : C_2$ (as 18T4) $[3, 3]$
18.0.109932594211669278076171875.2 x18 + 126x12 - 783x6 + 1728 \( -\,3^{37}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[2, 2]$
18.0.119907013147065124216135739.1 x18 - 8x17 + 32x16 - 80x15 + 215x14 - 426x13 + 1103x12 - 1508x11 + 3243x10 - 3606x9 + 7335x8 - 6028x7 + 7654x6 - 7690x5 + 3739x4 - 2416x3 + 3272x2 + 1888x + 944 \( -\,7^{12}\cdot 59^{9} \) $C_3^2 : C_2$ (as 18T4) $[3, 3]$
18.0.134467867946269093836238848.1 x18 - 35x12 + 907x6 + 27 \( -\,2^{12}\cdot 3^{21}\cdot 11^{12} \) $C_3^2 : C_2$ (as 18T4) $[2, 6]$
18.0.242190571378050467501912064.1 x18 - 2x17 - 4x16 + 22x15 + 44x14 - 74x13 + 223x12 + 312x11 - 1620x10 - 576x9 + 5508x8 - 2916x7 - 3861x6 + 7614x5 + 2916x4 - 486x3 + 2916x2 + 1458x + 729 \( -\,2^{12}\cdot 3^{9}\cdot 113^{9} \) $C_3^2 : C_2$ (as 18T4) $[3, 6]$
18.0.272438055977283000000000000.2 x18 - 3x17 + 5x16 - 22x15 + 69x14 - 125x13 + 204x12 - 417x11 + 873x10 - 1568x9 + 1977x8 - 1405x7 + 2837x6 - 7788x5 + 7654x4 - 1164x3 - 48x2 - 144x + 36 \( -\,2^{12}\cdot 3^{9}\cdot 5^{12}\cdot 7^{12} \) $C_3^2 : C_2$ (as 18T4) $[3]$
18.0.373295255190912955087663104.2 x18 + 18x16 + 99x14 + 36x12 - 813x10 - 1026x8 + 3469x6 + 12240x4 + 17820x2 + 6156 \( -\,2^{12}\cdot 3^{24}\cdot 19^{9} \) $C_3^2 : C_2$ (as 18T4) $[3]$ (GRH)
18.0.502592611936843000000000000.1 x18 - 2x17 - 6x16 + 22x15 + 24x14 - 200x13 + 553x12 - 586x11 + 462x10 - 1000x9 + 5130x8 - 10366x7 + 5855x6 + 100x5 + 6984x4 - 27518x3 + 32286x2 - 14018x + 8471 \( -\,2^{12}\cdot 5^{12}\cdot 43^{9} \) $C_3^2 : C_2$ (as 18T4) $[3, 3]$
18.0.998220592474975337089609728.1 x18 - 95x12 + 3667x6 + 27 \( -\,2^{12}\cdot 3^{21}\cdot 13^{12} \) $C_3^2 : C_2$ (as 18T4) $[3]$ (GRH)
18.0.2782483037193954337646484375.2 x18 + 21x16 - 35x15 + 189x14 - 336x13 + 1132x12 - 1764x11 + 4200x10 - 6552x9 + 10080x8 - 12180x7 + 13756x6 - 11844x5 + 10143x4 - 5684x3 + 3087x2 - 1029x + 343 \( -\,3^{24}\cdot 5^{12}\cdot 7^{9} \) $C_3^2 : C_2$ (as 18T4) $[3, 3]$ (GRH)
18.0.4775035397693072542278153399.1 x18 + 9x16 + 81x14 - 72x13 + 399x12 - 972x11 + 2241x10 - 2056x9 + 7209x8 - 9792x7 + 11457x6 - 5994x5 + 13860x4 - 6792x3 + 1296x2 + 6048x + 3136 \( -\,3^{37}\cdot 13^{9} \) $C_3^2 : C_2$ (as 18T4) $[4]$ (GRH)
18.0.5559060566555523000000000000.1 x18 + 9x12 + 4887x6 + 27 \( -\,2^{12}\cdot 3^{33}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[2, 6]$ (GRH)
18.0.5559060566555523000000000000.2 x18 + 3x16 + 42x14 + 295x12 - 102x10 - 2481x8 + 1405x6 + 6696x4 - 9324x2 + 3468 \( -\,2^{12}\cdot 3^{33}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 3]$ (GRH)
18.0.5559060566555523000000000000.3 x18 - 39x12 + 927x6 + 19683 \( -\,2^{12}\cdot 3^{33}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3]$ (GRH)
18.0.5627055140868788987624861696.1 x18 - 6x17 + 53x16 - 224x15 + 1059x14 - 3090x13 + 9543x12 - 18332x11 + 38972x10 - 39464x9 + 60140x8 + 22376x7 + 29584x6 + 113584x5 + 243424x4 - 171840x3 + 703168x2 - 494560x + 271568 \( -\,2^{12}\cdot 11^{9}\cdot 17^{12} \) $C_3^2 : C_2$ (as 18T4) $[3]$ (GRH)
18.0.6232508863425350301616650963.1 x18 - 90x12 + 8937x6 + 1728 \( -\,3^{37}\cdot 7^{12} \) $C_3^2 : C_2$ (as 18T4) $[2, 6]$ (GRH)
18.0.9254651051409408000000000000.4 x18 - 6x16 + 54x14 - 996x12 + 3321x10 + 5274x8 - 256x6 - 13920x4 - 38400x2 + 51200 \( -\,2^{27}\cdot 3^{24}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3]$ (GRH)
18.0.14026877608108874998608211968.1 x18 + 24x14 + 205x12 - 312x10 + 5412x8 - 6005x6 + 33456x4 - 3612x2 + 123 \( -\,2^{12}\cdot 3^{21}\cdot 41^{9} \) $C_3^2 : C_2$ (as 18T4) $[2, 2, 6]$ (GRH)
18.0.17957500407834968547439685632.1 x18 - 9x17 + 47x16 - 172x15 + 548x14 - 1540x13 + 3670x12 - 7174x11 + 12609x10 - 20783x9 + 28227x8 - 27838x7 + 33492x6 - 52450x5 + 33052x4 + 11642x3 - 27707x2 + 14385x + 11025 \( -\,2^{12}\cdot 547^{9} \) $C_3^2 : C_2$ (as 18T4) $[3, 3]$ (GRH)
18.0.19432680584168369411623747584.4 x18 - 6x17 + 21x16 - 56x15 + 207x14 - 702x13 + 1563x12 - 1116x11 - 3756x10 + 12472x9 - 8532x8 - 18192x7 + 49264x6 - 36096x5 - 192x4 - 5376x3 + 63744x2 - 73728x + 24576 \( -\,2^{27}\cdot 3^{21}\cdot 7^{12} \) $C_3^2 : C_2$ (as 18T4) $[6]$ (GRH)
18.0.24962803242374579500132282368.1 x18 + 6x16 + 24x14 - 132x13 + 13x12 - 120x11 - 348x10 + 864x9 + 2532x8 + 1536x7 + 4219x6 - 2976x5 - 5622x4 + 7200x3 + 16140x2 + 10440x + 2523 \( -\,2^{12}\cdot 3^{21}\cdot 17^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 3]$ (GRH)
18.0.27206534396294947000000000000.1 x18 - 3x17 - x16 + 60x15 - 45x14 - 23x13 + 564x12 - 1907x11 + 4705x10 - 7980x9 + 11689x8 - 15497x7 + 18411x6 - 17490x5 + 12020x4 - 5480x3 + 1300x2 - 100x + 100 \( -\,2^{12}\cdot 5^{12}\cdot 67^{9} \) $C_3^2 : C_2$ (as 18T4) $[2, 6]$ (GRH)
18.0.35347840065093568067138671875.1 x18 - 9x17 + 39x16 - 108x15 + 216x14 - 336x13 + 358x12 - 42x11 - 654x10 + 1224x9 - 1044x8 + 192x7 + 1849x6 - 4557x5 + 5559x4 - 3996x3 + 1740x2 - 432x + 48 \( -\,3^{21}\cdot 5^{12}\cdot 7^{12} \) $C_3^2 : C_2$ (as 18T4) $[3]$ (GRH)
18.0.61773685738999443000000000000.1 x18 - 3x17 + 5x16 + 14x15 - 81x14 + 169x13 - 258x12 - 27x11 + 1341x10 - 4988x9 + 10815x8 - 11791x7 + 6239x6 + 9090x5 - 16910x4 + 16140x3 + 2700x2 - 5400x + 8100 \( -\,2^{12}\cdot 3^{9}\cdot 5^{12}\cdot 11^{12} \) $C_3^2 : C_2$ (as 18T4) $[3]$ (GRH)
18.0.64119276021132037084693359375.1 x18 - 9x17 + 60x16 - 276x15 + 1059x14 - 3297x13 + 8326x12 - 17001x11 + 28578x10 - 40029x9 + 55638x8 - 80625x7 + 148498x6 - 237165x5 + 364521x4 - 394488x3 + 378474x2 - 212265x + 118815 \( -\,3^{21}\cdot 5^{9}\cdot 11^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 6]$ (GRH)
18.0.91176404162771495736000000000.4 x18 + 9x16 - 4x15 + 72x14 + 162x13 + 371x12 + 198x11 - 972x10 + 2976x9 + 10161x8 + 40986x7 + 67349x6 + 63342x5 + 188904x4 + 273560x3 + 182700x2 + 147000x + 122500 \( -\,2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 7^{9} \) $C_3^2 : C_2$ (as 18T4) $[3, 18]$ (GRH)
18.0.94830820568684146627640045568.4 x18 + 6x16 + 24x14 - 156x13 + 181x12 - 168x11 - 12x10 + 864x9 + 1956x8 - 1968x7 - 773x6 + 384x5 + 810x4 + 14112x3 + 32844x2 + 27720x + 9075 \( -\,2^{12}\cdot 3^{21}\cdot 19^{12} \) $C_3^2 : C_2$ (as 18T4) $[6, 18]$ (GRH)
18.0.232360475811152994149020729344.2 x18 - 21x16 - 6x15 + 240x14 - 216x13 - 846x12 + 2148x11 + 2037x10 - 12424x9 + 2787x8 + 32706x7 - 12422x6 - 2592x5 + 218880x4 + 247136x3 + 7968x2 - 96768x + 25088 \( -\,2^{18}\cdot 3^{24}\cdot 11^{12} \) $C_3^2 : C_2$ (as 18T4) $[2, 6]$ (GRH)
18.0.315164892649262158461997559808.1 x18 - 9x17 + 39x16 - 108x15 + 195x14 - 189x13 - 524x12 + 3339x11 - 8067x10 + 10800x9 - 13371x8 + 23229x7 + 48007x6 - 214326x5 + 311760x4 - 243648x3 + 86328x2 - 3456x + 48 \( -\,2^{12}\cdot 3^{33}\cdot 7^{12} \) $C_3^2 : C_2$ (as 18T4) $[2, 6]$ (GRH)
18.0.315164892649262158461997559808.2 x18 - 9x17 + 45x16 - 138x15 + 279x14 - 369x13 + 318x12 - 315x11 + 1413x10 - 5320x9 + 12681x8 - 22095x7 + 29967x6 - 25938x5 + 5652x4 + 8688x3 - 2448x2 - 396x + 484 \( -\,2^{12}\cdot 3^{33}\cdot 7^{12} \) $C_3^2 : C_2$ (as 18T4) $[2, 6]$ (GRH)
18.0.315164892649262158461997559808.6 x18 - 87x12 + 8991x6 + 19683 \( -\,2^{12}\cdot 3^{33}\cdot 7^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 3, 3]$ (GRH)
18.0.326499494057574490808000000000.1 x18 + 20x16 + 156x14 + 1645x12 + 5776x10 + 32200x8 + 36851x6 + 291260x4 + 564716x2 + 471875 \( -\,2^{12}\cdot 5^{9}\cdot 151^{9} \) $C_3^2 : C_2$ (as 18T4) $[3, 12]$ (GRH)
18.0.450283905890997363000000000000.1 x18 - 171x12 + 9747x6 + 27 \( -\,2^{12}\cdot 3^{37}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 6, 6]$ (GRH)
18.0.450283905890997363000000000000.2 x18 - 9x17 + 45x16 - 126x15 + 189x14 - 27x13 - 216x12 - 729x11 + 3807x10 - 5414x9 - 423x8 + 17991x7 - 36621x6 + 11718x5 + 99414x4 - 188676x3 + 121500x2 + 11016x + 1156 \( -\,2^{12}\cdot 3^{37}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 6, 6]$ (GRH)
18.0.450283905890997363000000000000.3 x18 - 9x17 + 45x16 - 150x15 + 369x14 - 711x13 + 1200x12 - 1989x11 + 2601x10 - 1364x9 - 3177x8 + 9243x7 - 10983x6 + 5760x5 + 3600x4 - 9228x3 + 9036x2 - 4788x + 1444 \( -\,2^{12}\cdot 3^{37}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 3, 3]$ (GRH)
18.0.450283905890997363000000000000.4 x18 - 9x17 + 45x16 - 132x15 + 234x14 - 198x13 - 42x12 + 36x11 + 1791x10 - 7439x9 + 17235x8 - 30852x7 + 45834x6 - 41490x5 - 1530x4 + 32460x3 - 9675x2 - 2925x + 4225 \( -\,2^{12}\cdot 3^{37}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 3, 3]$ (GRH)
18.0.450283905890997363000000000000.5 x18 - 9x17 + 45x16 - 126x15 + 189x14 - 27x13 - 516x12 + 1071x11 + 1557x10 - 14664x9 + 43227x8 - 82809x7 + 123129x6 - 113832x5 + 17064x4 + 45324x3 + 13500x2 + 8316x + 4356 \( -\,2^{12}\cdot 3^{37}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 3, 3]$ (GRH)
18.0.450283905890997363000000000000.6 x18 + 504x12 - 12528x6 + 110592 \( -\,2^{12}\cdot 3^{37}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 3, 3]$ (GRH)
18.0.450283905890997363000000000000.7 x18 - 9x17 + 45x16 - 114x15 + 99x14 + 315x13 - 834x12 - 639x11 + 6543x10 - 11714x9 + 5733x8 - 10035x7 + 74517x6 - 126324x5 - 58824x4 + 291912x3 - 119808x2 - 178992x + 204304 \( -\,2^{12}\cdot 3^{37}\cdot 5^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 3, 3, 3]$ (GRH)
18.0.458576209465793523000000000000.3 x18 + 664x12 - 368x6 + 110592 \( -\,2^{12}\cdot 3^{9}\cdot 5^{12}\cdot 13^{12} \) $C_3^2 : C_2$ (as 18T4) $[3, 9]$ (GRH)
18.0.519235183203048555634413069867.3 x18 - 3x16 - 36x15 + 171x14 - 312x13 + 616x12 - 2430x11 + 7284x10 - 19902x9 + 51336x8 - 111702x7 + 202515x6 - 314298x5 + 421431x4 - 437878x3 + 392661x2 - 281418x + 110764 \( -\,3^{24}\cdot 107^{9} \) $C_3^2 : C_2$ (as 18T4) $[6, 6]$ (GRH)
18.0.581414905561488081454979002368.1 x18 - 24x16 + 180x14 + 101x12 - 6168x10 + 14616x8 + 39119x6 + 35820x4 - 19368x2 + 2107 \( -\,2^{12}\cdot 3^{24}\cdot 43^{9} \) $C_3^2 : C_2$ (as 18T4) $[3, 3]$ (GRH)
18.0.887414471860576333752000000000.1 x18 + 30x16 + 351x14 + 1540x12 - 1209x10 - 13950x8 + 35161x6 - 26640x4 + 1296x2 + 7020 \( -\,2^{12}\cdot 3^{21}\cdot 5^{9}\cdot 13^{9} \) $C_3^2 : C_2$ (as 18T4) $[6, 6]$ (GRH)

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