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Label Polynomial Discriminant Galois group Class group
18.0.29509806056472403181568.1 x18 - 9x17 + 36x16 - 81x15 + 108x14 - 81x13 + 21x12 + 36x11 - 81x10 + 81x9 - 9x8 - 54x7 + 45x6 - 27x5 + 27x4 - 18x2 + 12 \( -\,2^{16}\cdot 3^{37} \) $C_2\times He_3:C_2$ (as 18T41) Trivial
18.0.93265559882184385363968.1 x18 - 3x17 + 6x16 - 3x15 - 3x14 + 6x13 - 9x12 + 15x11 - 39x10 - 2x9 + 48x8 - 42x7 + 3x6 + 21x5 + 39x4 + 18x3 + 3x2 + 3x + 1 \( -\,2^{24}\cdot 3^{33} \) $C_2\times He_3:C_2$ (as 18T41) $[3]$
18.2.118039224225889612726272.1 x18 - 6x15 - 12x12 - 74x9 - 12x6 - 6x3 + 1 \( 2^{18}\cdot 3^{37} \) $C_2\times He_3:C_2$ (as 18T41) Trivial
18.2.293153584564451408203125.1 x18 - 3x15 + 3x12 - 14x9 + 15x6 + 24x3 - 1 \( 3^{36}\cdot 5^{9} \) $C_2\times He_3:C_2$ (as 18T41) Trivial
18.0.16521714136449317314070839296.1 x18 - 12x15 + 72x12 - 292x9 + 576x6 + 96x3 + 8 \( -\,2^{24}\cdot 3^{44} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.2.49565142409347951942212517888.1 x18 + 36x14 - 45x12 + 396x10 - 324x8 + 1467x6 - 648x4 + 1296x2 - 75 \( 2^{24}\cdot 3^{45} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.2.7878167217468889863048000000000.1 x18 - 24x15 + 180x12 + 5152x9 + 7056x6 + 3072x3 - 4096 \( 2^{12}\cdot 3^{44}\cdot 5^{9} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.0.8459117637862050464804269719552.1 x18 + 24x12 + 624x6 + 8 \( -\,2^{33}\cdot 3^{44} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.2.8459117637862050464804269719552.1 x18 - 24x12 + 624x6 - 8 \( 2^{33}\cdot 3^{44} \) $C_2\times He_3:C_2$ (as 18T41) $[2]$ (GRH)
18.0.23634501652406669589144000000000.1 x18 - 27x15 - 126x14 + 117x12 + 1296x11 + 5796x10 + 2079x9 + 2592x8 - 2592x7 - 71352x6 + 4320x5 + 20736x4 - 25920x3 + 331776x2 - 138240x + 38400 \( -\,2^{12}\cdot 3^{45}\cdot 5^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2]$ (GRH)
18.0.25377352913586151394412809158656.1 x18 - 36x14 - 144x12 + 396x10 + 2592x8 + 3888x6 + 2592x4 + 432x2 + 24 \( -\,2^{33}\cdot 3^{45} \) $C_2\times He_3:C_2$ (as 18T41) $[2, 2]$ (GRH)
18.2.25377352913586151394412809158656.1 x18 - 36x14 + 144x12 + 396x10 - 2592x8 + 3888x6 - 2592x4 + 432x2 - 24 \( 2^{33}\cdot 3^{45} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.0.25528356304590234835421802344448.1 x18 + 27x16 - 60x15 + 540x14 - 1188x13 + 5961x12 - 14364x11 + 46620x10 - 80304x9 + 142317x8 - 137592x7 + 164619x6 - 111132x5 + 124362x4 - 49392x3 + 31752x2 + 5292x + 1764 \( -\,2^{12}\cdot 3^{37}\cdot 7^{12} \) $C_2\times He_3:C_2$ (as 18T41) $[48]$ (GRH)
18.0.59566164710710547949317538803712.1 x18 - 30x15 + 351x12 - 1890x9 + 4977x6 + 1176x3 + 343 \( -\,2^{12}\cdot 3^{36}\cdot 7^{13} \) $C_2\times He_3:C_2$ (as 18T41) $[48]$ (GRH)
18.0.162771181452299835524978080837632.1 x18 - 9x17 + 54x16 - 216x15 + 684x14 - 1764x13 + 4008x12 - 8334x11 + 15741x10 - 27063x9 + 41706x8 - 50346x7 + 47298x6 - 97992x5 + 209844x4 - 186948x3 + 39240x2 + 12816x + 6112 \( -\,2^{12}\cdot 3^{44}\cdot 7^{9} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.2.488313544356899506574934242512896.1 x18 - 24x15 - 126x14 + 252x13 - 129x12 + 2124x11 + 5310x10 - 26240x9 + 31968x8 - 68634x7 - 128073x6 + 865368x5 - 878454x4 - 250188x3 + 404766x2 + 228402x - 168143 \( 2^{12}\cdot 3^{45}\cdot 7^{9} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.0.9511068774268243823056556964950016.3 x18 - 9x17 + 63x16 - 288x15 + 1116x14 - 3492x13 + 9780x12 - 24174x11 + 53955x10 - 108675x9 + 196839x8 - 310590x7 + 436710x6 - 700686x5 + 1053576x4 - 898146x3 + 399015x2 - 211203x + 106415 \( -\,2^{12}\cdot 3^{44}\cdot 11^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[3]$ (GRH)
18.2.28533206322804731469169670894850048.1 x18 - 33x15 - 234x14 + 468x13 + 177x12 + 4662x11 + 13086x10 - 72977x9 + 39096x8 - 134568x7 - 227046x6 + 3146436x5 - 3175020x4 - 4732980x3 + 5449824x2 + 3425472x - 3710192 \( 2^{12}\cdot 3^{45}\cdot 11^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[3]$ (GRH)
18.0.32268972922752572879044608000000000.1 x18 - 84x15 + 3000x12 - 53956x9 + 391392x6 + 489888x3 + 157464 \( -\,2^{24}\cdot 3^{44}\cdot 5^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2, 2]$ (GRH)
18.2.42774537890835454566245668796878848.1 x18 - 9x17 + 9x16 + 120x15 - 216x14 - 1080x13 + 2712x12 + 5022x11 - 17145x10 - 15875x9 + 77481x8 + 26334x7 - 265014x6 + 337122x5 - 245160x4 + 721170x3 - 1119177x2 + 692145x - 201483 \( 2^{12}\cdot 3^{44}\cdot 13^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[6]$ (GRH)
18.2.96806918768257718637133824000000000.1 x18 - 108x15 - 630x14 + 10755x12 + 42930x11 + 44730x10 - 156168x9 - 684450x8 - 869940x7 + 657207x6 + 4138290x5 + 5417280x4 + 576396x3 - 8442360x2 - 11406420x - 6970479 \( 2^{24}\cdot 3^{45}\cdot 5^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2, 2]$ (GRH)
18.18.104564147423601601885887702402859008.1 x18 - 72x16 + 2052x14 - 30789x12 + 269892x10 - 1428840x8 + 4484403x6 - 7636356x4 + 5381964x2 - 1323 \( 2^{24}\cdot 3^{37}\cdot 7^{12} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.2.123096362772951404110125000000000000.1 x18 - 240x12 + 62400x6 - 8000 \( 2^{12}\cdot 3^{44}\cdot 5^{15} \) $C_2\times He_3:C_2$ (as 18T41) $[3]$ (GRH)
18.0.128323613672506363698737006390636544.1 x18 - 21x15 + 414x14 + 828x13 + 4281x12 - 2394x11 + 26370x10 - 47605x9 + 161568x8 - 567216x7 + 890862x6 - 1532268x5 + 3698316x4 - 5016612x3 + 4302216x2 - 2485872x + 666832 \( -\,2^{12}\cdot 3^{45}\cdot 13^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2, 36]$ (GRH)
18.18.243983010655070404400404638940004352.1 x18 - 54x16 + 1107x14 - 10752x12 + 50715x10 - 112266x8 + 122157x6 - 65268x4 + 15876x2 - 1372 \( 2^{24}\cdot 3^{36}\cdot 7^{13} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.0.369289088318854212330375000000000000.1 x18 - 9x15 - 90x14 + 315x12 + 1080x11 + 3420x10 + 5805x9 + 11340x8 + 6480x7 - 9180x6 - 32940x5 - 32400x4 - 1944x3 + 49680x2 + 28080x + 22056 \( -\,2^{12}\cdot 3^{45}\cdot 5^{15} \) $C_2\times He_3:C_2$ (as 18T41) $[6]$ (GRH)
18.2.478338621956052404233641711607222272.1 x18 - 9x17 + 192x15 - 216x14 - 2304x13 + 4032x12 + 16326x11 - 35847x10 - 76955x9 + 204984x8 + 232506x7 - 793350x6 + 139896x5 + 520524x4 + 1788924x3 - 3052656x2 + 1155456x - 512704 \( 2^{12}\cdot 3^{44}\cdot 17^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2]$ (GRH)
18.2.666710759228620126310310219110940672.1 x18 - 132x15 + 5160x12 + 99748x9 + 611712x6 + 769824x3 - 157464 \( 2^{24}\cdot 3^{44}\cdot 7^{9} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.0.1301600072766989568748477298570440704.1 x18 - 9x17 + 81x16 - 432x15 + 2196x14 - 8460x13 + 30900x12 - 93870x11 + 266895x10 - 657675x9 + 1494549x8 - 2967102x7 + 5367378x6 - 8902854x5 + 13103532x4 - 14146866x3 + 12402243x2 - 9066771x + 4065589 \( -\,2^{12}\cdot 3^{44}\cdot 19^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[3]$ (GRH)
18.0.1435015865868157212700925134821666816.1 x18 - 30x15 + 522x14 + 1044x13 + 6729x12 - 5040x11 + 42570x10 - 132088x9 + 322596x8 - 1551690x7 + 2671395x6 - 4740084x5 + 13758246x4 - 18105654x3 + 11021922x2 - 6170886x + 2904619 \( -\,2^{12}\cdot 3^{45}\cdot 17^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2, 6]$ (GRH)
18.0.2000132277685860378930930657332822016.1 x18 - 108x15 + 126x14 + 7191x12 + 35154x11 + 112014x10 + 187920x9 + 1659042x8 - 3068604x7 + 16914231x6 - 36738198x5 + 93863448x4 - 168009228x3 + 248784480x2 - 230812092x + 163085133 \( -\,2^{24}\cdot 3^{45}\cdot 7^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2, 18]$ (GRH)
18.2.3904800218300968706245431895711322112.1 x18 - 51x15 - 450x14 + 900x13 + 1545x12 + 12330x11 + 40626x10 - 291299x9 - 30240x8 + 144720x7 - 287778x6 + 20146284x5 - 27337428x4 - 84735996x3 + 136845864x2 + 113599728x - 201675056 \( 2^{12}\cdot 3^{45}\cdot 19^{9} \) $C_2\times He_3:C_2$ (as 18T41) Trivial (GRH)
18.0.4033621615344071609880576000000000000.1 x18 - 30x15 + 450x12 - 8500x9 + 22500x6 + 600000x3 + 8000000 \( -\,2^{24}\cdot 3^{44}\cdot 5^{12} \) $C_2\times He_3:C_2$ (as 18T41) $[3]$ (GRH)
18.0.7265168307811659818615258509987442688.1 x18 - 9x17 + 90x16 - 504x15 + 2844x14 - 11700x13 + 47256x12 - 153774x11 + 480933x10 - 1269783x9 + 3159846x8 - 6738858x7 + 13325322x6 - 23140440x5 + 36128628x4 - 42759972x3 + 43262136x2 - 33133680x + 16877600 \( -\,2^{12}\cdot 3^{44}\cdot 23^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[36]$ (GRH)
18.2.12100864846032214829641728000000000000.1 x18 - 30x15 + 90x14 - 651x12 - 22050x11 - 85410x10 - 402550x9 - 1471230x8 - 3258900x7 - 5782233x6 - 7134930x5 - 6882300x4 - 4907100x3 - 2316780x2 - 937800x - 474743 \( 2^{24}\cdot 3^{45}\cdot 5^{12} \) $C_2\times He_3:C_2$ (as 18T41) $[3]$ (GRH)
18.0.16521714136449317314070839296000000000.1 x18 + 3000x12 + 9750000x6 + 15625000 \( -\,2^{33}\cdot 3^{44}\cdot 5^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2, 2]$ (GRH)
18.2.16521714136449317314070839296000000000.1 x18 - 3000x12 + 9750000x6 - 15625000 \( 2^{33}\cdot 3^{44}\cdot 5^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2, 2]$ (GRH)
18.0.18112863051681503783771887307342217216.1 x18 + 1584x12 + 689472x6 + 34012224 \( -\,2^{24}\cdot 3^{32}\cdot 17^{12} \) $C_2\times He_3:C_2$ (as 18T41) $[9]$ (GRH)
18.2.21725707073464655295329902915276443648.5 x18 - 150x15 + 12996x12 - 141480x9 + 231984x6 - 116640x3 - 373248 \( 2^{12}\cdot 3^{32}\cdot 17^{15} \) $C_2\times He_3:C_2$ (as 18T41) $[9]$ (GRH)
18.2.21795504923434979455845775529962328064.1 x18 - 60x15 - 558x14 + 1116x13 + 2499x12 + 17460x11 + 60390x10 - 480272x9 - 135864x8 + 892350x7 - 162705x6 + 40765104x5 - 64912734x4 - 233119176x3 + 446766822x2 + 393171066x - 871019771 \( 2^{12}\cdot 3^{45}\cdot 23^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[12]$ (GRH)
18.0.49565142409347951942212517888000000000.1 x18 - 900x14 - 18000x12 + 247500x10 + 8100000x8 + 60750000x6 + 202500000x4 + 168750000x2 + 46875000 \( -\,2^{33}\cdot 3^{45}\cdot 5^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2, 2, 18]$ (GRH)
18.2.49565142409347951942212517888000000000.1 x18 - 900x14 + 18000x12 + 247500x10 - 8100000x8 + 60750000x6 - 202500000x4 + 168750000x2 - 46875000 \( 2^{33}\cdot 3^{45}\cdot 5^{9} \) $C_2\times He_3:C_2$ (as 18T41) $[2, 2]$ (GRH)
18.2.54338589155044511351315661922026651648.2 x18 - 198x15 + 9774x12 + 9612x9 - 134460x6 + 150336x3 + 13824 \( 2^{24}\cdot 3^{33}\cdot 17^{12} \) $C_2\times He_3:C_2$ (as 18T41) $[9]$ (GRH)
18.0.65177121220393965885989708745829330944.6 x18 - 168x15 + 9312x12 - 108288x9 + 1294848x6 - 4036608x3 + 13824000 \( -\,2^{12}\cdot 3^{33}\cdot 17^{15} \) $C_2\times He_3:C_2$ (as 18T41) $[3, 18]$ (GRH)
18.0.68808685040765708380760273519552495616.1 x18 - 42x15 + 882x12 - 28836x9 + 272484x6 + 3608064x3 + 23887872 \( -\,2^{24}\cdot 3^{32}\cdot 19^{12} \) $C_2\times He_3:C_2$ (as 18T41) $[18]$ (GRH)
18.0.115224309251614256294832694353176408064.2 x18 - 96x15 + 6120x12 - 147888x9 + 1424448x6 - 4981824x3 + 5832000 \( -\,2^{12}\cdot 3^{32}\cdot 19^{15} \) $C_2\times He_3:C_2$ (as 18T41) $[3, 9]$ (GRH)
18.2.345672927754842768884498083059529224192.1 x18 - 12x15 + 3936x12 - 39528x9 + 4597632x6 - 60604416x3 + 56623104 \( 2^{12}\cdot 3^{33}\cdot 19^{15} \) $C_2\times He_3:C_2$ (as 18T41) $[9]$ (GRH)
18.2.8636886144486190692792838720008000000000.1 x18 - 9x17 + 27x16 + 84x15 - 810x14 + 2286x13 + 30x12 - 17712x11 + 49635x10 - 37579x9 - 60795x8 - 376128x7 + 1198338x6 - 3779586x5 - 3956958x4 + 9731004x3 - 17365923x2 - 3206385x + 37749839 \( 2^{12}\cdot 3^{32}\cdot 5^{9}\cdot 17^{12} \) $C_2\times He_3:C_2$ (as 18T41) $[3, 9]$ (GRH)
18.0.9273785882460929937291206301359215214592.1 x18 - 1074x12 + 788004x6 + 23887872 \( -\,2^{33}\cdot 3^{32}\cdot 17^{12} \) $C_2\times He_3:C_2$ (as 18T41) $[18]$ (GRH)
18.2.9273785882460929937291206301359215214592.2 x18 + 1074x12 + 788004x6 - 23887872 \( 2^{33}\cdot 3^{32}\cdot 17^{12} \) $C_2\times He_3:C_2$ (as 18T41) $[3, 9]$ (GRH)
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