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Label Polynomial Discriminant Galois group Class group
18.0.2954312706550833698643.1 x18 - x9 + 1 \( -\,3^{45} \) $C_{18}$ (as 18T1) Trivial
18.0.5480386857784802185939.1 x18 - x17 + x16 - x15 + x14 - x13 + x12 - x11 + x10 - x9 + x8 - x7 + x6 - x5 + x4 - x3 + x2 - x + 1 \( -\,19^{17} \) $C_{18}$ (as 18T1) Trivial
18.0.5677392343251487443465123.1 x18 - x17 + 9x16 - 6x15 + 50x14 - 29x13 + 162x12 - 63x11 + 361x10 - 118x9 + 494x8 - 77x7 + 431x6 - 71x5 + 185x4 + 10x3 + 35x2 - 5x + 1 \( -\,3^{9}\cdot 19^{16} \) $C_{18}$ (as 18T1) $[9]$
18.0.75613185918270483380568064.1 x18 + 17x16 + 120x14 + 455x12 + 1001x10 + 1287x8 + 924x6 + 330x4 + 45x2 + 1 \( -\,2^{18}\cdot 19^{16} \) $C_{18}$ (as 18T1) $[19]$
18.18.107870454521778261425837337.1 x18 - x17 - 18x16 + 18x15 + 134x14 - 134x13 - 531x12 + 531x11 + 1198x10 - 1198x9 - 1519x8 + 1519x7 + 989x6 - 989x5 - 265x4 + 265x3 + 20x2 - 20x + 1 \( 3^{9}\cdot 19^{17} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.258151783382020583032356864.7 x18 + 18x16 + 135x14 + 546x12 + 1287x10 + 1782x8 + 1386x6 + 540x4 + 81x2 + 1 \( -\,2^{18}\cdot 3^{44} \) $C_{18}$ (as 18T1) $[19]$
18.18.456487940826035155404146917.1 x18 - x17 - 17x16 + 16x15 + 120x14 - 105x13 - 455x12 + 364x11 + 1001x10 - 715x9 - 1287x8 + 792x7 + 924x6 - 462x5 - 330x4 + 120x3 + 45x2 - 9x - 1 \( 37^{17} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.18.563362135874260093126953125.1 x18 - x17 - 25x16 + 20x15 + 232x14 - 137x13 - 1018x12 + 403x11 + 2291x10 - 566x9 - 2742x8 + 387x7 + 1711x6 - 131x5 - 505x4 + 30x3 + 55x2 - 5x - 1 \( 5^{9}\cdot 19^{16} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.18.774455350146061749097070592.1 x18 - 18x16 + 135x14 - 546x12 + 1287x10 - 1782x8 + 1386x6 - 540x4 + 81x2 - 3 \( 2^{18}\cdot 3^{45} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.18.1436650532447139184230793216.1 x18 - 19x16 + 152x14 - 665x12 + 1729x10 - 2717x8 + 2508x6 - 1254x4 + 285x2 - 19 \( 2^{18}\cdot 19^{17} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.18.1923380668327365689220703125.1 x18 - 27x16 + 270x14 - 1269x12 + 3042x10 - 76x9 - 3888x8 + 261x7 + 2601x6 - 297x5 - 810x4 + 120x3 + 81x2 - 9x - 1 \( 3^{44}\cdot 5^{9} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.5770142004982097067662109375.1 x18 + 18x16 + 135x14 + 546x12 + 1287x10 - 76x9 + 1782x8 - 684x7 + 1386x6 - 2052x5 + 540x4 - 2280x3 + 81x2 - 684x + 5779 \( -\,3^{45}\cdot 5^{9} \) $C_{18}$ (as 18T1) $[74]$ (GRH)
18.0.10703880581610941769412109375.1 x18 - x17 + 20x16 - 20x15 + 172x14 - 172x13 + 837x12 - 837x11 + 2566x10 - 2566x9 + 5283x8 - 5283x7 + 7791x6 - 7791x5 + 9045x4 - 9045x3 + 9330x2 - 9330x + 9349 \( -\,5^{9}\cdot 19^{17} \) $C_{18}$ (as 18T1) $[152]$ (GRH)
18.0.11639651445632252525480175367.1 x18 - x17 + 26x16 - 19x15 + 319x14 - 179x13 + 2258x12 - 914x11 + 9881x10 - 2825x9 + 26418x8 - 4536x7 + 41176x6 - 4496x5 + 32480x4 + 10240x2 - 1280x + 512 \( -\,7^{9}\cdot 19^{16} \) $C_{18}$ (as 18T1) $[2, 74]$ (GRH)
18.0.38713951190154487490850848768.1 x18 + 34x16 + 480x14 + 3640x12 + 16016x10 + 41184x8 + 59136x6 + 42240x4 + 11520x2 + 512 \( -\,2^{27}\cdot 19^{16} \) $C_{18}$ (as 18T1) $[171]$ (GRH)
18.18.38713951190154487490850848768.1 x18 - 34x16 + 480x14 - 3640x12 + 16016x10 - 41184x8 + 59136x6 - 42240x4 + 11520x2 - 512 \( 2^{27}\cdot 19^{16} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.39739057971752889532465351767.1 x18 + 27x16 + 351x14 + 2646x12 + 12465x10 - 5x9 + 35964x8 + 468x7 + 61488x6 + 4752x5 + 51840x4 + 9600x3 + 20736x2 + 2304x + 512 \( -\,3^{44}\cdot 7^{9} \) $C_{18}$ (as 18T1) $[163]$ (GRH)
18.18.119217173915258668597396055301.1 x18 - 36x16 + 540x14 - 4368x12 + 20592x10 - 5x9 - 57024x8 + 90x7 + 88704x6 - 540x5 - 69120x4 + 1200x3 + 20736x2 - 720x - 1511 \( 3^{45}\cdot 7^{9} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.132173713091594538512566714368.2 x18 + 36x16 + 540x14 + 4368x12 + 20592x10 + 57024x8 + 88704x6 + 69120x4 + 20736x2 + 512 \( -\,2^{27}\cdot 3^{44} \) $C_{18}$ (as 18T1) $[333]$ (GRH)
18.18.132173713091594538512566714368.1 x18 - 36x16 + 540x14 - 4368x12 + 20592x10 - 57024x8 + 88704x6 - 69120x4 + 20736x2 - 512 \( 2^{27}\cdot 3^{44} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.18.221153377467012797984123331973.1 x18 - x17 - 37x16 + 37x15 + 571x14 - 571x13 - 4749x12 + 4749x11 + 22915x10 - 22915x9 - 64029x8 + 64029x7 + 96483x6 - 96483x5 - 64029x4 + 64029x3 + 8931x2 - 8931x - 797 \( 7^{9}\cdot 19^{17} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.242839247007536485508643885603.1 x18 - x17 + 17x16 - 6x15 + 201x14 - 76x13 + 999x12 - 218x11 + 3519x10 - 623x9 + 5540x8 + 1505x7 + 5069x6 - 129x5 + 528x4 - 97x3 + 56x2 - 7x + 1 \( -\,3^{9}\cdot 37^{16} \) $C_{18}$ (as 18T1) $[171]$ (GRH)
18.0.396521139274783615537700143104.1 x18 + 36x16 + 540x14 + 4368x12 + 20592x10 + 57024x8 + 88704x6 + 69120x4 + 20736x2 + 1536 \( -\,2^{27}\cdot 3^{45} \) $C_{18}$ (as 18T1) $[542]$ (GRH)
18.18.396521139274783615537700143104.1 x18 - 36x16 + 540x14 - 4368x12 + 20592x10 - 57024x8 + 88704x6 - 69120x4 + 20736x2 - 1536 \( 2^{27}\cdot 3^{45} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.680129765110548404696137774571.1 x18 - 7x17 + 31x16 - 98x15 + 331x14 - 957x13 + 2693x12 - 6227x11 + 15226x10 - 30674x9 + 66392x8 - 111391x7 + 216508x6 - 293668x5 + 517517x4 - 511304x3 + 833369x2 - 453934x + 713641 \( -\,11^{9}\cdot 19^{16} \) $C_{18}$ (as 18T1) $[2, 542]$ (GRH)
18.0.735565072612935262326166126592.1 x18 + 38x16 + 608x14 + 5320x12 + 27664x10 + 86944x8 + 160512x6 + 160512x4 + 72960x2 + 9728 \( -\,2^{27}\cdot 19^{17} \) $C_{18}$ (as 18T1) $[1026]$ (GRH)
18.18.735565072612935262326166126592.1 x18 - 38x16 + 608x14 - 5320x12 + 27664x10 - 86944x8 + 160512x6 - 160512x4 + 72960x2 - 9728 \( 2^{27}\cdot 19^{17} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.18.1488294338429317924379721203712.1 x18 - 2x17 - 42x16 + 78x15 + 680x14 - 1150x13 - 5337x12 + 7992x11 + 20953x10 - 26642x9 - 38251x8 + 38696x7 + 26450x6 - 19276x5 - 4165x4 + 2054x3 + 53x2 - 40x + 1 \( 2^{18}\cdot 3^{9}\cdot 19^{16} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.2322038274967832964613417227771.2 x18 - 9x17 + 45x16 - 156x15 + 504x14 - 1512x13 + 4272x12 - 10422x11 + 24552x10 - 51962x9 + 108099x8 - 193914x7 + 351249x6 - 518733x5 + 814050x4 - 933768x3 + 1272483x2 - 860841x + 992091 \( -\,3^{44}\cdot 11^{9} \) $C_{18}$ (as 18T1) $[1791]$ (GRH)
18.18.3058776789325072365774692364013.1 x18 - 7x17 - 23x16 + 238x15 + 67x14 - 3057x13 + 2147x12 + 18205x11 - 22172x10 - 48410x9 + 80696x8 + 38369x7 - 112670x6 + 27104x5 + 41513x4 - 25352x3 + 2633x2 + 1022x - 191 \( 13^{9}\cdot 19^{16} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.3234204723240544858872018632704.1 x18 + 33x16 + 410x14 + 2443x12 + 7424x10 + 11040x8 + 6723x6 + 1135x4 + 63x2 + 1 \( -\,2^{18}\cdot 37^{16} \) $C_{18}$ (as 18T1) $[171]$ (GRH)
18.18.6966114824903498893840251683313.1 x18 - 54x16 + 1215x14 - 14742x12 + 104247x10 - 136x9 - 433026x8 + 3672x7 + 1010394x6 - 33048x5 - 1180980x4 + 110160x3 + 531441x2 - 99144x - 40553 \( 3^{45}\cdot 11^{9} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.8985052139278849963819823767311.1 x18 - x17 + 20x16 - 21x15 + 120x14 - 142x13 + 174x12 - 302x11 - 405x10 - 1196x9 + 785x8 - 6238x7 + 9767x6 + 981x5 - 3327x4 + 13403x3 + 21875x2 + 620x + 22717 \( -\,3^{9}\cdot 37^{17} \) $C_{18}$ (as 18T1) $[152]$ (GRH)
18.18.10443002414754749649962321483613.1 x18 - 9x17 - 9x16 + 276x15 - 360x14 - 3024x13 + 6864x12 + 13338x11 - 44460x10 - 12218x9 + 118251x8 - 56754x7 - 104295x6 + 107991x5 - 10584x4 - 23004x3 + 8559x2 - 297x - 159 \( 3^{44}\cdot 13^{9} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.11088656920413061413017818359375.2 x18 - 7x17 + 40x16 - 154x15 + 627x14 - 1979x13 + 6508x12 - 16865x11 + 47380x10 - 103535x9 + 254065x8 - 459765x7 + 999805x6 - 1439914x5 + 2800752x4 - 2907231x3 + 5123532x2 - 2913750x + 4775041 \( -\,3^{9}\cdot 5^{9}\cdot 19^{16} \) $C_{18}$ (as 18T1) $[3258]$ (GRH)
18.18.12922465537100419689226617716849.1 x18 - x17 - 56x16 + 56x15 + 1312x14 - 1312x13 - 16643x12 + 16643x11 + 123406x10 - 123406x9 - 536825x8 + 536825x7 + 1291507x6 - 1291507x5 - 1450991x4 + 1450991x3 + 418894x2 - 418894x + 44917 \( 11^{9}\cdot 19^{17} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.18.24096702957455403051316876953125.1 x18 - 7x17 - 21x16 + 230x15 - 39x14 - 2523x13 + 2827x12 + 12069x11 - 19596x10 - 25476x9 + 52436x8 + 21175x7 - 56437x6 - 10039x5 + 24080x4 + 4861x3 - 1984x2 - 565x - 31 \( 5^{9}\cdot 37^{16} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.28277592430157040563214702870528.1 x18 + 57x16 + 1368x14 + 17955x12 + 140049x10 + 660231x8 + 1828332x6 + 2742498x4 + 1869885x2 + 373977 \( -\,2^{18}\cdot 3^{9}\cdot 19^{17} \) $C_{18}$ (as 18T1) $[2, 2786]$ (GRH)
18.0.31329007244264248949886964450839.1 x18 + 54x16 + 1215x14 + 14742x12 + 104247x10 - 1810x9 + 433026x8 - 48870x7 + 1010394x6 - 439830x5 + 1180980x4 - 1466100x3 + 531441x2 - 1319490x + 3335149 \( -\,3^{45}\cdot 13^{9} \) $C_{18}$ (as 18T1) $[2524]$ (GRH)
18.18.34205654728777159191037355893457.1 x18 - 7x17 - 32x16 + 294x15 + 275x14 - 4779x13 + 1076x12 + 37663x11 - 29140x10 - 146783x9 + 161417x8 + 251979x7 - 350891x6 - 118682x5 + 269024x4 - 41471x3 - 43388x2 + 12154x - 191 \( 17^{9}\cdot 19^{16} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.40891490652933723328906846968243.1 x18 - 12691x9 + 40353607 \( -\,3^{45}\cdot 7^{12} \) $C_{18}$ (as 18T1) $[543]$ (GRH)
18.0.40891490652933723328906846968243.2 x18 - 5831x9 + 40353607 \( -\,3^{45}\cdot 7^{12} \) $C_{18}$ (as 18T1) $[327]$ (GRH)
18.18.47477585226700098686074966922953.1 x18 - x17 - 34x16 + 29x15 + 435x14 - 311x13 - 2671x12 + 1551x11 + 8348x10 - 3867x9 - 13016x8 + 4608x7 + 9365x6 - 1994x5 - 2859x4 + 250x3 + 224x2 - 32x + 1 \( 73^{17} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.58116758997176374949719154916247.1 x18 - x17 + 58x16 - 58x15 + 1426x14 - 1426x13 + 19381x12 - 19381x11 + 159430x10 - 159430x9 + 819661x8 - 819661x7 + 2647993x6 - 2647993x5 + 5390491x4 - 5390491x3 + 7260376x2 - 7260376x + 7634353 \( -\,13^{9}\cdot 19^{17} \) $C_{18}$ (as 18T1) $[9774]$ (GRH)
18.0.75855608471185389708554302866739.1 x18 - x17 + x16 - 39x15 + 39x14 - 39x13 + 476x12 + 1177x11 + 951x10 - 1673x9 - 14857x8 - 2167x7 + 23181x6 + 3723x5 + 245519x4 - 597570x3 + 418761x2 - 77749x + 32263 \( -\,7^{12}\cdot 19^{17} \) $C_{18}$ (as 18T1) $[3, 3, 3, 3, 3]$ (GRH)
18.0.75855608471185389708554302866739.2 x18 - x17 + x16 - 39x15 + 39x14 - 39x13 + 476x12 - 818x11 + 5739x10 - 10185x9 + 13605x8 - 52973x7 + 10679x6 - 11572x5 + 80200x4 + 256689x3 + 421421x2 + 316197x + 116851 \( -\,7^{12}\cdot 19^{17} \) $C_{18}$ (as 18T1) $[3, 3, 3, 3]$ (GRH)
18.18.116781890125989356502353933497857.1 x18 - 9x17 - 18x16 + 348x15 - 252x14 - 5040x13 + 8472x12 + 33174x11 - 76374x10 - 91106x9 + 292437x8 + 35910x7 - 455655x6 + 186741x5 + 192555x4 - 131820x3 - 2259x2 + 14355x - 2161 \( 3^{44}\cdot 17^{9} \) $C_{18}$ (as 18T1) Trivial (GRH)
18.0.119665574759900159778264689410048.1 x18 + 37x16 + 518x14 + 3515x12 + 12284x10 + 22200x8 + 20683x6 + 9287x4 + 1591x2 + 37 \( -\,2^{18}\cdot 37^{17} \) $C_{18}$ (as 18T1) $[1526]$ (GRH)
18.0.147682003746622037852672000000000.1 x18 - 2x17 + 30x16 - 50x15 + 552x14 - 814x13 + 6983x12 - 8936x11 + 65641x10 - 72082x9 + 465597x8 - 424984x7 + 2471666x6 - 1778572x5 + 9429355x4 - 4814010x3 + 23461605x2 - 6474360x + 29134601 \( -\,2^{18}\cdot 5^{9}\cdot 19^{16} \) $C_{18}$ (as 18T1) $[8582]$ (GRH)
18.18.210684481487848166847338548828125.1 x18 - x17 - 75x16 + 75x15 + 2357x14 - 2357x13 - 40203x12 + 40203x11 + 402421x10 - 402421x9 - 2379787x8 + 2379787x7 + 7892981x6 - 7892981x5 - 12652555x4 + 12652555x3 + 6025205x2 - 6025205x + 1044469 \( 3^{9}\cdot 5^{9}\cdot 19^{17} \) $C_{18}$ (as 18T1) $[2]$ (GRH)
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