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Results (49 matches)

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Label Polynomial Discriminant Galois group Class group
11.3.124...376.1 x11 - 11x3 - 8 \( 2^{25}\cdot 11^{11}\cdot 13 \) $S_{11}$ (as 11T8) trivial (GRH)
11.1.116...287.1 x11 - 99x2 - 81 \( -\,3^{22}\cdot 11^{11}\cdot 13 \) $S_{11}$ (as 11T8) trivial (GRH)
11.1.942...247.1 x11 + 11x9 - 59049 \( -\,3^{26}\cdot 11^{11}\cdot 13 \) $S_{11}$ (as 11T8) trivial (GRH)
11.1.942...247.2 x11 - 363x2 - 594x - 243 \( -\,3^{26}\cdot 11^{11}\cdot 13 \) $S_{11}$ (as 11T8) trivial (GRH)
11.1.208...752.1 x11 - 44x9 + 726x7 - 5324x5 + 14641x3 - 22528 \( -\,2^{18}\cdot 11^{19}\cdot 13 \) $S_{11}$ (as 11T8) trivial (GRH)
11.1.380...727.1 x11 - 11x9 - 216513 \( -\,3^{14}\cdot 11^{19}\cdot 13 \) $S_{11}$ (as 11T8) trivial (GRH)
11.1.380...727.2 x11 - 33x9 - 17537553 \( -\,3^{14}\cdot 11^{19}\cdot 13 \) $S_{11}$ (as 11T8) trivial (GRH)
11.1.751...896.1 x11 - 484x7 + 58564x3 - 1362944 \( -\,2^{33}\cdot 11^{20}\cdot 13 \) $S_{11}$ (as 11T8) trivial (GRH)
15.1.3703260525677583.1 x15 - 2x14 + x13 - x12 - 5x11 + 4x10 - 3x9 + 2x8 + 6x7 - 3x6 + 3x5 - 4x4 - 5x3 - 3x2 - 3x - 1 \( -\,3\cdot 13^{3}\cdot 561866260913 \) 15T104 trivial
15.3.11354350039657729.1 x15 - 4x14 + 5x13 + x12 - 7x11 + x10 + 7x9 - 2x8 - 8x7 + 22x6 - 37x5 + 35x4 - 20x3 + 11x2 - 7x + 1 \( 13^{2}\cdot 127^{2}\cdot 1609^{3} \) 15T78 trivial
16.12.134...584.1 x16 - 6x15 - 2x14 + 176x13 - 989x12 - 412x11 + 14946x10 - 19310x9 - 58059x8 + 112806x7 + 17708x6 + 13772x5 - 313401x4 + 252950x3 + 32720x2 - 44094x - 7545 \( 2^{24}\cdot 3^{4}\cdot 13^{2}\cdot 157^{2}\cdot 1327^{4}\cdot 7649 \) 16T1947 trivial (GRH)
18.0.828...936.1 x18 + 4x12 - 4x9 + 13x6 - 26x3 + 13 \( -\,2^{18}\cdot 3^{18}\cdot 13^{8} \) 18T650 trivial (GRH)
18.0.828...936.2 x18 - 6x12 - 6x9 + 13x6 + 26x3 + 13 \( -\,2^{18}\cdot 3^{18}\cdot 13^{8} \) 18T650 trivial (GRH)
18.0.272...627.1 x18 - 5x15 + x12 - 58x9 + 1639x6 - 7062x3 + 11323 \( -\,3^{27}\cdot 13^{2}\cdot 19^{6}\cdot 67^{2} \) 18T584 trivial (GRH)
18.0.122...168.1 x18 - 2x17 + 5x16 - 4x15 + 4x14 - 4x11 + x10 - 6x9 - 5x8 - 2x7 + 16x4 + 24x3 + 17x2 + 6x + 1 \( -\,2^{16}\cdot 3^{9}\cdot 7^{16}\cdot 13^{4} \) 18T937 trivial (GRH)
18.0.193...747.1 x18 - x15 - 3x12 - 6x9 + 11x6 + 22x3 + 13 \( -\,3^{27}\cdot 13^{2}\cdot 107^{6} \) 18T653 trivial (GRH)
18.0.369...987.1 x18 - 8x15 - 37x12 + 258x9 + 2229x6 - 5395x3 + 41743 \( -\,3^{27}\cdot 13^{4}\cdot 19^{8} \) 18T454 $[3]$ (GRH)
18.0.369...987.2 x18 - 2x15 - 37x12 - 132x9 + 4503x6 - 19825x3 + 41743 \( -\,3^{27}\cdot 13^{4}\cdot 19^{8} \) 18T454 $[3]$ (GRH)
18.0.129...712.1 x18 - 6x17 + 17x16 - 24x15 + 16x14 + 14x11 - 35x10 + 42x9 + 7x8 + 28x7 + 52x4 + 52x3 + 65x2 + 26x + 13 \( -\,2^{12}\cdot 3^{9}\cdot 7^{16}\cdot 13^{6} \) 18T937 trivial (GRH)
18.0.291...000.1 x18 - 22x15 + 250x12 - 1634x9 + 9425x6 - 27040x3 + 54080 \( -\,2^{18}\cdot 3^{20}\cdot 5^{8}\cdot 13^{8} \) 18T413 $[3]$ (GRH)
18.6.944...312.1 x18 - 19x16 - 14x15 + 117x14 + 104x13 - 418x12 - 444x11 + 890x10 + 1282x9 - 793x8 - 2154x7 - 769x6 + 932x5 + 1107x4 + 526x3 + 134x2 + 18x + 1 \( 2^{24}\cdot 3^{13}\cdot 13^{4}\cdot 17^{4}\cdot 23^{6} \) 18T541 $[3]$ (GRH)
18.0.206...907.2 x18 - 42x15 - 167x12 + 13136x9 - 110969x6 + 5921929x3 + 128210329 \( -\,3^{27}\cdot 13^{4}\cdot 19^{6}\cdot 67^{4} \) 18T584 $[3]$ (GRH)
18.18.631...832.1 x18 - 72x16 + 2079x14 - 31272x12 + 266535x10 - 4466x9 - 1305720x8 + 88686x7 + 3537846x6 - 560898x5 - 4745520x4 + 1142700x3 + 2313441x2 - 311922x - 360386 \( 2^{18}\cdot 3^{45}\cdot 13^{8} \) $(C_9\times D_9):C_3$ (as 18T158) trivial (GRH)
18.14.197...648.1 x18 - 47x16 - 47x15 + 899x14 + 1798x13 - 8043x12 - 26826x11 + 21861x10 + 185806x9 + 154879x8 - 491467x7 - 1167834x6 - 436976x5 + 1652420x4 + 2980937x3 + 2338635x2 + 935454x + 155909 \( 2^{6}\cdot 13^{2}\cdot 17^{9}\cdot 67^{2}\cdot 101^{7}\cdot 179^{2} \) 18T921 trivial (GRH)
18.2.231...512.1 x18 - 72x15 + 36x14 + 5712x12 + 12024x11 + 77958x10 - 5152x9 - 638496x8 - 3394872x7 - 7824204x6 + 1372608x5 + 40365648x4 + 148451496x3 + 254837349x2 + 293877216x + 300134656 \( 2^{38}\cdot 3^{45}\cdot 13^{4} \) 18T952 $[3]$ (GRH)
18.6.122...152.1 x18 + 72x16 - 48x15 + 1539x14 - 2052x13 + 12780x12 - 24192x11 + 42615x10 - 74216x9 + 18144x8 + 143568x7 - 358539x6 + 677484x5 - 921780x4 + 780192x3 - 386640x2 + 103104x - 11456 \( 2^{28}\cdot 3^{45}\cdot 13^{6}\cdot 179^{2} \) 18T891 trivial (GRH)
18.0.388...587.1 x18 - 5x17 - 388x16 + 1895x15 + 53742x14 - 2501483x13 - 5379364x12 + 1291779016x11 + 11535679898x10 - 177256309790x9 + 563135892127x8 - 47099222096866x7 - 1006994261594410x6 - 9171517908797241x5 + 182299081236148981x4 + 2029933165042808933x3 + 14137926945484811926x2 + 24100348226462845274x + 331301229942500093733 \( -\,3^{5}\cdot 13^{6}\cdot 61^{12}\cdot 7069^{6} \) 18T611 $[3, 3]$ (GRH)
18.0.388...587.2 x18 - 6x17 + 21x16 + 5137x15 - 51804x14 - 1290722x13 + 36154469x12 - 521223572x11 + 6038836206x10 - 16578533427x9 + 304983625322x8 - 8454795436553x7 + 33178851617452x6 + 692158306635455x5 - 2754562473379645x4 - 43951803605317053x3 + 188500024937395669x2 + 212655440349014754x + 286329779695199889 \( -\,3^{5}\cdot 13^{6}\cdot 61^{12}\cdot 7069^{6} \) 18T611 $[3, 3]$ (GRH)
18.0.349...283.1 x18 - 1788x15 + 1966668x12 - 1619227253x9 + 2349501559548x6 - 2551860249998748x3 + 1705037985527826781 \( -\,3^{7}\cdot 13^{6}\cdot 61^{12}\cdot 7069^{6} \) 18T347 $[3, 3]$ (GRH)
18.0.314...547.1 x18 - 3x17 - 1741x16 + 5750x15 + 1345004x14 - 4490355x13 - 612411438x12 + 1760207911x11 + 185064723741x10 - 322833949732x9 - 39427315041634x8 + 10809763495833x7 + 5939165295762443x6 + 3211879322637265x5 - 571978159937264939x4 + 122210076997098114x3 + 23161926248083405077x2 - 70066206954230444829x + 728888560740521913681 \( -\,3^{9}\cdot 13^{6}\cdot 61^{12}\cdot 7069^{6} \) 18T609 $[6, 6]$ (GRH)
18.18.973...400.1 x18 - 120x16 - 296x15 + 3264x14 + 9408x13 - 38656x12 - 109824x11 + 251904x10 + 614912x9 - 1007616x8 - 1757184x7 + 2473984x6 + 2408448x5 - 3342336x4 - 1212416x3 + 1966080x2 - 266240 \( 2^{27}\cdot 3^{18}\cdot 5^{2}\cdot 13\cdot 43\cdot 781247\cdot 20541943834793\cdot 23806568934241927\cdot 35075122994025941 \) $S_{18}$ (as 18T983) trivial (GRH)
19.13.801...664.1 x19 - 2x18 - 18x17 + 32x16 + 132x15 - 202x14 - 502x13 + 645x12 + 1045x11 - 1122x10 - 1176x9 + 1078x8 + 700x7 - 557x6 - 220x5 + 151x4 + 34x3 - 20x2 - 2x + 1 \( -\,2^{3}\cdot 13^{2}\cdot 17\cdot 3229\cdot 34365587\cdot 85132367\cdot 3692009831 \) $S_{19}$ (as 19T8) trivial (GRH)
20.4.438...216.1 x20 - 6x19 - 32x18 + 310x17 - 469x16 - 3502x15 + 23272x14 - 25660x13 - 272270x12 + 560690x11 + 3789962x10 - 12395748x9 - 17547575x8 + 99212146x7 - 13520212x6 - 294729262x5 + 16568237x4 + 379284204x3 + 703850006x2 + 914384780x + 329131259 \( 2^{30}\cdot 13^{2}\cdot 127^{2}\cdot 1609^{4}\cdot 149563^{2} \) 20T1048 trivial (GRH)
20.8.253...000.1 x20 - 1008x18 - 8064x17 + 308644x16 + 5180224x15 - 6775416x14 - 816447168x13 - 7805753008x12 - 14705332352x11 + 312302109824x10 + 3437586736128x9 + 18843275841536x8 + 66362572400640x7 + 160541265039360x6 + 272705816576000x5 + 325266292633600x4 + 267064385536000x3 + 143885746176000x2 + 45833912320000x + 6547701760000 \( 2^{24}\cdot 3^{10}\cdot 5^{8}\cdot 7\cdot 13^{2}\cdot 61^{12}\cdot 97^{4}\cdot 103^{4}\cdot 509^{2}\cdot 28447^{2} \) 20T1107 trivial (GRH)
20.16.345...000.1 x20 - 4068x18 - 32544x17 + 4247054x16 + 68929184x15 - 1149507396x14 - 36277810848x13 - 188726719143x12 + 3814685417568x11 + 74673095388144x10 + 637303513042368x9 + 3319238672357216x8 + 11545267037187840x7 + 27847847642876160x6 + 47276566606976000x5 + 56384349017401600x4 + 46295149129216000x3 + 24942345133056000x2 + 7945229393920000x + 1135032770560000 \( 2^{20}\cdot 3^{10}\cdot 5^{8}\cdot 13^{4}\cdot 61^{10}\cdot 12613^{4}\cdot 166539805319^{2} \) 20T1077 trivial (GRH)
21.3.396...527.1 x21 - 5x20 + 11x19 - 20x18 + 37x17 - 68x16 + 120x15 - 168x14 + 237x13 - 331x12 + 362x11 - 431x10 + 452x9 - 381x8 + 350x7 - 238x6 + 169x5 - 90x4 + 43x3 + 6x2 + 27 \( -\,13^{2}\cdot 1801^{2}\cdot 193327^{3} \) 21T139 trivial (GRH)
21.5.112...600.1 x21 - x20 - 3x19 + 10x18 - 9x17 - 5x16 + 83x15 - 139x14 - 436x13 - 411x12 - 872x11 - 742x10 + 583x9 + 984x8 + 1484x7 + 1498x6 - 868x5 - 1614x4 - 396x3 - 242x2 - 180x + 50 \( 2^{8}\cdot 5^{2}\cdot 13^{6}\cdot 229^{6}\cdot 159191^{2} \) 21T148 trivial (GRH)
21.21.122...944.1 x21 - 7x20 - x19 + 114x18 - 219x17 - 472x16 + 1808x15 - 333x14 - 4832x13 + 5022x12 + 3881x11 - 8733x10 + 1621x9 + 5276x8 - 3399x7 - 644x6 + 1288x5 - 333x4 - 95x3 + 69x2 - 14x + 1 \( 2^{18}\cdot 13^{2}\cdot 73^{12}\cdot 347443^{2} \) 21T86 trivial (GRH)
21.19.460...104.1 x21 - 45x19 - 30x18 + 729x17 + 972x16 - 4266x15 - 9180x14 - 6687x13 - 2872x12 + 131652x11 + 443208x10 + 46436x9 - 1786608x8 - 2821416x7 - 29552x6 + 4752864x5 + 6645312x4 + 4669568x3 + 1886976x2 + 419328x + 39936 \( -\,2^{15}\cdot 3^{23}\cdot 13^{2}\cdot 313^{12} \) 21T137 trivial (GRH)
21.15.283...256.1 x21 - 6x20 - 129x19 + 738x18 + 6841x17 - 34182x16 - 206917x15 + 754770x14 + 4078383x13 - 7593138x12 - 52093363x11 + 8626390x10 + 365734083x9 + 439496302x8 - 804532503x7 - 2198991242x6 - 1696579116x5 - 3038803440x4 - 11303652912x3 - 18939196800x2 - 14663981568x - 4441714880 \( -\,2^{26}\cdot 13^{2}\cdot 73^{12}\cdot 1699^{2}\cdot 19440739^{2} \) 21T117 $[3]$ (GRH)
22.0.233...016.1 x22 + 58x20 + 1489x18 + 22320x16 + 216663x14 + 1424964x12 + 6438231x10 + 19757580x8 + 39484992x6 + 46601624x4 + 25144376x2 + 898976 \( -\,2^{45}\cdot 3^{28}\cdot 7^{4}\cdot 13\cdot 23^{4}\cdot 137^{16}\cdot 2161 \) 22T52 n/a
22.14.935...064.1 x22 - 58x20 + 1489x18 - 22320x16 + 216663x14 - 1424964x12 + 6438231x10 - 19757580x8 + 39484992x6 - 46601624x4 + 25144376x2 - 898976 \( 2^{47}\cdot 3^{28}\cdot 7^{4}\cdot 13\cdot 23^{4}\cdot 137^{16}\cdot 2161 \) 22T52 trivial (GRH)
30.0.136...619.1 x30 - 3x + 3 \( -\,3^{30}\cdot 13\cdot 5081745477824752989649090137328383374885887 \) $S_{30}$ (as 30T5712) $[2]$ (GRH)
30.0.141...531.1 x30 - x + 3 \( -\,13\cdot 179\cdot 560893979\cdot 1599364314633798641\cdot 6769077172765732520137982927 \) $S_{30}$ (as 30T5712) trivial (GRH)
30.2.239...125.1 x30 - 5x - 3 \( 5^{30}\cdot 13\cdot 5801281\cdot 34046874574873365201475419661436609 \) $S_{30}$ (as 30T5712) n/a
37.1.146...709.1 x37 + 2x - 1 \( 13\cdot 79\cdot 3203\cdot 230203\cdot 34944191\cdot 52002217\cdot 4124383231\cdot 2576354638936903184957678084959 \) $S_{37}$ (as 37T11) trivial (GRH)
37.1.739...704.1 x37 + 2x - 2 \( 2^{36}\cdot 11\cdot 13\cdot 29\cdot 8111\cdot 320127488203456295874894895225917443149549690432217 \) $S_{37}$ (as 37T11) trivial (GRH)
37.1.124...256.1 x37 + 2x - 4 \( 2^{70}\cdot 13\cdot 137\cdot 195791\cdot 10489284688357\cdot 5723750340436657\cdot 504174169295944373011 \) $S_{37}$ (as 37T11) n/a
38.0.195...488.1 x38 - 2x + 5 \( -\,2^{39}\cdot 13\cdot 35869\cdot 88799\cdot 604309\cdot 6594677\cdot 27890279\cdot 25456155281264080123\cdot 303856164543774260275357 \) $S_{38}$ (as 38T76) n/a
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