Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying matches 1-50 of )

Label	Polynomial	Discriminant	Galois group	Class group
18.0.10703880581610941769412109375.1	x^18 - x^17 + 20x^16 - 20x^15 + 172x^14 - 172x^13 + 837x^12 - 837x^11 + 2566x^10 - 2566x^9 + 5283x^8 - 5283x^7 + 7791x^6 - 7791x^5 + 9045x^4 - 9045x^3 + 9330x^2 - 9330x + 9349	\( -\,5^{9}\cdot 19^{17} \)	$C_{18}$ (as 18T1)	$[152]$ (GRH)
18.0.11639651445632252525480175367.1	x^18 - x^17 + 26x^16 - 19x^15 + 319x^14 - 179x^13 + 2258x^12 - 914x^11 + 9881x^10 - 2825x^9 + 26418x^8 - 4536x^7 + 41176x^6 - 4496x^5 + 32480x^4 + 10240x^2 - 1280x + 512	\( -\,7^{9}\cdot 19^{16} \)	$C_{18}$ (as 18T1)	$[2, 74]$ (GRH)
18.0.12488057521927227046014543503.1	x^18 - 8x^17 + 44x^16 - 148x^15 + 337x^14 - 355x^13 - 409x^12 + 2535x^11 - 3290x^10 - 6263x^9 + 43736x^8 - 119075x^7 + 221321x^6 - 296751x^5 + 303777x^4 - 226521x^3 + 141287x^2 - 71712x + 44507	\( -\,7^{15}\cdot 138041^{3} \)	18T285	$[2, 56]$ (GRH)
18.0.38713951190154487490850848768.1	x^18 + 34x^16 + 480x^14 + 3640x^12 + 16016x^10 + 41184x^8 + 59136x^6 + 42240x^4 + 11520x^2 + 512	\( -\,2^{27}\cdot 19^{16} \)	$C_{18}$ (as 18T1)	$[171]$ (GRH)
18.0.39739057971752889532465351767.1	x^18 + 27x^16 + 351x^14 + 2646x^12 + 12465x^10 - 5x^9 + 35964x^8 + 468x^7 + 61488x^6 + 4752x^5 + 51840x^4 + 9600x^3 + 20736x^2 + 2304x + 512	\( -\,3^{44}\cdot 7^{9} \)	$C_{18}$ (as 18T1)	$[163]$ (GRH)
18.0.41301528122037146650360676352.1	x^18 + 12x^16 - 40x^15 + 96x^14 - 444x^13 + 1674x^12 - 2472x^11 + 16878x^10 - 19734x^9 + 64794x^8 - 118380x^7 + 147569x^6 - 491256x^5 + 1646274x^4 - 2357414x^3 + 7131054x^2 - 6384660x + 1632457	\( -\,2^{27}\cdot 3^{27}\cdot 7^{9} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 26]$ (GRH)
18.0.47844481638506531328000000000.1	x^18 - 4x^17 + 18x^16 - 92x^15 + 137x^14 - 262x^13 + 928x^12 + 1544x^11 - 1155x^10 - 2378x^9 - 11207x^8 - 11994x^7 + 36962x^6 - 121254x^5 + 174674x^4 - 268108x^3 + 686430x^2 - 163192x + 580021	\( -\,2^{18}\cdot 3^{9}\cdot 5^{9}\cdot 7^{15} \)	$S_3 \times C_6$ (as 18T6)	$[2, 2, 26]$ (GRH)
18.0.54381578892591924651626528931.1	x^18 - 8x^17 + 27x^16 - 81x^15 + 291x^14 - 804x^13 + 1229x^12 + 793x^11 + 3756x^10 + 1662x^9 + 4817x^8 + 2413x^7 + 2650x^6 - 147x^5 + 464x^4 - 14x^3 + 28x^2 - x + 1	\( -\,3^{9}\cdot 13^{12}\cdot 17^{9} \)	$S_3 \times C_3$ (as 18T3)	$[3, 3, 18]$ (GRH)
18.0.62175293115232802505366962176.1	x^18 + 30x^16 + 349x^14 + 2085x^12 + 7021x^10 + 13685x^8 + 15239x^6 + 9016x^4 + 2254x^2 + 49	\( -\,2^{18}\cdot 7^{14}\cdot 769^{4} \)	18T552	$[6, 24]$ (GRH)
18.0.75791969904071417486171701248.1	x^18 + 30x^16 + 357x^14 + 2216x^12 + 7917x^10 + 16836x^8 + 21078x^6 + 14613x^4 + 4866x^2 + 577	\( -\,2^{18}\cdot 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T472	$[3, 84]$ (GRH)
18.0.75791969904071417486171701248.2	x^18 + 33x^16 + 432x^14 + 2878x^12 + 10569x^10 + 22212x^8 + 26600x^6 + 17148x^4 + 5193x^2 + 577	\( -\,2^{18}\cdot 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T879	$[240]$ (GRH)
18.0.84535014172552012147112280064.1	x^18 + 40x^16 + 606x^14 + 4498x^12 + 17745x^10 + 37370x^8 + 40081x^6 + 20600x^4 + 4112x^2 + 64	\( -\,2^{18}\cdot 7^{12}\cdot 13^{12} \)	$C_6 \times C_3$ (as 18T2)	$[3, 6, 6]$ (GRH)
18.0.92384419220890933620945190912.1	x^18 + 27x^16 + 289x^14 + 1645x^12 + 5523x^10 + 11298x^8 + 13839x^6 + 9334x^4 + 2678x^2 + 13	\( -\,2^{18}\cdot 7^{16}\cdot 13^{9} \)	$C_2\times C_3^2.A_4$ (as 18T92)	$[3, 42]$ (GRH)
18.0.92384419220890933620945190912.2	x^18 + 26x^16 + 274x^14 + 1498x^12 + 4522x^10 + 7469x^8 + 6433x^6 + 2652x^4 + 429x^2 + 13	\( -\,2^{18}\cdot 7^{16}\cdot 13^{9} \)	$C_2\times C_3^2.A_4$ (as 18T92)	$[114]$ (GRH)
18.0.94830820568684146627640045568.4	x^18 + 6x^16 + 24x^14 - 156x^13 + 181x^12 - 168x^11 - 12x^10 + 864x^9 + 1956x^8 - 1968x^7 - 773x^6 + 384x^5 + 810x^4 + 14112x^3 + 32844x^2 + 27720x + 9075	\( -\,2^{12}\cdot 3^{21}\cdot 19^{12} \)	$C_3^2 : C_2$ (as 18T4)	$[6, 18]$ (GRH)
18.0.102359054154765255044328108199.1	x^18 - 9x^17 + 62x^16 - 292x^15 + 1146x^14 - 3626x^13 + 9891x^12 - 22842x^11 + 46111x^10 - 80086x^9 + 121818x^8 - 159244x^7 + 180716x^6 - 173115x^5 + 140578x^4 - 91800x^3 + 48036x^2 - 17345x + 4181	\( -\,19^{17}\cdot 37\cdot 151\cdot 3343 \)	18T460	$[2, 2, 76]$ (GRH)
18.0.103514451522112291747997679616.1	x^18 + 25x^16 + 263x^14 + 1528x^12 + 5404x^10 + 12064x^8 + 16994x^6 + 14559x^4 + 6882x^2 + 1369	\( -\,2^{18}\cdot 19^{16}\cdot 37^{2} \)	18T264	$[2, 162]$ (GRH)
18.0.132173713091594538512566714368.2	x^18 + 36x^16 + 540x^14 + 4368x^12 + 20592x^10 + 57024x^8 + 88704x^6 + 69120x^4 + 20736x^2 + 512	\( -\,2^{27}\cdot 3^{44} \)	$C_{18}$ (as 18T1)	$[333]$ (GRH)
18.0.141204899984457152700528984064.1	x^18 + 24x^16 + 220x^14 + 1010x^12 + 2543x^10 + 3581x^8 + 2690x^6 + 905x^4 + 66x^2 + 1	\( -\,2^{18}\cdot 257^{6}\cdot 43237^{2} \)	18T556	$[2, 68]$ (GRH)
18.0.143831668082131915073650688000.1	x^18 + 20x^16 + 167x^14 + 757x^12 + 2025x^10 + 3248x^8 + 3022x^6 + 1477x^4 + 293x^2 + 5	\( -\,2^{30}\cdot 5^{3}\cdot 37^{6}\cdot 107^{2}\cdot 191^{2} \)	18T556	$[2, 60]$ (GRH)
18.0.147354494188655680463387247047.1	x^18 + 28x^16 - 31x^15 + 343x^14 - 560x^13 + 2535x^12 - 4606x^11 + 14791x^10 - 17924x^9 + 29428x^8 + 15897x^7 - 50004x^6 + 185423x^5 - 114961x^4 + 122123x^3 + 237580x^2 - 217679x + 451879	\( -\,7^{12}\cdot 97^{3}\cdot 22679^{3} \)	18T472	$[104]$ (GRH)
18.0.164037019762900412649715544064.1	x^18 - x^17 + 13x^16 - 2x^15 + 115x^14 - 91x^13 + 1177x^12 - 1431x^11 + 6780x^10 - 7238x^9 + 35125x^8 - 55927x^7 + 162275x^6 - 210997x^5 + 444163x^4 - 469025x^3 + 586289x^2 - 145088x + 90787	\( -\,2^{12}\cdot 3^{6}\cdot 11^{9}\cdot 13^{12} \)	$S_3 \times C_6$ (as 18T6)	$[126]$ (GRH)
18.0.168399912313071389456086597632.1	x^18 - 2x^17 + 47x^16 - 74x^15 + 907x^14 - 1134x^13 + 9377x^12 - 9216x^11 + 56719x^10 - 43522x^9 + 205793x^8 - 125158x^7 + 442963x^6 - 223626x^5 + 549366x^4 - 241380x^3 + 372456x^2 - 127008x + 74088	\( -\,2^{18}\cdot 3^{9}\cdot 7^{12}\cdot 11^{9} \)	$S_3 \times C_3$ (as 18T3)	$[3, 6, 18]$ (GRH)
18.0.188521017135728366078671192064.1	x^18 - 6x^17 + 31x^16 - 124x^15 + 403x^14 - 1144x^13 + 2830x^12 - 6420x^11 + 13956x^10 - 27780x^9 + 51861x^8 - 91584x^7 + 173635x^6 - 319924x^5 + 597495x^4 - 843778x^3 + 865576x^2 - 666536x + 330469	\( -\,2^{24}\cdot 37^{6}\cdot 16361^{3} \)	18T394	$[4, 68]$ (GRH)
18.0.202215111299126210886918044067.1	x^18 - 6x^17 + 6x^16 + 6x^15 + 267x^14 - 1599x^13 + 3156x^12 - 267x^11 - 4575x^10 - 6847x^9 + 34635x^8 + 2436x^7 - 52743x^6 - 51519x^5 + 250608x^4 + 227274x^3 - 605661x^2 - 261210x + 836587	\( -\,3^{31}\cdot 41^{9} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 38]$ (GRH)
18.0.206148603259625688967552734375.1	x^18 - 6x^17 + 21x^16 - 38x^15 + 72x^14 - 72x^13 + 82x^12 + 540x^11 - 123x^10 - 880x^9 + 17883x^8 - 34212x^7 + 79951x^6 - 92796x^5 + 178851x^4 - 124326x^3 + 112827x^2 - 54930x + 114211	\( -\,3^{27}\cdot 5^{9}\cdot 7^{12} \)	$C_6 \times C_3$ (as 18T2)	$[2, 2, 74]$ (GRH)
18.0.216895506996594951140594638751.1	x^18 - 9x^17 + 60x^16 - 276x^15 + 1040x^14 - 3164x^13 + 8190x^12 - 17914x^11 + 33819x^10 - 54695x^9 + 76338x^8 - 90906x^7 + 92078x^6 - 77770x^5 + 53800x^4 - 29270x^3 + 11843x^2 - 3165x + 433	\( -\,7^{16}\cdot 13^{8}\cdot 8000831 \)	18T586	$[165]$ (GRH)
18.0.220306167525977029404855894016.1	x^18 + 28x^16 - 6x^15 + 294x^14 - 98x^13 + 2049x^12 - 490x^11 + 9401x^10 + 62x^9 + 25921x^8 + 5572x^7 + 50645x^6 + 13328x^5 + 75068x^4 + 19698x^3 + 60025x^2 + 17150x + 42875	\( -\,2^{27}\cdot 7^{12}\cdot 17^{9} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 28]$ (GRH)
18.0.242839247007536485508643885603.1	x^18 - x^17 + 17x^16 - 6x^15 + 201x^14 - 76x^13 + 999x^12 - 218x^11 + 3519x^10 - 623x^9 + 5540x^8 + 1505x^7 + 5069x^6 - 129x^5 + 528x^4 - 97x^3 + 56x^2 - 7x + 1	\( -\,3^{9}\cdot 37^{16} \)	$C_{18}$ (as 18T1)	$[171]$ (GRH)
18.0.314658276613728674017349730304.1	x^18 + 32x^16 + 392x^14 + 2337x^12 + 7216x^10 + 11256x^8 + 7946x^6 + 2128x^4 + 120x^2 + 1	\( -\,2^{18}\cdot 13^{12}\cdot 61^{6} \)	$S_3 \times C_6$ (as 18T6)	$[3, 3, 12]$ (GRH)
18.0.333998778547472552821465808896.1	x^18 + 24x^16 + 228x^14 + 1129x^12 + 3177x^10 + 5133x^8 + 4523x^6 + 1874x^4 + 231x^2 + 1	\( -\,2^{30}\cdot 19^{6}\cdot 137^{6} \)	18T370	$[2, 64]$ (GRH)
18.0.396521139274783615537700143104.1	x^18 + 36x^16 + 540x^14 + 4368x^12 + 20592x^10 + 57024x^8 + 88704x^6 + 69120x^4 + 20736x^2 + 1536	\( -\,2^{27}\cdot 3^{45} \)	$C_{18}$ (as 18T1)	$[542]$ (GRH)
18.0.442064923298304690829165330432.1	x^18 - 6x^17 + 29x^16 - 102x^15 + 336x^14 - 890x^13 + 2170x^12 - 4566x^11 + 9356x^10 - 15604x^9 + 22168x^8 - 24046x^7 + 21992x^6 - 15918x^5 + 17462x^4 - 15366x^3 + 13571x^2 - 3898x + 6053	\( -\,2^{26}\cdot 37^{6}\cdot 13693^{3} \)	18T394	$[2, 100]$ (GRH)
18.0.450283905890997363000000000000.1	x^18 - 171x^12 + 9747x^6 + 27	\( -\,2^{12}\cdot 3^{37}\cdot 5^{12} \)	$C_3^2 : C_2$ (as 18T4)	$[3, 6, 6]$ (GRH)
18.0.450283905890997363000000000000.2	x^18 - 9x^17 + 45x^16 - 126x^15 + 189x^14 - 27x^13 - 216x^12 - 729x^11 + 3807x^10 - 5414x^9 - 423x^8 + 17991x^7 - 36621x^6 + 11718x^5 + 99414x^4 - 188676x^3 + 121500x^2 + 11016x + 1156	\( -\,2^{12}\cdot 3^{37}\cdot 5^{12} \)	$C_3^2 : C_2$ (as 18T4)	$[3, 6, 6]$ (GRH)
18.0.453054841581020940100929875968.2	x^18 - x^17 + 5x^16 + 19x^15 + 8x^14 + 68x^13 + 90x^12 - 118x^11 + 653x^10 + 1339x^9 - 771x^8 + 51x^7 + 4810x^6 + 2562x^5 + 2212x^4 + 7728x^3 + 4256x^2 + 2688x + 7168	\( -\,2^{12}\cdot 7^{15}\cdot 13^{12} \)	$S_3 \times C_6$ (as 18T6)	$[156]$ (GRH)
18.0.519235183203048555634413069867.2	x^18 - 6x^17 + 12x^16 - 28x^15 + 171x^14 - 192x^13 - 252x^12 + 624x^11 + 537x^10 + 4550x^9 + 11598x^8 + 23070x^7 + 61893x^6 + 117033x^5 + 211056x^4 + 282511x^3 + 269637x^2 + 183555x + 59273	\( -\,3^{24}\cdot 107^{9} \)	$S_3 \times C_3$ (as 18T3)	$[2, 2, 2, 18]$ (GRH)
18.0.524682375772545974113841184768.4	x^18 - 12x^16 - 8x^15 + 117x^14 + 96x^13 + 246x^12 + 438x^11 + 2376x^10 + 3532x^9 + 21948x^8 + 13782x^7 + 114732x^6 + 44268x^5 + 331017x^4 + 87920x^3 + 531078x^2 + 90444x + 386513	\( -\,2^{27}\cdot 3^{24}\cdot 7^{12} \)	$C_6 \times C_3$ (as 18T2)	$[18, 18]$ (GRH)
18.0.537713931394153787585294237696.1	x^18 + 26x^16 + 277x^14 + 1739x^12 + 8504x^10 + 34994x^8 + 100505x^6 + 170701x^4 + 150743x^2 + 52919	\( -\,2^{18}\cdot 7^{12}\cdot 52919^{3} \)	18T401	$[128]$ (GRH)
18.0.584519553822414728713847701504.1	x^18 + 22x^16 + 204x^14 + 1040x^12 + 3188x^10 + 6032x^8 + 6943x^6 + 4582x^4 + 1508x^2 + 169	\( -\,2^{18}\cdot 7^{12}\cdot 13^{2}\cdot 41^{2}\cdot 23813^{2} \)	18T879	$[2, 2, 66]$ (GRH)
18.0.602991213815902363206590020563.2	x^18 + 26x^16 - 28x^15 + 495x^14 - 518x^13 + 4312x^12 - 5250x^11 + 27163x^10 - 25326x^9 + 69607x^8 - 33026x^7 + 104749x^6 - 50344x^5 + 66332x^4 - 14224x^3 + 19600x^2 - 4704x + 3136	\( -\,3^{9}\cdot 7^{12}\cdot 19^{12} \)	$C_6 \times C_3$ (as 18T2)	$[6, 18]$ (GRH)
18.0.677479543132411644552981573632.1	x^18 - 10x^16 - 5x^15 + 84x^14 - 15x^13 - 186x^12 - 92x^11 + 1232x^10 - 405x^9 + 2987x^8 - 2817x^7 + 13566x^6 + 895x^5 + 29602x^4 - 626x^3 + 31305x^2 - 11895x + 61027	\( -\,2^{12}\cdot 7^{12}\cdot 37^{6}\cdot 167^{3} \)	$C_2\times S_3\times A_4$ (as 18T60)	$[216]$ (GRH)
18.0.685529707511808000000000000000.1	x^18 + 30x^16 + 360x^14 + 2370x^12 + 6300x^10 - 27000x^8 - 168300x^6 + 81000x^4 + 5886000x^2 + 18252000	\( -\,2^{31}\cdot 3^{21}\cdot 5^{15} \)	$C_2\times C_3^2:S_3$ (as 18T52)	$[2, 6, 18]$ (GRH)
18.0.691976677792049302709773533184.1	x^18 + 29x^16 + 338x^14 + 2070x^12 + 7345x^10 + 15603x^8 + 19532x^6 + 13258x^4 + 3756x^2 + 1	\( -\,2^{18}\cdot 1129^{8} \)	$D_{18}$ (as 18T13)	$[178]$ (GRH)
18.0.691976677792049302709773533184.2	x^18 + 19x^16 + 144x^14 + 566x^12 + 1256x^10 + 1607x^8 + 1160x^6 + 438x^4 + 69x^2 + 1	\( -\,2^{18}\cdot 1129^{8} \)	$C_2\times C_2^2:D_9$ (as 18T67)	$[200]$ (GRH)
18.0.725588521883853198293196716319.1	x^18 - 6x^17 + 3x^16 + 40x^15 - 3x^14 - 438x^13 + 1141x^12 + 126x^11 + 3081x^10 - 444x^9 + 14067x^8 + 28818x^7 + 68469x^6 + 96822x^5 + 113724x^4 + 94392x^3 + 60912x^2 + 23328x + 5184	\( -\,3^{27}\cdot 7^{9}\cdot 11^{9} \)	$S_3 \times C_3$ (as 18T3)	$[3, 6, 18]$ (GRH)
18.0.726566512595229689293941092352.2	x^18 - x^17 + 14x^16 + 17x^15 + 123x^14 + 149x^13 + 565x^12 + 814x^11 + 1779x^10 + 1863x^9 + 2434x^8 + 1956x^7 + 2058x^6 + 1369x^5 + 766x^4 + 264x^3 + 69x^2 + 10x + 1	\( -\,2^{12}\cdot 3^{9}\cdot 37^{14} \)	$S_3 \times C_6$ (as 18T6)	$[3, 6, 6]$ (GRH)
18.0.833176180046218838523368177664.3	x^18 - 18x^15 + 121x^12 - 414x^9 + 2587x^6 - 1080x^3 + 729	\( -\,2^{24}\cdot 3^{21}\cdot 7^{15} \)	$C_2\times C_3:S_3$ (as 18T12)	$[3, 6, 6]$ (GRH)
18.0.975771436849265818910759059456.1	x^18 + 34x^16 + 442x^14 + 2878x^12 + 10264x^10 + 20724x^8 + 24144x^6 + 15974x^4 + 5529x^2 + 769	\( -\,2^{18}\cdot 7^{12}\cdot 769^{5} \)	18T696	$[792]$ (GRH)
18.0.1115141259295002959559738261504.1	x^18 - 6x^17 + 39x^16 - 156x^15 + 741x^14 - 2964x^13 + 12243x^12 - 42762x^11 + 134040x^10 - 356156x^9 + 818277x^8 - 1613178x^7 + 2750907x^6 - 3956256x^5 + 4799817x^4 - 4605120x^3 + 3278853x^2 - 1452222x + 298719	\( -\,2^{27}\cdot 3^{30}\cdot 7^{9} \)	$S_3 \times C_6$ (as 18T6)	$[2, 6, 12]$ (GRH)

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