Global number field search results

Further refine search

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
12.0.528345816354901963089.1	x^12 - x^11 + 99x^10 - 71x^9 + 3536x^8 - 1548x^7 + 55630x^6 - 5985x^5 + 377279x^4 + 187264x^3 + 822528x^2 + 1079414x + 1930411	\( 3^{6}\cdot 7^{10}\cdot 37^{6} \)	$C_6\times C_2$ (as 12T2)	$[6, 168]$ (GRH)
12.0.564668382613504000000.1	x^12 - 6x^11 + 61x^10 - 250x^9 + 1244x^8 - 3542x^7 + 8985x^6 - 15542x^5 + 32704x^4 - 43170x^3 + 56065x^2 - 36550x + 84475	\( 2^{18}\cdot 5^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 252]$ (GRH)
12.0.564668382613504000000.2	x^12 - 2x^11 + 51x^10 - 82x^9 + 1279x^8 - 1658x^7 + 19320x^6 - 19260x^5 + 182902x^4 - 126884x^3 + 1022917x^2 - 377314x + 2641211	\( 2^{18}\cdot 5^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 84]$ (GRH)
12.0.843466573910016000000.6	x^12 + 110x^10 + 4400x^8 + 78000x^6 + 600000x^4 + 1600000x^2 + 1000000	\( 2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 532]$ (GRH)
12.0.843466573910016000000.7	x^12 - 2x^11 + 49x^10 - 76x^9 + 1230x^8 - 1624x^7 + 19118x^6 - 20370x^5 + 188576x^4 - 153516x^3 + 1131480x^2 - 565856x + 3101281	\( 2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[30, 60]$ (GRH)
12.0.843466573910016000000.8	x^12 - 6x^11 + 93x^10 - 410x^9 + 3372x^8 - 11094x^7 + 60185x^6 - 143382x^5 + 553824x^4 - 880834x^3 + 2459025x^2 - 2040774x + 5366971	\( 2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[20, 140]$ (GRH)
12.0.863624717099249717248.1	x^12 + 91x^10 + 3185x^8 + 53508x^6 + 436982x^4 + 1529437x^2 + 1529437	\( 2^{12}\cdot 7^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[10, 130]$ (GRH)
12.0.871453576365136287601.1	x^12 - 4x^11 + 61x^10 - 188x^9 + 1705x^8 - 4046x^7 + 27480x^6 - 48151x^5 + 269067x^4 - 313697x^3 + 1522264x^2 - 891138x + 3924623	\( 13^{10}\cdot 43^{6} \)	$C_6\times C_2$ (as 12T2)	$[2184]$ (GRH)
12.0.943909854783176577024.2	x^12 + 27x^10 + 501x^8 + 7735x^6 + 73521x^4 + 356943x^2 + 683929	\( 2^{12}\cdot 3^{18}\cdot 29^{6} \)	$C_6\times C_2$ (as 12T2)	$[9, 126]$ (GRH)
12.0.977386981628298828125.1	x^12 - x^11 + 93x^10 - 94x^9 + 3204x^8 - 3298x^7 + 52912x^6 - 59464x^5 + 463265x^4 - 537436x^3 + 2225015x^2 - 1732597x + 5417371	\( 5^{9}\cdot 7^{10}\cdot 11^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 628]$ (GRH)
12.0.978162634246022205561.1	x^12 - x^11 + 110x^10 - 79x^9 + 4369x^8 - 1920x^7 + 76481x^6 - 8490x^5 + 577579x^4 + 278581x^3 + 1416470x^2 + 1806919x + 3282511	\( 3^{6}\cdot 7^{10}\cdot 41^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 14, 14]$ (GRH)
12.0.1066018797345756936877.1	x^12 - x^11 + 92x^10 - 92x^9 + 3277x^8 - 3277x^7 + 56785x^6 - 56785x^5 + 493767x^4 - 493767x^3 + 2023204x^2 - 2023204x + 3552641	\( 13^{11}\cdot 29^{6} \)	$C_{12}$ (as 12T1)	$[2, 628]$ (GRH)
12.0.1301723250337256492529.1	x^12 - 4x^11 + 59x^10 - 184x^9 + 1656x^8 - 3896x^7 + 27033x^6 - 45972x^5 + 271828x^4 - 290946x^3 + 1620818x^2 - 766937x + 4461997	\( 3^{6}\cdot 7^{10}\cdot 43^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 8, 8, 8]$ (GRH)
12.0.1340505915846345703125.1	x^12 + 78x^10 - x^9 + 2079x^8 - 441x^7 + 25088x^6 - 15957x^5 + 152430x^4 - 166064x^3 + 599634x^2 - 332247x + 1522711	\( 3^{18}\cdot 5^{9}\cdot 11^{6} \)	$C_{12}$ (as 12T1)	$[2, 2, 458]$ (GRH)
12.0.1486006368571562353321.4	x^12 - 4x^11 + 67x^10 - 208x^9 + 2040x^8 - 4886x^7 + 35616x^6 - 63001x^5 + 375610x^4 - 441883x^3 + 2275171x^2 - 1343635x + 6235475	\( 13^{10}\cdot 47^{6} \)	$C_6\times C_2$ (as 12T2)	$[20, 140]$ (GRH)
12.0.1494252487142601854976.2	x^12 + 31x^10 + 401x^8 + 2883x^6 + 13353x^4 + 46331x^2 + 142129	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 504]$ (GRH)
12.0.1494252487142601854976.3	x^12 + 39x^10 + 793x^8 + 10543x^6 + 89401x^4 + 428675x^2 + 877969	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[3, 18, 36]$ (GRH)
12.0.1494252487142601854976.4	x^12 + 121x^10 + 5324x^8 + 103818x^6 + 878460x^4 + 2576816x^2 + 1771561	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[6, 504]$ (GRH)
12.0.1709948423405886890625.1	x^12 - 56x^9 + 126x^8 + 840x^7 + 3836x^6 - 3528x^5 - 1911x^4 + 26264x^3 + 209916x^2 - 23520x + 50176	\( 3^{18}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[1554]$ (GRH)
12.0.1787367473421924696064.3	x^12 - 2x^11 + 47x^10 - 96x^9 + 1107x^8 - 2310x^7 + 14855x^6 - 30618x^5 + 133099x^4 - 198676x^3 + 663283x^2 - 229794x + 1573111	\( 2^{18}\cdot 7^{10}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 430]$ (GRH)
12.0.2151700443648000000000.1	x^12 - 4x^11 + 88x^10 - 276x^9 + 3259x^8 - 7972x^7 + 64062x^6 - 116656x^5 + 705880x^4 - 876724x^3 + 4423460x^2 - 2965388x + 12267361	\( 2^{18}\cdot 3^{6}\cdot 5^{9}\cdot 7^{8} \)	$C_{12}$ (as 12T1)	$[2, 962]$ (GRH)
12.0.2219704058347157210409.1	x^12 - 4x^11 + 65x^10 - 204x^9 + 1985x^8 - 4720x^7 + 35085x^6 - 60340x^5 + 379456x^4 - 412622x^3 + 2412291x^2 - 1175923x + 7035133	\( 3^{6}\cdot 7^{10}\cdot 47^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 930]$ (GRH)
12.0.2314517744209204100853.1	x^12 - x^11 + 105x^10 - 105x^9 + 4265x^8 - 4265x^7 + 84137x^6 - 84137x^5 + 829609x^4 - 829609x^3 + 3811497x^2 - 3811497x + 7219369	\( 3^{6}\cdot 11^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	$[2, 22, 44]$ (GRH)
12.0.2334520781612309807104.2	x^12 - 4x^11 + 46x^10 - 136x^9 + 1016x^8 - 2364x^7 + 13958x^6 - 24876x^5 + 121251x^4 - 149724x^3 + 599732x^2 - 390180x + 1308601	\( 2^{24}\cdot 7^{8}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[3, 6, 84]$ (GRH)
12.0.2425797698386816634049.4	x^12 - 4x^11 + 73x^10 - 228x^9 + 2405x^8 - 5806x^7 + 45212x^6 - 80635x^5 + 510913x^4 - 605817x^3 + 3299030x^2 - 1963242x + 9579751	\( 3^{6}\cdot 13^{10}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 6, 252]$ (GRH)
12.0.2435758881214464000000.3	x^12 - 2x^11 + 13x^10 - 10x^9 + 294x^8 - 514x^7 + 4907x^6 - 8316x^5 + 50219x^4 - 58470x^3 + 274854x^2 - 156080x + 680545	\( 2^{18}\cdot 3^{6}\cdot 5^{6}\cdot 13^{8} \)	$C_6\times C_2$ (as 12T2)	$[2, 6, 156]$ (GRH)
12.0.2548231104297008664576.1	x^12 - 2x^11 + 9x^10 - 14x^9 + 287x^8 - 366x^7 + 4117x^6 - 3108x^5 + 39521x^4 - 23428x^3 + 264195x^2 - 99100x + 697801	\( 2^{12}\cdot 3^{6}\cdot 7^{8}\cdot 23^{6} \)	$C_6\times C_2$ (as 12T2)	$[6, 234]$ (GRH)
12.0.2917096519063104000000.4	x^12 - 6x^11 + 57x^10 - 230x^9 + 1374x^8 - 4182x^7 + 18835x^6 - 42768x^5 + 156027x^4 - 245226x^3 + 739656x^2 - 623538x + 1615461	\( 2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 7^{6} \)	$C_6\times C_2$ (as 12T2)	$[6, 372]$ (GRH)
12.0.2917096519063104000000.6	x^12 - 6x^11 + 93x^10 - 410x^9 + 3246x^8 - 10590x^7 + 52415x^6 - 121836x^5 + 417807x^4 - 644122x^3 + 1500732x^2 - 1197330x + 2996281	\( 2^{12}\cdot 3^{18}\cdot 5^{6}\cdot 7^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 868]$ (GRH)
12.0.3485941424972233703424.1	x^12 + 24x^10 - 4x^9 + 417x^8 + 36x^7 + 5034x^6 + 1164x^5 + 40692x^4 + 11468x^3 + 194268x^2 + 42156x + 433313	\( 2^{24}\cdot 3^{16}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[1638]$ (GRH)
12.0.3816011369976660765625.4	x^12 - 4x^11 + 79x^10 - 248x^9 + 2800x^8 - 6806x^7 + 56388x^6 - 101293x^5 + 679716x^4 - 811595x^3 + 4660873x^2 - 2792379x + 14297009	\( 5^{6}\cdot 11^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 168]$ (GRH)
12.0.4071252050148030418944.4	x^12 - 6x^11 + 61x^10 - 250x^9 + 1625x^8 - 5066x^7 + 24737x^6 - 57464x^5 + 230015x^4 - 369700x^3 + 1243465x^2 - 1067418x + 3269113	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 4, 4, 56]$ (GRH)
12.0.4071252050148030418944.5	x^12 - 2x^11 + 67x^10 - 106x^9 + 2172x^8 - 2860x^7 + 42260x^6 - 44478x^5 + 511259x^4 - 400386x^3 + 3655953x^2 - 1692824x + 11827921	\( 2^{12}\cdot 3^{6}\cdot 7^{10}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 4, 4, 84]$ (GRH)
12.0.4071485358141415428096.1	x^12 + 39x^10 + 897x^8 + 15371x^6 + 167745x^4 + 975759x^2 + 2289169	\( 2^{12}\cdot 3^{18}\cdot 37^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 2, 2, 104]$ (GRH)
12.0.4251690914950152454144.4	x^12 - 18x^10 + 304x^8 + 136x^6 + 16464x^4 + 80832x^2 + 341056	\( 2^{18}\cdot 7^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[7, 168]$ (GRH)
12.0.4251690914950152454144.5	x^12 - 2x^11 + 75x^10 - 122x^9 + 2619x^8 - 3418x^7 + 53384x^6 - 53204x^5 + 664294x^4 - 455716x^3 + 4767669x^2 - 1713202x + 15418831	\( 2^{18}\cdot 7^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	$[3, 3, 3, 168]$ (GRH)
12.0.4564184019624502972209.1	x^12 - x^11 + 143x^10 - 103x^9 + 7396x^8 - 3276x^7 + 168806x^6 - 19929x^5 + 1664623x^4 + 755704x^3 + 5432804x^2 + 6541378x + 12660103	\( 3^{6}\cdot 7^{10}\cdot 53^{6} \)	$C_6\times C_2$ (as 12T2)	$[7, 840]$ (GRH)
12.0.4598193252144577023133.1	x^12 - x^11 + 118x^10 - 118x^9 + 5383x^8 - 5383x^7 + 119107x^6 - 119107x^5 + 1313209x^4 - 1313209x^3 + 6686668x^2 - 6686668x + 13595401	\( 13^{11}\cdot 37^{6} \)	$C_{12}$ (as 12T1)	$[3650]$ (GRH)
12.0.4610822547295466454717.1	x^12 - 6x^11 + 81x^10 - 339x^9 + 2340x^8 - 6972x^7 + 32022x^6 - 66453x^5 + 222861x^4 - 304709x^3 + 774483x^2 - 565143x + 1083077	\( 3^{16}\cdot 19^{2}\cdot 197^{5} \)	$(C_2^2.\SL(2,3)):C_2$ (as 12T104)	$[2, 2, 2, 254]$ (GRH)
12.0.4610822547295466454717.2	x^12 + 78x^10 - 56x^9 + 2382x^8 - 3312x^7 + 37524x^6 - 73200x^5 + 326154x^4 - 749119x^3 + 1563774x^2 - 2934414x + 4081249	\( 3^{16}\cdot 19^{2}\cdot 197^{5} \)	$(C_2^2.\SL(2,3)):C_2$ (as 12T104)	$[2, 2, 508]$ (GRH)
12.0.5317553698152529526784.5	x^12 - 2x^11 + 39x^10 - 64x^9 + 999x^8 - 1282x^7 + 17923x^6 - 16158x^5 + 209715x^4 - 125512x^3 + 1468591x^2 - 476098x + 4495807	\( 2^{18}\cdot 3^{6}\cdot 7^{8}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 152]$ (GRH)
12.0.5495959053321957412864.1	x^12 + 51x^10 + 1285x^8 + 20259x^6 + 200769x^4 + 1128523x^2 + 2725801	\( 2^{12}\cdot 7^{10}\cdot 41^{6} \)	$C_6\times C_2$ (as 12T2)	$[4, 4, 168]$ (GRH)
12.0.5700120876856238765625.1	x^12 - x^11 + 50x^10 - 36x^9 + 1184x^8 - 680x^7 + 12769x^6 - 1666x^5 + 71134x^4 - 119413x^3 + 143129x^2 - 513709x + 435799	\( 3^{6}\cdot 5^{6}\cdot 7^{10}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[3, 12, 36]$ (GRH)
12.0.5700120876856238765625.7	x^12 - 4x^11 + 77x^10 - 244x^9 + 2733x^8 - 6608x^7 + 55665x^6 - 97524x^5 + 686488x^4 - 765750x^3 + 4908575x^2 - 2505239x + 15923671	\( 3^{6}\cdot 5^{6}\cdot 7^{10}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[6, 888]$ (GRH)
12.0.5700120876856238765625.8	x^12 - 4x^11 + 113x^10 - 322x^9 + 5088x^8 - 9320x^7 + 115149x^6 - 104688x^5 + 1418605x^4 - 402906x^3 + 9700034x^2 - 2068070x + 31120741	\( 3^{6}\cdot 5^{6}\cdot 7^{10}\cdot 11^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 2, 1332]$ (GRH)
12.0.5701857246143068573696.1	x^12 + 99x^10 + 3279x^8 + 42448x^6 + 239580x^4 + 585335x^2 + 491401	\( 2^{12}\cdot 7^{8}\cdot 701^{4} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	$[2, 756]$ (GRH)
12.0.5701857246143068573696.2	x^12 + 86x^10 + 2819x^8 + 43533x^6 + 312364x^4 + 844705x^2 + 491401	\( 2^{12}\cdot 7^{8}\cdot 701^{4} \)	$C_2\times C_4:D_4:C_3$ (as 12T89)	$[2, 672]$ (GRH)
12.0.5814944753134268792209.1	x^12 - 4x^11 + 85x^10 - 268x^9 + 3225x^8 - 7886x^7 + 69264x^6 - 125215x^5 + 887119x^4 - 1065793x^3 + 6437932x^2 - 3880090x + 20804159	\( 13^{10}\cdot 59^{6} \)	$C_6\times C_2$ (as 12T2)	$[7, 693]$ (GRH)
12.0.6127442253232770770881.2	x^12 - 2x^11 + 73x^10 - 130x^9 + 2798x^8 - 4010x^7 + 61894x^6 - 67675x^5 + 877154x^4 - 561523x^3 + 7495456x^2 - 1439524x + 29958664	\( 7^{10}\cdot 167^{6} \)	$C_2^2 \times A_4$ (as 12T25)	$[2, 2, 528]$ (GRH)
12.0.6209018810244211212288.1	x^12 - 4x^11 + 113x^10 - 434x^9 + 5206x^8 - 17324x^7 + 118617x^6 - 319124x^5 + 1328608x^4 - 2507766x^3 + 5953375x^2 - 4561268x + 4200913	\( 2^{16}\cdot 3^{6}\cdot 37^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 2, 14, 28]$ (GRH)

In order to download results, .