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 346)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.21523360500000000.1	x^12 + 6x^10 - 10x^9 + 36x^8 - 60x^7 + 276x^6 - 720x^5 + 1776x^4 - 2360x^3 + 2160x^2 - 1200x + 400	\( 2^{8}\cdot 3^{16}\cdot 5^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2]$
12.0.33270205387539712.1	x^12 - 2x^11 + 14x^10 - 13x^9 + 39x^8 + 54x^7 + 179x^6 + 486x^5 + 1161x^4 + 1475x^3 + 1463x^2 + 931x + 343	\( 2^{8}\cdot 37^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2]$
12.12.193710244500000000.1	x^12 - 24x^10 - 10x^9 + 216x^8 + 180x^7 - 844x^6 - 1080x^5 + 1056x^4 + 2200x^3 + 720x^2 - 240x - 80	\( 2^{8}\cdot 3^{18}\cdot 5^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.0.1060449937300000000.1	x^12 - 3x^11 + 2x^9 + 43x^8 - 74x^7 - 71x^6 - 26x^5 + 271x^4 + 720x^3 - 406x^2 - 1633x + 1699	\( 2^{8}\cdot 5^{8}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2]$
12.0.2273168619161481613.1	x^12 - 4x^11 + 22x^10 - 87x^9 + 172x^8 - 668x^7 + 1077x^6 - 2082x^5 + 6332x^4 - 607x^3 + 21724x^2 + 4618x + 26261	\( 11^{8}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2]$
12.0.3487878720500000000.1	x^12 - x^11 + 12x^10 - 18x^9 + 145x^8 + 78x^7 + 1427x^6 + 156x^5 + 15931x^4 - 7080x^3 + 3150x^2 - 1375x + 625	\( 2^{8}\cdot 5^{9}\cdot 17^{8} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 2, 2]$
12.12.5509980288000000000.1	x^12 - 39x^10 + 486x^8 - 120x^7 - 2259x^6 + 1380x^5 + 3126x^4 - 2980x^3 - 15x^2 + 420x + 5	\( 2^{16}\cdot 3^{16}\cdot 5^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.0.8491781520500000000.1	x^12 - x^11 + 15x^10 - 15x^9 + 211x^8 - 780x^7 + 3839x^6 - 13190x^5 + 45121x^4 - 106605x^3 + 202860x^2 - 230256x + 136161	\( 2^{8}\cdot 5^{9}\cdot 19^{8} \)	$C_3 : C_4$ (as 12T5)	$[4, 12]$
12.12.8517172579210166272.1	x^12 - 4x^11 - 35x^10 + 158x^9 + 322x^8 - 1932x^7 - 227x^6 + 8104x^5 - 4280x^4 - 10266x^3 + 7031x^2 + 1128x - 67	\( 2^{16}\cdot 37^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.12.24253979727516450048.1	x^12 - 2x^11 - 60x^10 + 61x^9 + 1223x^8 + 54x^7 - 9515x^6 - 8838x^5 + 17219x^4 + 21899x^3 - 609x^2 - 2695x + 343	\( 2^{8}\cdot 3^{6}\cdot 37^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.12.25420364506063119857.1	x^12 - 3x^11 - 24x^10 + 69x^9 + 176x^8 - 499x^7 - 326x^6 + 1172x^5 - 411x^4 - 211x^3 + 40x^2 + 16x + 1	\( 11^{8}\cdot 17^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.0.26511248432500000000.1	x^12 - 4x^11 + 26x^10 - 15x^9 + 25x^8 + 666x^7 - 1189x^6 + 4836x^5 + 2075x^4 - 7025x^3 + 54071x^2 - 35249x + 68051	\( 2^{8}\cdot 5^{10}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 4, 4]$
12.0.39155492640500000000.1	x^12 - x^11 + 16x^10 - 14x^9 + 237x^8 - 334x^7 + 3651x^6 - 4632x^5 + 53719x^4 - 61132x^3 + 69938x^2 - 73695x + 83521	\( 2^{8}\cdot 5^{9}\cdot 23^{8} \)	$C_3 : C_4$ (as 12T5)	$[4, 4]$ (GRH)
12.0.46506419261251953125.1	x^12 - 4x^11 + 23x^10 - 25x^9 + 311x^8 + 635x^7 + 5347x^6 + 19242x^5 + 57661x^4 + 63330x^3 + 67590x^2 + 18225x + 2025	\( 5^{9}\cdot 47^{8} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 2, 2]$ (GRH)
12.0.49589822592000000000.1	x^12 + 18x^10 - 28x^9 + 234x^8 - 108x^7 + 936x^6 - 36x^5 + 5112x^4 - 4456x^3 + 24156x^2 - 9504x + 19036	\( 2^{16}\cdot 3^{18}\cdot 5^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 4, 4]$
12.0.116861165018676718848.1	x^12 + 24x^10 - 2x^9 + 216x^8 - 36x^7 + 2484x^6 - 216x^5 + 20736x^4 + 29864x^3 + 58320x^2 + 181776x + 145232	\( 2^{8}\cdot 3^{16}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	$[3, 6, 6]$
12.12.271475183948800000000.1	x^12 - 6x^11 - 38x^10 + 206x^9 + 515x^8 - 2348x^7 - 2964x^6 + 10132x^5 + 7015x^4 - 12222x^3 - 7526x^2 + 2126x + 1093	\( 2^{16}\cdot 5^{8}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.12.275053402918539275173.1	x^12 - 5x^11 - 34x^10 + 204x^9 + 211x^8 - 2360x^7 + 1659x^6 + 5901x^5 - 5641x^4 - 3679x^3 + 2925x^2 + 468x - 351	\( 11^{10}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.0.279983429807196390656.1	x^12 - 2x^11 + 42x^10 - 41x^9 + 107x^8 + 250x^7 + 1649x^6 + 4230x^5 + 14153x^4 + 18097x^3 + 24757x^2 + 18411x + 6859	\( 2^{8}\cdot 101^{9} \)	$C_3 : C_4$ (as 12T5)	$[4, 20]$ (GRH)
12.0.352638738432000000000.1	x^12 + 6x^10 + 216x^8 - 240x^7 + 1296x^6 + 960x^5 + 12216x^4 + 640x^3 + 89040x^2 + 107040x + 299120	\( 2^{22}\cdot 3^{16}\cdot 5^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 8, 8]$ (GRH)
12.12.352638738432000000000.1	x^12 - 54x^10 + 936x^8 - 240x^7 - 5984x^6 + 3360x^5 + 10056x^4 - 4160x^3 - 4080x^2 + 1440x - 80	\( 2^{22}\cdot 3^{16}\cdot 5^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.0.426445518720500000000.1	x^12 - 4x^11 + 28x^10 - 65x^9 + 581x^8 + 310x^7 + 8967x^6 + 19812x^5 + 145651x^4 - 119595x^3 + 47535x^2 - 7125x + 9025	\( 2^{8}\cdot 5^{9}\cdot 31^{8} \)	$C_3 : C_4$ (as 12T5)	$[3, 6, 6]$ (GRH)
12.0.519846959180308000000.1	x^12 - 2x^11 + 88x^10 - 87x^9 + 2333x^8 + 646x^7 + 27041x^6 + 44886x^5 + 212283x^4 + 330183x^3 + 712233x^2 + 610173x + 531441	\( 2^{8}\cdot 5^{6}\cdot 37^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 2, 4, 20]$ (GRH)
12.0.545099045069450641408.1	x^12 + 74x^10 + 2072x^8 + 27380x^6 + 169756x^4 + 405224x^2 + 202612	\( 2^{22}\cdot 37^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 4, 100]$ (GRH)
12.12.545099045069450641408.1	x^12 - 74x^10 + 2072x^8 - 27380x^6 + 169756x^4 - 405224x^2 + 202612	\( 2^{22}\cdot 37^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.0.624485065329505575549.2	x^12 - 3x^11 - 9x^10 - 25x^9 + 180x^8 - 1113x^7 + 6164x^6 - 10653x^5 + 30396x^4 - 21701x^3 + 15279x^2 - 4650x + 2693	\( 3^{16}\cdot 29^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 2, 2]$ (GRH)
12.12.773068004291700000000.1	x^12 - 3x^11 - 39x^10 + 119x^9 + 433x^8 - 1478x^7 - 1267x^6 + 6292x^5 - 1003x^4 - 7353x^3 + 2298x^2 + 2384x - 173	\( 2^{8}\cdot 3^{6}\cdot 5^{8}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.12.892896952448000000000.1	x^12 - 4x^11 - 53x^10 + 198x^9 + 890x^8 - 3088x^7 - 5373x^6 + 17254x^5 + 16066x^4 - 39580x^3 - 27645x^2 + 32370x + 22405	\( 2^{16}\cdot 5^{9}\cdot 17^{8} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.0.1007996950224500000000.1	x^12 - 4x^11 + 32x^10 - 23x^9 + 303x^8 - 38x^7 + 3223x^6 - 10028x^5 + 28963x^4 - 82513x^3 + 121977x^2 - 15829x + 6311	\( 2^{8}\cdot 5^{9}\cdot 17^{10} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 2, 2, 2]$ (GRH)
12.12.1051750485168090469632.1	x^12 - 54x^10 - 2x^9 + 684x^8 - 348x^7 - 2300x^6 + 720x^5 + 3264x^4 + 120x^3 - 1584x^2 - 432x + 48	\( 2^{8}\cdot 3^{18}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	$[3]$ (GRH)
12.12.1657139923368720095877.1	x^12 - 3x^11 - 55x^10 + 159x^9 + 904x^8 - 3065x^7 - 3952x^6 + 21883x^5 - 12742x^4 - 32763x^3 + 48637x^2 - 20240x + 1249	\( 3^{6}\cdot 11^{8}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.0.1731886157602686265669.1	x^12 - 5x^11 + 54x^10 - 122x^9 + 433x^8 - 1078x^7 + 4875x^6 - 10397x^5 + 23869x^4 + 14489x^3 + 73305x^2 - 134592x + 105011	\( 229^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 2, 34]$ (GRH)
12.12.2173896069248000000000.1	x^12 - 6x^11 - 50x^10 + 300x^9 + 836x^8 - 4720x^7 - 6416x^6 + 27160x^5 + 25256x^4 - 47040x^3 - 36000x^2 + 15424x + 4496	\( 2^{16}\cdot 5^{9}\cdot 19^{8} \)	$C_3 : C_4$ (as 12T5)	$[3]$ (GRH)
12.12.2532201839464500000000.1	x^12 - 3x^11 - 48x^10 + 140x^9 + 711x^8 - 2100x^7 - 2867x^6 + 10476x^5 - 5589x^4 - 1770x^3 + 870x^2 - 15x - 5	\( 2^{8}\cdot 3^{16}\cdot 5^{9}\cdot 7^{6} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.12.2542663587244500000000.1	x^12 - x^11 - 58x^10 + 48x^9 + 1113x^8 - 872x^7 - 8557x^6 + 5848x^5 + 27233x^4 - 10622x^3 - 36288x^2 + 1659x + 12391	\( 2^{8}\cdot 3^{6}\cdot 5^{9}\cdot 17^{8} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.12.3065533128900500000000.1	x^12 - 4x^11 - 60x^10 + 255x^9 + 871x^8 - 4400x^7 - 841x^6 + 22500x^5 - 26729x^4 - 645x^3 + 11135x^2 - 829x - 1129	\( 2^{8}\cdot 5^{9}\cdot 19^{10} \)	$C_3 : C_4$ (as 12T5)	$[3]$ (GRH)
12.0.3075864105233637502697.1	x^12 - 5x^11 + 41x^10 - 81x^9 + 278x^8 - 316x^7 + 2315x^6 - 7280x^5 + 17286x^4 + 34538x^3 + 86932x^2 + 51353x + 332929	\( 11^{10}\cdot 17^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 34]$ (GRH)
12.0.3173748645888000000000.1	x^12 + 60x^10 + 1260x^8 + 12300x^6 + 59400x^4 + 135000x^2 + 112500	\( 2^{22}\cdot 3^{18}\cdot 5^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 10, 10]$ (GRH)
12.12.3173748645888000000000.1	x^12 - 60x^10 + 1260x^8 - 12300x^6 + 59400x^4 - 135000x^2 + 112500	\( 2^{22}\cdot 3^{18}\cdot 5^{9} \)	$C_3 : C_4$ (as 12T5)	$[2]$ (GRH)
12.12.3914206393638659577088.1	x^12 - 2x^11 - 134x^10 + 135x^9 + 5885x^8 + 646x^7 - 100609x^6 - 114510x^5 + 523305x^4 + 785727x^3 - 690363x^2 - 846369x + 531441	\( 2^{8}\cdot 7^{6}\cdot 37^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.12.4297083967217611046912.2	x^12 - 52x^10 - 8x^9 + 864x^8 - 32x^7 - 5804x^6 + 1456x^5 + 15613x^4 - 4192x^3 - 15456x^2 + 1336x + 3902	\( 2^{33}\cdot 29^{8} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.0.4297083967217611046912.146	x^12 - 28x^10 - 8x^9 + 384x^8 - 160x^7 - 1900x^6 + 1072x^5 + 1869x^4 + 11552x^3 + 52808x^2 - 9288x + 33262	\( 2^{33}\cdot 29^{8} \)	$C_3 : C_4$ (as 12T5)	$[2, 2, 4, 4]$ (GRH)
12.12.4891005035897482905857.1	x^12 - x^11 - 81x^10 - 55x^9 + 2187x^8 + 4623x^7 - 19442x^6 - 69890x^5 + 4263x^4 + 257547x^3 + 289908x^2 - 19988x - 119128	\( 257^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.12.5620365587965550179941.2	x^12 - 57x^10 - 92x^9 + 990x^8 + 2802x^7 - 4810x^6 - 25443x^5 - 15819x^4 + 57737x^3 + 116550x^2 + 83475x + 21625	\( 3^{18}\cdot 29^{9} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.12.6190508728444500000000.1	x^12 - 3x^11 - 58x^10 + 150x^9 + 1101x^8 - 2730x^7 - 8177x^6 + 21366x^5 + 17601x^4 - 62100x^3 + 23900x^2 + 12135x - 6005	\( 2^{8}\cdot 3^{6}\cdot 5^{9}\cdot 19^{8} \)	$C_3 : C_4$ (as 12T5)	$[3]$ (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)
12.12.6786879598720000000000.1	x^12 - 4x^11 - 71x^10 + 290x^9 + 1260x^8 - 5024x^7 - 5579x^6 + 18984x^5 + 8220x^4 - 16870x^3 - 831x^2 + 3024x - 459	\( 2^{16}\cdot 5^{10}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	$[2]$ (GRH)
12.12.9310898664085428686848.1	x^12 - 4x^11 - 61x^10 + 218x^9 + 1110x^8 - 3512x^7 - 7551x^6 + 20532x^5 + 15967x^4 - 36774x^3 - 14482x^2 + 18652x + 7036	\( 2^{12}\cdot 11^{8}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 2]$ (GRH)
12.12.10023806115968000000000.1	x^12 - 4x^11 - 69x^10 + 294x^9 + 1442x^8 - 6896x^7 - 8589x^6 + 56982x^5 + 1674x^4 - 166988x^3 + 55283x^2 + 123410x + 3581	\( 2^{16}\cdot 5^{9}\cdot 23^{8} \)	$C_3 : C_4$ (as 12T5)	Trivial (GRH)
12.0.17374411772723200000000.1	x^12 - 6x^11 + 79x^10 - 262x^9 + 2036x^8 - 2582x^7 + 18759x^6 + 7090x^5 + 60484x^4 - 119238x^3 + 740767x^2 - 672574x + 1284583	\( 2^{22}\cdot 5^{8}\cdot 13^{9} \)	$C_3 : C_4$ (as 12T5)	$[2, 16, 16]$ (GRH)