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 89)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.78596470597476110303232.1	x^20 - 6x^19 + 18x^18 - 32x^17 + 25x^16 + 42x^15 - 168x^14 + 261x^13 - 200x^12 - 26x^11 + 307x^10 - 499x^9 + 556x^8 - 504x^7 + 375x^6 - 237x^5 + 130x^4 - 58x^3 + 21x^2 - 6x + 1	\( 2^{20}\cdot 3^{10}\cdot 13^{5}\cdot 43^{4} \)	20T1036	Trivial
20.2.164475020247040000000000.1	x^20 - 6x^19 + 12x^18 - 36x^16 + 44x^15 + 17x^14 - 60x^13 + x^12 + 28x^11 + 86x^10 - 122x^9 - 84x^8 + 232x^7 - 72x^6 - 128x^5 + 100x^4 + 12x^3 - 28x^2 + 4	\( -\,2^{28}\cdot 5^{10}\cdot 89^{4} \)	20T1036	Trivial
20.0.164942747145088782041088.1	x^20 - x^19 - x^18 - 9x^17 + x^16 + 12x^15 + 41x^14 + 24x^13 - 49x^12 - 103x^11 - 54x^10 + 46x^9 + 127x^8 + 118x^7 - 22x^6 - 124x^5 - 70x^4 + 12x^3 + 32x^2 + 16x + 4	\( 2^{24}\cdot 3^{10}\cdot 7^{4}\cdot 37^{5} \)	20T1036	Trivial (GRH)
20.2.2631600323952640000000000.3	x^20 + 3x^18 - 2x^16 - 9x^14 - 14x^12 - 61x^10 - 85x^8 - 64x^6 - 108x^4 - 64x^2 - 16	\( -\,2^{32}\cdot 5^{10}\cdot 89^{4} \)	20T1036	Trivial (GRH)
20.0.14638276801986560000000000.1	x^20 - 3x^19 + 4x^18 - 5x^17 + 4x^16 + 15x^15 - 21x^14 + 22x^13 - 17x^12 - 17x^11 + 28x^10 - 27x^9 + 24x^8 - 7x^7 - 19x^6 - 58x^5 + 20x^4 + 72x^3 + 68x^2 + 28x + 4	\( 2^{28}\cdot 5^{10}\cdot 89^{5} \)	20T1036	Trivial (GRH)
20.0.14638276801986560000000000.2	x^20 - 3x^18 - 3x^16 + 16x^14 - 27x^12 + 25x^10 + 53x^8 - 132x^6 + 169x^4 - 63x^2 + 89	\( 2^{28}\cdot 5^{10}\cdot 89^{5} \)	20T1036	Trivial (GRH)
20.4.22872307503104000000000000.1	x^20 - 6x^19 + 16x^18 - 28x^17 + 39x^16 - 34x^15 - 2x^14 + 80x^13 - 215x^12 + 302x^11 - 262x^10 + 236x^9 - 200x^8 + 52x^7 + 40x^6 - 8x^5 - 216x^4 + 176x^3 + 32x^2 - 80x + 16	\( 2^{24}\cdot 5^{12}\cdot 89^{5} \)	20T1036	Trivial (GRH)
20.4.22872307503104000000000000.2	x^20 - 4x^19 + 7x^18 - 4x^17 - 20x^16 + 72x^15 - 128x^14 + 118x^13 + 22x^12 - 310x^11 + 632x^10 - 790x^9 + 678x^8 - 374x^7 + 47x^6 + 146x^5 - 145x^4 + 72x^3 - 28x^2 + 8x - 1	\( 2^{24}\cdot 5^{12}\cdot 89^{5} \)	20T1036	Trivial (GRH)
20.2.84297516676069491318359375.1	x^20 - 2x^19 + 6x^18 - 23x^16 + 81x^15 - 131x^14 + 183x^13 - 179x^12 + 176x^11 - 153x^10 + 176x^9 - 179x^8 + 183x^7 - 131x^6 + 81x^5 - 23x^4 + 6x^2 - 2x + 1	\( -\,5^{10}\cdot 71^{5}\cdot 263^{4} \)	20T1036	Trivial (GRH)
20.6.84297516676069491318359375.1	x^20 - 6x^19 + 19x^18 - 41x^17 + 80x^16 - 159x^15 + 289x^14 - 403x^13 + 439x^12 - 503x^11 + 551x^10 - 211x^9 - 480x^8 + 812x^7 - 502x^6 + 72x^5 + 90x^4 - 84x^3 + 48x^2 - 12x - 1	\( -\,5^{10}\cdot 71^{5}\cdot 263^{4} \)	20T1036	Trivial (GRH)
20.6.84297516676069491318359375.2	x^20 - 10x^19 + 39x^18 - 63x^17 - 11x^16 + 172x^15 - 143x^14 - 140x^13 + 162x^12 + 145x^11 - 74x^10 - 217x^9 + 15x^8 + 192x^7 + 59x^6 - 60x^5 - 56x^4 - 10x^3 + 11x^2 + 6x + 1	\( -\,5^{10}\cdot 71^{5}\cdot 263^{4} \)	20T1036	Trivial (GRH)
20.8.12597585226954885292036718592.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 113x^16 + 292x^15 - 70x^14 - 540x^13 + 620x^12 + 232x^11 - 892x^10 + 340x^9 + 589x^8 - 486x^7 - 207x^6 + 274x^5 + 35x^4 - 92x^3 + 6x^2 + 16x - 4	\( 2^{34}\cdot 2657^{4}\cdot 14713 \)	20T1036	Trivial (GRH)
20.10.36828270473700466119927660544.1	x^20 - 8x^18 + 28x^16 - 62x^14 + 97x^12 - 96x^10 + 47x^8 + 2x^6 - 22x^4 + 12x^2 - 1	\( -\,2^{46}\cdot 4783^{4} \)	20T1036	Trivial (GRH)
20.2.200693173598803722240000000000.1	x^20 + 13x^18 + 67x^16 + 170x^14 + 207x^12 + 85x^10 - 5x^8 + 40x^6 + 27x^4 - 3x^2 - 1	\( -\,2^{32}\cdot 3^{4}\cdot 5^{10}\cdot 17^{4}\cdot 29^{4} \)	20T1036	Trivial (GRH)
20.10.263429739612717160369873046875.1	x^20 - 3x^19 - 4x^18 + 36x^17 - 105x^16 + 95x^15 + 67x^14 - 317x^13 + 503x^12 - 393x^11 + 560x^10 - 1052x^9 - 562x^8 + 3953x^7 - 722x^6 - 3055x^5 + 508x^4 + 538x^3 - 176x^2 - 12x + 1	\( -\,5^{15}\cdot 71^{5}\cdot 263^{4} \)	20T1036	Trivial (GRH)
20.4.1193284919305298257027191013376.1	x^20 - 4x^17 - 3x^16 - 8x^15 - 24x^14 - 24x^13 + 25x^12 + 56x^11 + 40x^10 + 128x^9 + 257x^8 + 136x^7 + 132x^6 - 60x^5 + 66x^4 + 152x^3 + 60x^2 + 24x + 4	\( 2^{44}\cdot 1361\cdot 2657^{4} \)	20T1036	Trivial (GRH)
20.8.1193284919305298257027191013376.1	x^20 - 10x^18 - 4x^17 + 32x^16 + 40x^15 - 40x^14 - 144x^13 + 15x^12 + 208x^11 + 54x^10 - 192x^9 - 146x^8 + 128x^7 + 20x^6 - 84x^5 + 32x^4 + 24x^3 + 8x^2 - 8x - 2	\( 2^{44}\cdot 1361\cdot 2657^{4} \)	20T1036	Trivial (GRH)
20.6.1790557435401043978240000000000.1	x^20 + x^18 - 33x^16 + 14x^14 + 275x^12 - 507x^10 + 454x^8 - 226x^6 + 44x^4 + 7x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{8}\cdot 13^{8} \)	20T1036	Trivial (GRH)
20.6.1790557435401043978240000000000.2	x^20 - 5x^18 + 15x^16 - 76x^14 - 91x^12 + 459x^10 + 89x^8 - 297x^6 + 82x^4 + 3x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{8}\cdot 13^{8} \)	20T1036	Trivial (GRH)
20.6.1795626388491734629237095661568.1	x^20 - 8x^16 + 15x^12 - 6x^8 + 4x^6 - 8x^2 - 2	\( -\,2^{55}\cdot 2657^{4} \)	20T1036	Trivial (GRH)
20.6.1795626388491734629237095661568.2	x^20 - 8x^16 + 15x^12 - 6x^8 - 4x^6 + 8x^2 - 2	\( -\,2^{55}\cdot 2657^{4} \)	20T1036	Trivial (GRH)
20.12.1947870881194502131483408203125.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 131x^16 + 232x^15 + 203x^14 - 687x^13 - 110x^12 + 1141x^11 - 57x^10 - 1228x^9 + 62x^8 + 905x^7 + 19x^6 - 417x^5 - 34x^4 + 91x^3 + 13x^2 - 6x - 1	\( 5^{10}\cdot 11^{8}\cdot 13^{8}\cdot 409\cdot 2789 \)	20T1036	Trivial (GRH)
20.4.2100120118277354902599466221568.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 607x^16 - 1388x^15 + 2562x^14 - 3844x^13 + 4652x^12 - 4408x^11 + 2996x^10 - 972x^9 - 747x^8 + 1522x^7 - 1371x^6 + 798x^5 - 301x^4 + 60x^3 + 6x^2 - 8x + 4	\( 2^{34}\cdot 17\cdot 223\cdot 647\cdot 2657^{4} \)	20T1036	Trivial (GRH)
20.12.2209110141965921447040000000000.1	x^20 - 10x^19 + 32x^18 - 3x^17 - 191x^16 + 304x^15 + 278x^14 - 1044x^13 + 280x^12 + 1414x^11 - 1170x^10 - 668x^9 + 1127x^8 - 202x^7 - 288x^6 + 225x^5 - 98x^4 - 14x^3 + 30x^2 - 3x - 1	\( 2^{16}\cdot 3^{4}\cdot 5^{10}\cdot 17^{4}\cdot 29^{4}\cdot 721381 \)	20T1036	Trivial (GRH)
20.4.3493871437868209307824814453125.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 571x^16 - 1304x^15 + 2475x^14 - 3991x^13 + 5560x^12 - 6775x^11 + 7293x^10 - 6980x^9 + 5954x^8 - 4507x^7 + 2977x^6 - 1661x^5 + 728x^4 - 217x^3 + 23x^2 + 10x - 1	\( 5^{10}\cdot 11^{8}\cdot 13^{8}\cdot 59\cdot 34679 \)	20T1036	Trivial (GRH)
20.6.3591252776983469258474191323136.1	x^20 + 10x^18 + 37x^16 + 56x^14 + x^12 - 106x^10 - 131x^8 - 48x^6 + 22x^4 + 16x^2 - 4	\( -\,2^{56}\cdot 2657^{4} \)	20T1036	Trivial (GRH)
20.6.3591252776983469258474191323136.2	x^20 - 10x^18 + 37x^16 - 56x^14 + x^12 + 106x^10 - 131x^8 + 48x^6 + 22x^4 - 16x^2 - 4	\( -\,2^{56}\cdot 2657^{4} \)	20T1036	Trivial (GRH)
20.12.5540004668440574658560000000000.1	x^20 - x^19 - 16x^18 + 43x^17 + 89x^16 - 454x^15 - 136x^14 + 2128x^13 - 738x^12 - 4750x^11 + 3318x^10 + 4722x^9 - 4006x^8 - 3020x^7 + 2620x^6 + 1564x^5 - 1480x^4 - 112x^3 + 296x^2 - 68x + 4	\( 2^{20}\cdot 5^{10}\cdot 13^{4}\cdot 29^{5}\cdot 31^{4} \)	20T1036	Trivial (GRH)
20.8.6494543075586159968315439453125.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 138x^16 + 288x^15 + 71x^14 - 743x^13 + 492x^12 + 805x^11 - 1248x^10 - 201x^9 + 1503x^8 - 417x^7 - 1102x^6 + 440x^5 + 486x^4 - 159x^3 - 105x^2 + 24x + 11	\( 5^{10}\cdot 71^{4}\cdot 179\cdot 263^{4}\cdot 30559 \)	20T1036	Trivial (GRH)
20.10.6627509702445811553907815481344.1	x^20 - 20x^18 - 4x^17 + 157x^16 + 56x^15 - 616x^14 - 296x^13 + 1305x^12 + 792x^11 - 1604x^10 - 1264x^9 + 1393x^8 + 1160x^7 - 1092x^6 - 428x^5 + 586x^4 - 56x^3 - 108x^2 + 40x - 4	\( -\,2^{44}\cdot 2657^{4}\cdot 7559 \)	20T1036	Trivial (GRH)
20.2.6627509702445811553907815481344.1	x^20 + 10x^18 - 4x^17 + 52x^16 - 24x^15 + 152x^14 - 96x^13 + 239x^12 - 240x^11 + 10x^10 - 672x^9 - 798x^8 - 1536x^7 - 2140x^6 - 2964x^5 - 2712x^4 - 2744x^3 - 2200x^2 - 1080x - 146	\( -\,2^{44}\cdot 2657^{4}\cdot 7559 \)	20T1036	Trivial (GRH)
20.4.7225543025699157100072731148288.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 526x^16 - 1148x^15 + 2064x^14 - 3130x^13 + 4076x^12 - 4618x^11 + 4578x^10 - 3954x^9 + 2924x^8 - 1792x^7 + 857x^6 - 278x^5 + 19x^4 + 46x^3 - 34x^2 + 12x - 1	\( 2^{34}\cdot 233\cdot 3449\cdot 4783^{4} \)	20T1036	Trivial (GRH)
20.10.9320949285183413497763458973696.1	x^20 - 20x^18 - 4x^17 + 157x^16 + 72x^15 - 616x^14 - 504x^13 + 1241x^12 + 1704x^11 - 1028x^10 - 2880x^9 - 399x^8 + 2232x^7 + 1220x^6 - 540x^5 - 606x^4 - 104x^3 + 44x^2 + 24x + 4	\( -\,2^{44}\cdot 2657^{4}\cdot 10631 \)	20T1036	Trivial (GRH)
20.2.9320949285183413497763458973696.1	x^20 + 10x^18 - 4x^17 + 52x^16 - 40x^15 + 152x^14 - 224x^13 + 303x^12 - 720x^11 + 394x^10 - 1504x^9 + 610x^8 - 1984x^7 + 924x^6 - 1940x^5 + 1288x^4 - 728x^3 + 696x^2 - 632x - 178	\( -\,2^{44}\cdot 2657^{4}\cdot 10631 \)	20T1036	Trivial (GRH)
20.8.13694589877568854538240000000000.1	x^20 - 11x^18 + 48x^16 - 97x^14 + 48x^12 + 181x^10 - 396x^8 + 321x^6 - 81x^4 - 24x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11\cdot 71^{4}\cdot 263^{4} \)	20T1036	Trivial (GRH)
20.4.19696131789411483760640000000000.1	x^20 + 7x^18 + 15x^16 - 16x^14 - 215x^12 - 516x^10 - 145x^8 + 881x^6 + 914x^4 + 184x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{9}\cdot 13^{8} \)	20T1036	Trivial (GRH)
20.8.19696131789411483760640000000000.1	x^20 - x^18 - 25x^16 - 11x^14 + 181x^12 + 139x^10 - 71x^8 + 154x^6 + 88x^4 - 77x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{9}\cdot 13^{8} \)	20T1036	Trivial (GRH)
20.0.19696131789411483760640000000000.2	x^20 + 24x^18 + 225x^16 + 1105x^14 + 3147x^12 + 5355x^10 + 5336x^8 + 2854x^6 + 639x^4 + 22x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{9}\cdot 13^{8} \)	20T1036	$[3]$ (GRH)
20.4.19696131789411483760640000000000.2	x^20 - 5x^18 - 21x^16 + 94x^14 - 23x^12 - 434x^10 + 805x^8 - 308x^6 - 363x^4 + 242x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{9}\cdot 13^{8} \)	20T1036	Trivial (GRH)
20.8.19696131789411483760640000000000.2	x^20 - 13x^18 + 63x^16 - 152x^14 + 221x^12 - 182x^10 - 49x^8 + 330x^6 - 317x^4 + 86x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{9}\cdot 13^{8} \)	20T1036	Trivial (GRH)
20.0.19696131789411483760640000000000.3	x^20 + 19x^18 + 135x^16 + 511x^14 + 1316x^12 + 2378x^10 + 2832x^8 + 2337x^6 + 1085x^4 + 206x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{9}\cdot 13^{8} \)	20T1036	$[2]$ (GRH)
20.10.84754091030152285568922271350784.1	x^20 - 12x^18 + 60x^16 - 164x^14 + 266x^12 - 248x^10 + 98x^8 + 36x^6 - 63x^4 + 28x^2 - 4	\( -\,2^{58}\cdot 41^{4}\cdot 101^{4} \)	20T1036	Trivial (GRH)
20.2.84754091030152285568922271350784.1	x^20 + 12x^18 + 60x^16 + 164x^14 + 266x^12 + 248x^10 + 98x^8 - 36x^6 - 63x^4 - 28x^2 - 4	\( -\,2^{58}\cdot 41^{4}\cdot 101^{4} \)	20T1036	Trivial (GRH)
20.10.100093443427536839687908943200256.1	x^20 - 10x^19 + 25x^18 + 60x^17 - 338x^16 + 52x^15 + 1674x^14 - 1408x^13 - 4588x^12 + 5324x^11 + 8042x^10 - 10164x^9 - 9693x^8 + 11062x^7 + 8043x^6 - 6696x^5 - 4102x^4 + 2052x^3 + 1008x^2 - 344x - 146	\( -\,2^{34}\cdot 191\cdot 2657^{4}\cdot 612049 \)	20T1036	Trivial (GRH)
20.2.131080726359896627934307983294464.1	x^20 + 20x^18 + 172x^16 + 832x^14 + 2479x^12 + 4660x^10 + 5374x^8 + 3380x^6 + 664x^4 - 344x^2 - 146	\( -\,2^{55}\cdot 73\cdot 2657^{4} \)	20T1036	Trivial (GRH)
20.4.291196495384907705490560000000000.1	x^20 - 5x^19 + 3x^18 + 37x^17 - 100x^16 + 155x^15 - 375x^14 + 621x^13 - 169x^12 - 356x^11 + 152x^10 - 712x^9 + 378x^8 + 1120x^7 + 1290x^6 - 1396x^5 - 2551x^4 + 397x^3 + 1205x^2 - 153x - 281	\( 2^{16}\cdot 5^{10}\cdot 13^{4}\cdot 29^{7}\cdot 31^{4} \)	20T1036	$[4]$ (GRH)
20.10.355694566977399050976640000000000.2	x^20 - 2x^19 - 17x^18 + 82x^17 + 111x^16 - 1024x^15 - 481x^14 + 5344x^13 + 2031x^12 - 12064x^11 - 3851x^10 + 11368x^9 - 4192x^8 - 10942x^7 + 8240x^6 + 7468x^5 - 3632x^4 - 900x^3 + 916x^2 - 120x - 80	\( -\,2^{16}\cdot 5^{10}\cdot 13^{4}\cdot 29^{4}\cdot 31^{7} \)	20T1036	Trivial (GRH)
20.0.640092585108940580184055833690112.1	x^20 + 20x^18 - 4x^17 + 197x^16 - 72x^15 + 1208x^14 - 648x^13 + 5113x^12 - 3560x^11 + 15572x^10 - 13008x^9 + 35017x^8 - 32248x^7 + 57740x^6 - 54220x^5 + 67754x^4 - 56792x^3 + 49668x^2 - 32600x + 16924	\( 2^{44}\cdot 439\cdot 1663\cdot 2657^{4} \)	20T1036	$[2]$ (GRH)
20.12.640092585108940580184055833690112.1	x^20 - 30x^18 - 4x^17 + 372x^16 + 104x^15 - 2472x^14 - 1088x^13 + 9519x^12 + 5840x^11 - 21342x^10 - 17120x^9 + 26242x^8 + 27136x^7 - 14684x^6 - 21780x^5 + 888x^4 + 7400x^3 + 1544x^2 - 632x - 178	\( 2^{44}\cdot 439\cdot 1663\cdot 2657^{4} \)	20T1036	Trivial (GRH)
20.0.716406706619839301926632399306752.1	x^20 + 20x^18 - 4x^17 + 197x^16 - 56x^15 + 1208x^14 - 408x^13 + 5049x^12 - 1880x^11 + 14868x^10 - 6240x^9 + 31177x^8 - 15304x^7 + 45716x^6 - 27900x^5 + 46178x^4 - 32520x^3 + 31004x^2 - 19112x + 17092	\( 2^{44}\cdot 79\cdot 2657^{4}\cdot 10343 \)	20T1036	$[2]$ (GRH)