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 72)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.921959696367613292449.1	x^20 - 2x^19 - x^18 + 5x^17 - 2x^16 - 3x^15 + 7x^14 - 24x^13 + 51x^12 - 67x^11 + 79x^10 - 95x^9 + 96x^8 - 81x^7 + 68x^6 - 53x^5 + 34x^4 - 20x^3 + 11x^2 - 4x + 1	\( 79\cdot 151\cdot 278005859^{2} \)	20T1110	Trivial
20.0.1607377523338966031377.1	x^20 - x^19 + 5x^18 - 3x^17 + 9x^16 - x^15 + 7x^14 + 4x^13 + 4x^12 + 5x^11 + 4x^10 + 3x^9 + 6x^8 + 5x^6 + 2x^5 - x^4 + 3x^3 + 1	\( 28753\cdot 236438047^{2} \)	20T1110	Trivial
20.0.21000418703935246305461.1	x^20 - 2x^19 + 4x^18 - 4x^17 + 6x^16 - 11x^15 + 13x^14 - 10x^13 + 2x^12 - 2x^11 + 6x^10 + x^9 - 9x^8 + 7x^7 - 2x^6 + 3x^5 + 4x^4 - 8x^3 - 2x^2 + 3x + 1	\( 41\cdot 661\cdot 880280981^{2} \)	20T1110	Trivial (GRH)
20.0.36090075817737580502393.1	x^20 - 3x^19 + 2x^18 + 4x^17 - 7x^16 + 2x^15 - 4x^14 + 10x^13 + 14x^12 - 45x^11 + 10x^10 + 51x^9 - 31x^8 - 25x^7 + 18x^6 + 8x^5 - 3x^3 - 3x^2 + x + 1	\( 47057\cdot 875753293^{2} \)	20T1110	Trivial (GRH)
20.2.128423465410486832559719.1	x^20 - 6x^19 + 18x^18 - 38x^17 + 55x^16 - 43x^15 + 19x^14 - 50x^13 + 174x^12 - 323x^11 + 285x^10 + 66x^9 - 384x^8 + 188x^7 + 331x^6 - 570x^5 + 395x^4 - 139x^3 + 18x^2 + 3x - 1	\( -\,53^{4}\cdot 71^{3}\cdot 213247^{2} \)	20T1110	Trivial (GRH)
20.4.157418066211172801132861.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 481x^16 - 992x^15 + 1649x^14 - 2241x^13 + 2504x^12 - 2297x^11 + 1713x^10 - 1014x^9 + 446x^8 - 109x^7 - 34x^6 + 66x^5 - 55x^4 + 34x^3 - 18x^2 + 7x - 1	\( 7^{4}\cdot 61^{2}\cdot 230101\cdot 276721^{2} \)	20T1110	Trivial (GRH)
20.2.229772481637155475554304.1	x^20 - 2x^19 - 3x^18 + 12x^17 + 7x^16 - 52x^15 + 19x^14 + 134x^13 - 150x^12 - 154x^11 + 362x^10 - 36x^9 - 384x^8 + 260x^7 + 134x^6 - 220x^5 + 53x^4 + 48x^3 - 37x^2 + 10x - 1	\( -\,2^{20}\cdot 503\cdot 617\cdot 840277^{2} \)	20T1110	Trivial (GRH)
20.4.362991394499666002398529.1	x^20 - 10x^19 + 55x^18 - 210x^17 + 615x^16 - 1452x^15 + 2849x^14 - 4733x^13 + 6738x^12 - 8279x^11 + 8816x^10 - 8149x^9 + 6543x^8 - 4563x^7 + 2767x^6 - 1459x^5 + 664x^4 - 253x^3 + 73x^2 - 13x + 1	\( 61\cdot 541\cdot 1483^{2}\cdot 2236369^{2} \)	20T1110	Trivial (GRH)
20.4.860635010905119986286592.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 525x^16 - 1140x^15 + 2024x^14 - 2990x^13 + 3712x^12 - 3890x^11 + 3438x^10 - 2544x^9 + 1546x^8 - 736x^7 + 237x^6 - 14x^5 - 41x^4 + 30x^3 - 11x^2 + 2x + 1	\( 2^{20}\cdot 103^{2}\cdot 8123^{2}\cdot 1172497 \)	20T1110	Trivial (GRH)
20.0.2598700405016807521784377.1	x^20 - x^19 + 4x^18 - 4x^17 + 10x^16 - 9x^15 + 16x^14 - 15x^13 + 21x^12 - 19x^11 + 23x^10 - 19x^9 + 21x^8 - 15x^7 + 16x^6 - 9x^5 + 10x^4 - 4x^3 + 4x^2 - x + 1	\( 31\cdot 223\cdot 16493^{2}\cdot 1175561^{2} \)	20T1110	Trivial (GRH)
20.6.3053557556770074858882467.1	x^20 - 2x^19 - 5x^18 + 9x^17 + 16x^16 - 18x^15 - 39x^14 + 26x^13 + 57x^12 - 31x^11 - 47x^10 + 35x^9 + 14x^8 - 31x^7 + 7x^6 + 16x^5 - 5x^3 - 5x^2 + 1	\( -\,8123\cdot 16493^{2}\cdot 1175561^{2} \)	20T1110	Trivial (GRH)
20.4.9427144873817627952090437.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 570x^16 - 1296x^15 + 2433x^14 - 3837x^13 + 5127x^12 - 5815x^11 + 5564x^10 - 4418x^9 + 2803x^8 - 1291x^7 + 283x^6 + 152x^5 - 201x^4 + 112x^3 - 33x^2 + 3x + 1	\( 167^{2}\cdot 1609^{2}\cdot 14557^{2}\cdot 616157 \)	20T1110	Trivial (GRH)
20.2.11533713053509947520712704.1	x^20 + 6x^18 + 16x^16 + 21x^14 + 5x^12 - 15x^10 - 6x^8 + 15x^6 + 15x^4 + 2x^2 - 1	\( -\,2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1110	Trivial (GRH)
20.6.11533713053509947520712704.1	x^20 - x^18 - 2x^14 + 14x^12 - 23x^10 + 9x^8 - 6x^6 + 8x^4 + 2x^2 - 1	\( -\,2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1110	Trivial (GRH)
20.2.11533713053509947520712704.2	x^20 - 2x^18 - 4x^16 + 16x^14 - 8x^12 - 34x^10 + 45x^8 + 9x^6 - 33x^4 + 10x^2 - 1	\( -\,2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1110	Trivial (GRH)
20.6.11533713053509947520712704.2	x^20 - 6x^18 + 11x^16 + 7x^14 - 68x^12 + 142x^10 - 158x^8 + 98x^6 - 29x^4 + 2x^2 - 1	\( -\,2^{20}\cdot 1483^{2}\cdot 2236369^{2} \)	20T1110	Trivial (GRH)
20.4.14643017051442167423125537.1	x^20 - 2x^19 - x^18 + 5x^17 - x^16 - 4x^15 - x^14 - x^13 + 2x^12 + 13x^11 - 9x^10 - 23x^9 + 14x^8 + 19x^7 - 8x^6 - 11x^5 + 4x^4 + 5x^3 - 3x^2 - x + 1	\( 16493^{2}\cdot 38953\cdot 1175561^{2} \)	20T1110	Trivial (GRH)
20.8.60439835638429253690927581.1	x^20 - 5x^19 + x^18 + 23x^17 - 25x^16 + 6x^15 + 21x^14 - 137x^13 + 110x^12 + 54x^11 - 131x^10 + 234x^9 - 158x^8 - 65x^7 + 121x^6 - 108x^5 + 85x^4 - 33x^3 + 6x^2 - 1	\( 13^{2}\cdot 23^{2}\cdot 24109\cdot 167456053^{2} \)	20T1110	Trivial (GRH)
20.8.88922288225119068196005649.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 105x^16 + 228x^15 + 89x^14 - 533x^13 + 32x^12 + 757x^11 - 70x^10 - 789x^9 - 47x^8 + 593x^7 + 161x^6 - 263x^5 - 142x^4 + 39x^3 + 47x^2 + 7x - 1	\( 1483^{2}\cdot 2236369^{2}\cdot 8084281 \)	20T1110	Trivial (GRH)
20.8.100648373134832267843226137.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 517x^16 - 1076x^15 + 1746x^14 - 2164x^13 + 1888x^12 - 772x^11 - 738x^10 + 1814x^9 - 1876x^8 + 1082x^7 - 143x^6 - 356x^5 + 356x^4 - 166x^3 + 35x^2 + x - 1	\( 113\cdot 943765631693^{2} \)	20T1110	Trivial (GRH)
20.6.136020861261848441903085083.1	x^20 - 10x^19 + 54x^18 - 201x^17 + 568x^16 - 1280x^15 + 2364x^14 - 3634x^13 + 4679x^12 - 5038x^11 + 4482x^10 - 3199x^9 + 1705x^8 - 528x^7 - 82x^6 + 218x^5 - 133x^4 + 36x^3 + 3x^2 - 5x + 1	\( -\,11\cdot 17\cdot 31^{2}\cdot 89\cdot 2916253411^{2} \)	20T1110	Trivial (GRH)
20.10.195532563918689056742899679.1	x^20 - x^19 - 13x^18 + 14x^17 + 70x^16 - 82x^15 - 203x^14 + 261x^13 + 351x^12 - 492x^11 - 397x^10 + 566x^9 + 346x^8 - 403x^7 - 262x^6 + 180x^5 + 142x^4 - 44x^3 - 36x^2 + 1	\( -\,16493^{2}\cdot 520151\cdot 1175561^{2} \)	20T1110	Trivial (GRH)
20.10.241050974838786899548191419.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 135x^16 + 264x^15 + 122x^14 - 680x^13 + 158x^12 + 898x^11 - 439x^10 - 737x^9 + 429x^8 + 396x^7 - 229x^6 - 136x^5 + 74x^4 + 28x^3 - 15x^2 - 2x + 1	\( -\,11^{2}\cdot 41\cdot 3691\cdot 3628255063^{2} \)	20T1110	Trivial (GRH)
20.12.343928789838259679743554901.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 134x^16 + 256x^15 + 140x^14 - 666x^13 + 58x^12 + 952x^11 - 245x^10 - 915x^9 + 220x^8 + 606x^7 - 73x^6 - 260x^5 - 5x^4 + 66x^3 + 4x^2 - 8x + 1	\( 101\cdot 277^{2}\cdot 6761\cdot 81019273^{2} \)	20T1110	Trivial (GRH)
20.8.824245663204905833908769809.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 108x^16 + 252x^15 + 29x^14 - 533x^13 + 241x^12 + 595x^11 - 417x^10 - 429x^9 + 350x^8 + 211x^7 - 180x^6 - 69x^5 + 63x^4 + 13x^3 - 14x^2 + 1	\( 7^{7}\cdot 29^{2}\cdot 89\cdot 263\cdot 7130407^{2} \)	20T1110	Trivial (GRH)
20.10.976514400368289676505645056.1	x^20 - 2x^18 - 4x^16 + 7x^14 + x^12 + 3x^10 + 3x^8 - 11x^6 + 4x^2 - 1	\( -\,2^{20}\cdot 30516826559^{2} \)	20T1110	Trivial (GRH)
20.2.976514400368289676505645056.1	x^20 + 12x^18 + 59x^16 + 153x^14 + 218x^12 + 136x^10 - 60x^8 - 168x^6 - 106x^4 - 21x^2 - 1	\( -\,2^{20}\cdot 30516826559^{2} \)	20T1110	Trivial (GRH)
20.2.1145452125032690182175850496.1	x^20 + 12x^18 + 63x^16 + 192x^14 + 377x^12 + 493x^10 + 422x^8 + 218x^6 + 50x^4 - 4x^2 - 1	\( -\,2^{20}\cdot 47903^{2}\cdot 689963^{2} \)	20T1110	Trivial (GRH)
20.2.1733490594360788648272592896.1	x^20 + 10x^18 + 44x^16 + 113x^14 + 186x^12 + 198x^10 + 125x^8 + 29x^6 - 14x^4 - 8x^2 - 1	\( -\,2^{20}\cdot 10753^{2}\cdot 3781213^{2} \)	20T1110	Trivial (GRH)
20.0.3152285206084903667199714077.1	x^20 - 10x^19 + 64x^18 - 291x^17 + 1058x^16 - 3160x^15 + 8043x^14 - 17627x^13 + 33806x^12 - 56911x^11 + 84740x^10 - 111383x^9 + 129548x^8 - 132345x^7 + 118478x^6 - 91436x^5 + 60287x^4 - 32699x^3 + 14244x^2 - 4407x + 883	\( 242156597\cdot 3607983971^{2} \)	20T1110	Trivial (GRH)
20.0.3228634861450426981433704777.1	x^20 - 10x^19 + 65x^18 - 300x^17 + 1110x^16 - 3372x^15 + 8729x^14 - 19433x^13 + 37811x^12 - 64457x^11 + 96986x^10 - 128514x^9 + 150298x^8 - 153991x^7 + 137900x^6 - 106229x^5 + 69797x^4 - 37704x^3 + 16382x^2 - 5069x + 1031	\( 47\cdot 1303\cdot 1483^{2}\cdot 4793\cdot 2236369^{2} \)	20T1110	$[2]$ (GRH)
20.0.5135440708035283317946681073.1	x^20 - 10x^19 + 63x^18 - 282x^17 + 1002x^16 - 2916x^15 + 7182x^14 - 15156x^13 + 27764x^12 - 44332x^11 + 61965x^10 - 75707x^9 + 80689x^8 - 74476x^7 + 58984x^6 - 39433x^5 + 21772x^4 - 9572x^3 + 3171x^2 - 709x + 83	\( 19\cdot 181\cdot 1367\cdot 47903^{2}\cdot 689963^{2} \)	20T1110	$[2]$ (GRH)
20.12.5784881150213084421820185529.1	x^20 - x^19 - 16x^18 + 14x^17 + 106x^16 - 79x^15 - 380x^14 + 233x^13 + 805x^12 - 393x^11 - 1033x^10 + 393x^9 + 805x^8 - 233x^7 - 380x^6 + 79x^5 + 106x^4 - 14x^3 - 16x^2 + x + 1	\( 181\cdot 16493^{2}\cdot 85021\cdot 1175561^{2} \)	20T1110	Trivial (GRH)
20.10.9428099289122298266741899264.1	x^20 - x^18 - 4x^16 + 3x^14 + 6x^10 + 4x^8 - 11x^6 + 4x^2 - 1	\( -\,2^{20}\cdot 111847^{2}\cdot 847789^{2} \)	20T1110	Trivial (GRH)
20.14.9428099289122298266741899264.1	x^20 - 11x^18 + 50x^16 - 121x^14 + 161x^12 - 85x^10 - 75x^8 + 158x^6 - 97x^4 + 19x^2 - 1	\( -\,2^{20}\cdot 111847^{2}\cdot 847789^{2} \)	20T1110	Trivial (GRH)
20.2.9428099289122298266741899264.1	x^20 + 11x^18 + 50x^16 + 121x^14 + 161x^12 + 85x^10 - 75x^8 - 158x^6 - 97x^4 - 19x^2 - 1	\( -\,2^{20}\cdot 111847^{2}\cdot 847789^{2} \)	20T1110	Trivial (GRH)
20.6.9428099289122298266741899264.1	x^20 + x^18 - 4x^16 - 3x^14 - 6x^10 + 4x^8 + 11x^6 - 4x^2 - 1	\( -\,2^{20}\cdot 111847^{2}\cdot 847789^{2} \)	20T1110	Trivial (GRH)
20.6.9576958940552699451731584915.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 480x^16 - 984x^15 + 1611x^14 - 2115x^13 + 2189x^12 - 1681x^11 + 764x^10 + 134x^9 - 613x^8 + 583x^7 - 282x^6 + 19x^5 + 67x^4 - 41x^3 + 6x^2 + 3x - 1	\( -\,5\cdot 31\cdot 353\cdot 418370073091^{2} \)	20T1110	Trivial (GRH)
20.14.15624230405892634824090320896.1	x^20 - 12x^18 + 59x^16 - 153x^14 + 218x^12 - 136x^10 - 60x^8 + 168x^6 - 106x^4 + 21x^2 - 1	\( -\,2^{24}\cdot 30516826559^{2} \)	20T1110	Trivial (GRH)
20.8.29698901212160310590136582349.1	x^20 - 10x^19 + 52x^18 - 183x^17 + 478x^16 - 968x^15 + 1546x^14 - 1940x^13 + 1846x^12 - 1170x^11 + 174x^10 + 664x^9 - 976x^8 + 758x^7 - 311x^6 - 34x^5 + 141x^4 - 95x^3 + 26x^2 + x - 1	\( 19^{2}\cdot 863^{2}\cdot 320101\cdot 18576431^{2} \)	20T1110	Trivial (GRH)
20.4.41571967174929761179600501561.1	x^20 - 10x^19 + 61x^18 - 264x^17 + 895x^16 - 2468x^15 + 5693x^14 - 11145x^13 + 18709x^12 - 27065x^11 + 33818x^10 - 36458x^9 + 33776x^8 - 26683x^7 + 17738x^6 - 9717x^5 + 4224x^4 - 1364x^3 + 280x^2 - 21x - 1	\( 433\cdot 1483^{2}\cdot 2593\cdot 129751961^{2} \)	20T1110	Trivial (GRH)
20.12.45019646858283152011859116121.1	x^20 - 10x^19 + 33x^18 - 12x^17 - 165x^16 + 300x^15 + 159x^14 - 855x^13 + 354x^12 + 983x^11 - 886x^10 - 449x^9 + 731x^8 + 7x^7 - 277x^6 + 43x^5 + 60x^4 - 7x^3 - 11x^2 + x + 1	\( 300929\cdot 386784463643^{2} \)	20T1110	Trivial (GRH)
20.16.47752675419906880734391798001.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 115x^16 + 308x^15 - 111x^14 - 533x^13 + 764x^12 + 5x^11 - 902x^10 + 731x^9 + 199x^8 - 623x^7 + 266x^6 + 134x^5 - 158x^4 + 28x^3 + 20x^2 - 9x + 1	\( 607^{2}\cdot 37649^{2}\cdot 41579^{2}\cdot 52889 \)	20T1110	Trivial (GRH)
20.6.52731124138705459644642216911.1	x^20 - 10x^19 + 53x^18 - 192x^17 + 517x^16 - 1076x^15 + 1750x^14 - 2192x^13 + 1994x^12 - 1044x^11 - 235x^10 + 1125x^9 - 1199x^8 + 660x^7 - 80x^6 - 171x^5 + 137x^4 - 40x^3 - 3x^2 + 5x - 1	\( -\,17783^{2}\cdot 53231\cdot 55968823^{2} \)	20T1110	Trivial (GRH)
20.8.57028481450596012381307212481.1	x^20 - 10x^19 + 51x^18 - 174x^17 + 435x^16 - 828x^15 + 1206x^14 - 1296x^13 + 882x^12 - 40x^11 - 813x^10 + 1199x^9 - 958x^8 + 364x^7 + 136x^6 - 305x^5 + 212x^4 - 70x^3 + 8x - 1	\( 79^{2}\cdot 875129\cdot 3231340877^{2} \)	20T1110	Trivial (GRH)
20.4.93107983005269278986985275392.1	x^20 - 10x^19 + 61x^18 - 264x^17 + 893x^16 - 2452x^15 + 5608x^14 - 10830x^13 + 17786x^12 - 24894x^11 + 29578x^10 - 29558x^9 + 24334x^8 - 15872x^7 + 7435x^6 - 1674x^5 - 797x^4 + 1044x^3 - 545x^2 + 156x - 19	\( 2^{20}\cdot 419\cdot 1627\cdot 360904847^{2} \)	20T1110	Trivial (GRH)
20.16.96099805831627363000043700224.1	x^20 - 10x^19 + 33x^18 - 12x^17 - 167x^16 + 316x^15 + 122x^14 - 876x^13 + 545x^12 + 838x^11 - 1187x^10 - 22x^9 + 876x^8 - 440x^7 - 208x^6 + 248x^5 - 30x^4 - 44x^3 + 15x^2 + 2x - 1	\( 2^{20}\cdot 9649^{2}\cdot 93629^{2}\cdot 112289 \)	20T1110	Trivial (GRH)
20.4.121011862707725664246565961728.1	x^20 + 14x^18 + 85x^16 + 292x^14 + 599x^12 + 618x^10 - 140x^8 - 1150x^6 - 974x^4 + 85x^2 + 307	\( 2^{20}\cdot 307\cdot 16493^{2}\cdot 1175561^{2} \)	20T1110	Trivial (GRH)
20.8.121011862707725664246565961728.1	x^20 - 14x^18 + 85x^16 - 292x^14 + 599x^12 - 618x^10 - 140x^8 + 1150x^6 - 974x^4 - 85x^2 + 307	\( 2^{20}\cdot 307\cdot 16493^{2}\cdot 1175561^{2} \)	20T1110	Trivial (GRH)
20.18.132433392941210467352853142111.1	x^20 - 10x^19 + 31x^18 + 6x^17 - 216x^16 + 300x^15 + 412x^14 - 1198x^13 + 62x^12 + 1890x^11 - 1091x^10 - 1327x^9 + 1343x^8 + 298x^7 - 689x^6 + 74x^5 + 166x^4 - 35x^3 - 20x^2 + 3x + 1	\( -\,37\cdot 6043\cdot 769611580061^{2} \)	20T1110	Trivial (GRH)