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 all 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
21.3.10904210824444953500612167.1	x^21 + x^19 - 2x^18 - 2x^17 - 3x^16 - x^15 + 4x^14 + 15x^13 + 3x^12 - 4x^11 - 29x^10 - 4x^9 + 12x^8 + 23x^7 + 16x^6 - 4x^5 - 7x^4 - 8x^3 - x^2 + 1	\( -\,31^{8}\cdot 67^{3}\cdot 349^{3} \)	21T74	Trivial (GRH)
21.1.21420980525151261442929721.1	x^21 - x^20 - x^19 + 2x^18 + 2x^17 + x^16 - 5x^15 - x^14 + 13x^13 + 9x^12 - 7x^11 - 16x^10 - x^9 + 21x^8 + 17x^7 - 3x^6 - 11x^5 - 3x^4 + 4x^3 + 3x^2 - 1	\( 23^{7}\cdot 184607^{3} \)	21T74	Trivial (GRH)
21.1.23714597990105054274863104.1	x^21 + x^19 - 5x^18 + 8x^17 - 5x^16 + 11x^15 - 40x^14 + 33x^13 + 2x^12 + 62x^11 - 87x^10 - 12x^9 - 43x^8 + 76x^7 + 27x^6 - 15x^5 - 7x^4 - 10x^3 + 2x^2 + x + 1	\( 2^{14}\cdot 11^{8}\cdot 41^{3}\cdot 461^{3} \)	21T74	Trivial (GRH)
21.5.85594961606810871789418849.1	x^21 - 4x^19 + 23x^17 - 4x^16 - 54x^15 + 19x^14 + 94x^13 - 41x^12 - 115x^11 + 59x^10 + 30x^9 - 81x^8 + 20x^7 + 46x^6 - 18x^5 - 5x^4 + 13x^3 - 3x^2 + 1	\( 23^{8}\cdot 239^{3}\cdot 431^{3} \)	21T74	Trivial (GRH)
21.3.188012010050973537326115059.1	x^21 - 3x^20 + 2x^19 - 4x^18 + 10x^17 - 9x^16 + 70x^15 - 167x^14 + 91x^13 + 110x^12 - 252x^11 + 50x^10 + 456x^9 - 519x^8 + x^7 + 487x^6 - 548x^5 + 272x^4 - 48x^3 + x^2 - 3x + 1	\( -\,59^{8}\cdot 10859^{3} \)	21T74	Trivial (GRH)
21.5.41784109442335295334261365153.1	x^21 - 3x^19 - 2x^18 + 15x^17 + 6x^16 - 23x^15 - 30x^14 + 23x^13 + 44x^12 + 12x^11 - 43x^10 - 61x^9 + 51x^8 + 34x^7 - 5x^6 - 30x^5 - 9x^4 + 13x^3 + 7x^2 - 1	\( 23^{7}\cdot 107^{3}\cdot 21557^{3} \)	21T74	Trivial (GRH)
21.7.105070765003019731854543276767.1	x^21 - x^20 - 6x^19 + 11x^18 + 47x^17 - 45x^16 - 170x^15 + 162x^14 + 400x^13 - 307x^12 - 750x^11 + 395x^10 + 733x^9 - 371x^8 - 425x^7 + 197x^6 + 204x^5 - 78x^4 - 36x^3 + 17x^2 - 1	\( -\,17^{3}\cdot 23^{8}\cdot 64879^{3} \)	21T74	Trivial (GRH)
21.3.9785353109399805100134419972096.1	x^21 - x^20 - 10x^19 + 8x^18 + 32x^17 - 59x^16 + 7x^15 + 422x^14 + 190x^13 - 795x^12 - 1054x^11 + 695x^10 + 3497x^9 - 381x^8 - 4108x^7 + 1137x^6 + 364x^5 - 117x^4 + x^3 + 12x^2 - 3x - 1	\( -\,2^{14}\cdot 37^{7}\cdot 184607^{3} \)	21T74	Trivial (GRH)
21.3.11238530872385902708009257189376.1	x^21 - x^20 - 3x^19 + 15x^18 - 14x^17 - 42x^16 + 112x^15 + 113x^14 + 10x^13 - 937x^12 - 860x^11 + 1848x^10 + 3892x^9 - 2944x^8 - 2961x^7 + 1339x^6 - 176x^5 - 182x^4 + 74x^3 - 4x^2 - 6x + 1	\( -\,2^{14}\cdot 37^{7}\cdot 193327^{3} \)	21T74	Trivial (GRH)
21.9.19349000070270070662923174526976.1	x^21 - 5x^20 + 20x^19 - 76x^18 + 244x^17 - 536x^16 + 482x^15 + 655x^14 - 2970x^13 + 3601x^12 + 274x^11 - 4051x^10 + 4053x^9 + 428x^8 - 4459x^7 + 1158x^6 + 825x^5 + 130x^4 + 898x^3 - 516x^2 - 260x + 73	\( 2^{14}\cdot 79^{8}\cdot 9199^{3} \)	21T74	Trivial (GRH)
21.7.27791403259100732442943003841279.1	x^21 - x^20 - 6x^19 + 9x^18 + 49x^17 - 53x^16 - 173x^15 + 212x^14 + 363x^13 - 424x^12 - 649x^11 + 526x^10 + 562x^9 - 475x^8 - 233x^7 + 217x^6 + 94x^5 - 67x^4 - 14x^3 + 14x^2 - 1	\( -\,23^{7}\cdot 71^{3}\cdot 283583^{3} \)	21T74	Trivial (GRH)
21.15.44431987193394849846026713481216.1	x^21 - 7x^20 - x^19 + 149x^18 - 531x^17 + 390x^16 + 1944x^15 - 5031x^14 + 1026x^13 + 11764x^12 - 13674x^11 - 8132x^10 + 22878x^9 - 4419x^8 - 15252x^7 + 8130x^6 + 3505x^5 - 3016x^4 + 142x^3 + 159x^2 - 25x + 1	\( -\,2^{14}\cdot 37^{8}\cdot 199^{3}\cdot 461^{3} \)	21T74	Trivial (GRH)
21.9.356929309835813972908052362379264.1	x^21 - x^20 + 4x^19 + x^18 - 17x^17 + 24x^16 - 107x^15 - 238x^14 - 467x^13 - 355x^12 + 497x^11 + 812x^10 + 3209x^9 - 222x^8 - 3450x^7 + 1169x^6 - 373x^5 + 2x^4 + 32x^3 - 12x^2 + 3x + 1	\( 2^{14}\cdot 37^{7}\cdot 71^{3}\cdot 8623^{3} \)	21T74	Trivial (GRH)
21.15.376429776359836117500418449727791.1	x^21 - 8x^20 + 16x^19 + 19x^18 - 103x^17 + 160x^16 - 174x^15 + 66x^14 - 206x^13 + 39x^12 + 4498x^11 - 10908x^10 + 7867x^9 + 6766x^8 - 19649x^7 + 7824x^6 + 13595x^5 - 6802x^4 - 4602x^3 + 1044x^2 + 735x + 79	\( -\,3^{7}\cdot 107^{8}\cdot 21557^{3} \)	21T74	Trivial (GRH)
21.21.12695436325929104475497760602812923904.1	x^21 - 4x^20 - 35x^19 + 143x^18 + 458x^17 - 1969x^16 - 2851x^15 + 13594x^14 + 8657x^13 - 51238x^12 - 10174x^11 + 106769x^10 - 4930x^9 - 118435x^8 + 19116x^7 + 64849x^6 - 11453x^5 - 15363x^4 + 1152x^3 + 1412x^2 + 107x + 1	\( 2^{14}\cdot 37^{7}\cdot 71^{3}\cdot 283583^{3} \)	21T74	Trivial (GRH)
21.21.24784147696206024568626130820393680896.1	x^21 - x^20 - 43x^19 + 38x^18 + 726x^17 - 563x^16 - 6224x^15 + 4226x^14 + 29487x^13 - 17408x^12 - 78852x^11 + 40272x^10 + 115576x^9 - 51908x^8 - 84389x^7 + 35680x^6 + 24314x^5 - 10479x^4 - 699x^3 + 279x^2 + 5x - 1	\( 2^{14}\cdot 3^{3}\cdot 37^{7}\cdot 8388019^{3} \)	21T74	Trivial (GRH)