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 36 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.1186012071116620699.1	x^18 - 5x^17 + 16x^16 - 39x^15 + 80x^14 - 141x^13 + 221x^12 - 312x^11 + 400x^10 - 465x^9 + 489x^8 - 463x^7 + 395x^6 - 300x^5 + 195x^4 - 101x^3 + 38x^2 - 9x + 1	\( -\,7^{4}\cdot 139\cdot 1373^{4} \)	18T966	Trivial
18.0.82005482125912529051.1	x^18 - 2x^17 - 2x^16 + 9x^15 - 18x^13 + 10x^12 + 24x^11 - 20x^10 - 17x^9 + 12x^8 + 19x^7 + 18x^6 - 4x^5 + 8x^4 + 12x^3 + 5x^2 + 3x + 1	\( -\,7^{5}\cdot 1373^{5} \)	18T966	Trivial
18.0.317540066758379947471.1	x^18 - 3x^16 - 3x^15 + 8x^14 + 13x^13 + 3x^12 - 9x^11 + x^10 + 9x^9 + x^8 - 9x^7 + 3x^6 + 13x^5 + 8x^4 - 3x^3 - 3x^2 + 1	\( -\,11^{4}\cdot 31\cdot 37^{4}\cdot 139^{4} \)	18T966	Trivial
18.6.378999434518066388917.1	x^18 - 3x^17 + 2x^16 - 5x^15 + 4x^14 + 29x^13 - 5x^12 - 83x^11 + 7x^10 + 105x^9 + 7x^8 - 83x^7 - 5x^6 + 29x^5 + 4x^4 - 5x^3 + 2x^2 - 3x + 1	\( 11^{4}\cdot 37^{5}\cdot 139^{4} \)	18T966	Trivial
18.4.1136998303554199166751.1	x^18 - 5x^17 + 10x^16 - 12x^15 + 41x^13 - 90x^12 + 125x^11 - 171x^10 + 201x^9 - 171x^8 + 125x^7 - 90x^6 + 41x^5 - 12x^3 + 10x^2 - 5x + 1	\( -\,3\cdot 11^{4}\cdot 37^{5}\cdot 139^{4} \)	18T966	Trivial
18.6.1444295142352631373981.1	x^18 - x^17 + 4x^16 + 4x^15 - 2x^14 + 12x^13 - 8x^12 - 12x^11 - 29x^10 - 52x^9 - 36x^8 - 46x^7 - 21x^6 - 2x^5 + 5x^4 + 11x^3 + 3x^2 + x + 1	\( 3\cdot 11^{4}\cdot 37^{4}\cdot 47\cdot 139^{4} \)	18T966	Trivial
18.4.1546727421952108776391.1	x^18 - 8x^16 - 5x^15 + 27x^14 + 36x^13 - 49x^12 - 95x^11 + 31x^10 + 147x^9 + 7x^8 - 126x^7 - 35x^6 + 76x^5 + 17x^4 - 24x^3 - 3x^2 + 5x - 1	\( -\,11^{4}\cdot 37^{4}\cdot 139^{4}\cdot 151 \)	18T966	Trivial
18.2.1646819397517400756221.1	x^18 - 4x^17 + 11x^16 - 35x^15 + 73x^14 - 142x^13 + 262x^12 - 387x^11 + 541x^10 - 687x^9 + 732x^8 - 722x^7 + 624x^6 - 446x^5 + 270x^4 - 136x^3 + 50x^2 - 11x + 1	\( 11^{4}\cdot 13\cdot 337\cdot 2251^{4} \)	18T966	Trivial
18.2.1854024260750540983621.1	x^18 - 5x^17 + 11x^16 - 15x^15 + 11x^14 - 3x^13 - x^12 - 9x^11 + 21x^10 - 31x^9 + 21x^8 - 9x^7 - x^6 - 3x^5 + 11x^4 - 15x^3 + 11x^2 - 5x + 1	\( 11^{4}\cdot 37^{4}\cdot 139^{4}\cdot 181 \)	18T966	Trivial
18.2.2017915908109704827477.1	x^18 - 4x^17 + 8x^16 - 11x^15 + 12x^14 - 11x^13 + 14x^12 - 19x^11 + 12x^10 + 14x^9 - 40x^8 + 49x^7 - 24x^6 - 16x^5 + 26x^4 - 11x^3 - 4x^2 + 8x - 3	\( 11^{4}\cdot 37^{4}\cdot 139^{4}\cdot 197 \)	18T966	Trivial
18.2.15657134090615596515328.1	x^18 + x^16 + x^14 + x^12 - 3x^8 - 9x^6 - 14x^4 - 14x^2 - 7	\( 2^{18}\cdot 7^{5}\cdot 1373^{4} \)	18T966	Trivial
18.8.66852546470398177734375.1	x^18 - 3x^17 + x^15 + 3x^14 + 3x^13 + 3x^12 + 6x^11 - 15x^10 - 3x^9 - 15x^8 + 6x^7 + 3x^6 + 3x^5 + 3x^4 + x^3 - 3x + 1	\( -\,3^{15}\cdot 5^{9}\cdot 13^{4}\cdot 17^{4} \)	18T966	Trivial
18.8.1949194091726415438200131.1	x^18 - 5x^17 + 14x^16 - 18x^15 - x^14 + 64x^13 - 144x^12 + 143x^11 + 46x^10 - 300x^9 + 345x^8 - 100x^7 - 300x^6 + 215x^5 + 133x^4 - 26x^3 - 69x^2 + 2x + 9	\( -\,11^{4}\cdot 37^{6}\cdot 139^{5} \)	18T966	Trivial (GRH)
18.0.2685200750332540417736704.2	x^18 + 4x^16 - x^14 - 12x^12 - 12x^10 - 5x^8 + 19x^6 + 26x^4 + 10x^2 + 1	\( -\,2^{18}\cdot 11^{4}\cdot 37^{4}\cdot 139^{4} \)	18T966	Trivial
18.10.2736002364807036533203125.1	x^18 - 6x^17 + 7x^16 + 25x^15 - 78x^14 + 53x^13 + 112x^12 - 204x^11 - 206x^10 + 631x^9 + 183x^8 - 1128x^7 + 281x^6 + 627x^5 - 124x^4 - 225x^3 + 65x - 13	\( 3^{12}\cdot 5^{10}\cdot 13^{5}\cdot 17^{5} \)	18T966	Trivial (GRH)
18.10.13680011824035182666015625.1	x^18 - 5x^17 - x^16 + 51x^15 - 81x^14 - 142x^13 + 416x^12 + 126x^11 - 916x^10 - 74x^9 + 1382x^8 + 195x^7 - 1530x^6 - 329x^5 + 941x^4 + 311x^3 - 220x^2 - 117x - 13	\( 3^{12}\cdot 5^{11}\cdot 13^{5}\cdot 17^{5} \)	18T966	Trivial (GRH)
18.12.1100643239877813258259445768.1	x^18 - 6x^17 + x^16 + 50x^15 - 67x^14 - 60x^13 + 27x^12 - 3x^11 + 983x^10 - 1488x^9 - 766x^8 + 2645x^7 - 1088x^6 - 647x^5 + 439x^4 - 21x^3 + 7x^2 - 6x - 2	\( -\,2^{3}\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial (GRH)
18.8.1100643239877813258259445768.1	x^18 - 10x^16 - 56x^14 + 42x^12 + 230x^10 + 59x^8 - 171x^6 - 77x^4 + 11x^2 + 2	\( -\,2^{3}\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial
18.10.1788545264801446544671599373.1	x^18 - x^17 - 13x^16 + 15x^15 + 52x^14 - 70x^13 - 74x^12 + 140x^11 + 31x^10 - 161x^9 + 31x^8 + 140x^7 - 74x^6 - 70x^5 + 52x^4 + 15x^3 - 13x^2 - x + 1	\( 13\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial (GRH)
18.6.1788545264801446544671599373.1	x^18 - 9x^17 + 55x^16 - 236x^15 + 772x^14 - 1988x^13 + 3957x^12 - 5984x^11 + 5741x^10 - 402x^9 - 11848x^8 + 27842x^7 - 40700x^6 + 43097x^5 - 34016x^4 + 19612x^3 - 7623x^2 + 1729x - 169	\( 13\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial
18.10.1788545264801446544671599373.2	x^18 - 8x^17 + 19x^16 - 5x^15 - 102x^14 + 281x^13 - 253x^12 - 265x^11 + 1047x^10 - 1096x^9 + 278x^8 + 491x^7 - 936x^6 + 881x^5 - 540x^4 + 225x^3 - 41x^2 - 5x + 2	\( 13\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial (GRH)
18.6.1788545264801446544671599373.2	x^18 + 5x^16 - 45x^14 - 193x^12 + 482x^10 + 1366x^8 - 960x^6 - 2924x^4 - 1083x^2 - 52	\( 13\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial
18.12.2614027694709806488366183699.1	x^18 - 7x^17 + 18x^16 - 40x^15 + 68x^14 + 82x^13 - 352x^12 + 235x^11 - 341x^10 + 311x^9 + 972x^8 + 494x^7 - 2963x^6 - 119x^5 + 2375x^4 - 477x^3 - 364x^2 + 139x - 13	\( -\,19\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial
18.4.2614027694709806488366183699.1	x^18 - 9x^17 + 51x^16 - 204x^15 + 533x^14 - 875x^13 + 616x^12 + 1049x^11 - 3880x^10 + 5947x^9 - 4860x^8 + 549x^7 + 4078x^6 - 5941x^5 + 4708x^4 - 2394x^3 + 781x^2 - 150x + 13	\( -\,19\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial
18.8.2614027694709806488366183699.1	x^18 - 2x^17 - 12x^16 + 32x^15 + 3x^14 - 34x^13 + 86x^12 - 338x^11 + 706x^10 - 301x^9 - 2833x^8 + 3354x^7 - 325x^6 - 4030x^5 + 2156x^4 + x^3 - 547x^2 - 92x - 4	\( -\,19\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial
18.4.4264992554526526375755352351.1	x^18 - x^17 - 18x^16 - 5x^15 + 159x^14 + 82x^13 - 777x^12 - 517x^11 + 1884x^10 + 793x^9 - 3070x^8 - 246x^7 + 2754x^6 - 765x^5 - 925x^4 + 689x^3 + 19x^2 - 3x - 4	\( -\,31\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	$[2]$
18.0.14308362118411572357372794984.1	x^18 - 3x^17 + 10x^16 - 17x^15 + 66x^14 - 99x^13 + 410x^12 - 286x^11 + 1264x^10 - 1653x^9 + 3829x^8 - 4955x^7 + 2704x^6 + 291x^5 - 3670x^4 + 2589x^3 + 739x^2 - 805x + 193	\( -\,2^{3}\cdot 13\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	$[2, 2]$ (GRH)
18.16.22563186417495171794318638244.1	x^18 - 27x^16 + 190x^14 - 305x^12 - 1406x^10 + 6214x^8 - 8812x^6 + 4829x^4 - 853x^2 + 41	\( -\,2^{2}\cdot 37^{4}\cdot 41\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial (GRH)
18.14.23663829657372985052578084012.1	x^18 - 3x^17 - 10x^16 + 49x^15 - 54x^14 - 174x^13 + 839x^12 - 648x^11 - 2289x^10 + 4469x^9 - 1755x^8 - 4579x^7 + 13237x^6 - 9659x^5 - 11639x^4 + 16371x^3 - 1163x^2 - 2668x - 341	\( 2^{2}\cdot 37^{4}\cdot 43\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial (GRH)
18.2.26553018162052244855509129153.1	x^18 - 9x^17 + 56x^16 - 244x^15 + 820x^14 - 2184x^13 + 4481x^12 - 6944x^11 + 6182x^10 + 2475x^9 - 23693x^8 + 53692x^7 - 80879x^6 + 89214x^5 - 73660x^4 + 44488x^3 - 18745x^2 + 4949x - 626	\( 37^{4}\cdot 151^{4}\cdot 193\cdot 613^{4} \)	18T966	$[2]$ (GRH)
18.16.563529338817440388228836233216.1	x^18 - 16x^16 + 91x^14 - 228x^12 + 234x^10 - 181x^6 + 135x^4 - 39x^2 + 4	\( -\,2^{12}\cdot 37^{4}\cdot 151^{4}\cdot 613^{4} \)	18T966	Trivial (GRH)
18.14.2706642070934839702211329523712.1	x^18 - 12x^16 + 2x^14 + 388x^12 - 1217x^10 - 904x^8 + 8226x^6 - 9732x^4 + 2097x^2 - 108	\( 2^{46}\cdot 3^{5}\cdot 3547^{4} \)	18T966	Trivial (GRH)
18.2.2706642070934839702211329523712.1	x^18 + 37x^16 + 564x^14 + 4564x^12 + 21044x^10 + 55148x^8 + 77424x^6 + 50784x^4 + 10224x^2 - 432	\( 2^{46}\cdot 3^{5}\cdot 3547^{4} \)	18T966	$[2]$ (GRH)
18.0.173225092539829740941525089517568.1	x^18 + 31x^16 + 354x^14 + 1898x^12 + 5215x^10 + 7345x^8 + 4896x^6 + 1300x^4 + 129x^2 + 3	\( -\,2^{52}\cdot 3^{5}\cdot 3547^{4} \)	18T966	$[166]$ (GRH)
18.18.173225092539829740941525089517568.1	x^18 - 32x^16 + 390x^14 - 2288x^12 + 6784x^10 - 10052x^8 + 7742x^6 - 3016x^4 + 495x^2 - 12	\( 2^{52}\cdot 3^{5}\cdot 3547^{4} \)	18T966	Trivial (GRH)
18.18.692900370159318963766100358070272.1	x^18 - 31x^16 + 354x^14 - 1898x^12 + 5215x^10 - 7345x^8 + 4896x^6 - 1300x^4 + 129x^2 - 3	\( 2^{54}\cdot 3^{5}\cdot 3547^{4} \)	18T966	Trivial (GRH)