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 173)

Label	Polynomial	Discriminant	Galois group	Class group
15.1.723352547563839.1	x^15 - x^14 - 2x^13 + 2x^12 - 2x^11 + 2x^10 + 5x^9 - 5x^8 + 4x^7 - 5x^6 - 4x^5 + 5x^4 - 2x^3 + x^2 + x + 1	\( -\,3^{3}\cdot 6653\cdot 4026880369 \)	15T104	Trivial
15.3.2164169497031757.1	x^15 - 7x^14 + 23x^13 - 45x^12 + 54x^11 - 32x^10 - 14x^9 + 55x^8 - 72x^7 + 69x^6 - 57x^5 + 39x^4 - 21x^3 + 9x^2 - 4x + 1	\( 3^{3}\cdot 69593\cdot 1151759887 \)	15T104	Trivial
15.3.2354315214908549.1	x^15 - x^14 + x^13 - x^12 - x^11 + 3x^10 - 2x^9 + 2x^8 - 2x^7 - x^6 + 2x^3 - x^2 + 2x - 1	\( 27765763\cdot 84792023 \)	15T104	Trivial
15.3.3276367268581097.1	x^15 - 6x^13 - x^12 + 16x^11 + 8x^10 - 20x^9 - 24x^8 + 4x^7 + 31x^6 + 15x^5 - 15x^4 - 14x^3 + x^2 + 4x + 1	\( 3276367268581097 \)	15T104	Trivial
15.1.3703260525677583.1	x^15 - 2x^14 + x^13 - x^12 - 5x^11 + 4x^10 - 3x^9 + 2x^8 + 6x^7 - 3x^6 + 3x^5 - 4x^4 - 5x^3 - 3x^2 - 3x - 1	\( -\,3\cdot 13^{3}\cdot 561866260913 \)	15T104	Trivial
15.1.5976545641547631.1	x^15 - 2x^14 + 5x^13 - 10x^12 + 13x^11 - 20x^10 + 23x^9 - 22x^8 + 22x^7 - 20x^6 + 18x^5 - 20x^4 + 21x^3 - 15x^2 + 6x - 1	\( -\,3\cdot 195479\cdot 10191283363 \)	15T104	Trivial
15.3.6114596477365737.1	x^15 - 3x^14 + 5x^13 - 2x^12 - 8x^11 + 18x^10 - 18x^9 + 20x^7 - 27x^6 + 15x^5 + 3x^4 - 11x^3 + 10x^2 - 5x + 1	\( 3^{4}\cdot 15601\cdot 4838718377 \)	15T104	Trivial
15.5.10496055636998343.1	x^15 - 4x^14 + 6x^13 - x^12 - 11x^11 + 18x^10 - 10x^9 - 9x^8 + 19x^7 - 12x^6 - 3x^5 + 9x^4 - 5x^3 - x^2 + 3x - 1	\( -\,3^{5}\cdot 157\cdot 2377\cdot 115742009 \)	15T104	Trivial
15.3.12853809661090929.1	x^15 - x^14 - x^13 + 3x^12 - x^10 - 4x^9 + 4x^8 + 2x^7 - 7x^6 - x^5 + 2x^4 - x^3 + 2x + 1	\( 3\cdot 4284603220363643 \)	15T104	Trivial
15.3.16680932154277329.1	x^15 - 2x^14 + 6x^13 - 14x^12 + 23x^11 - 35x^10 + 44x^9 - 41x^8 + 25x^7 - 4x^6 - 20x^5 + 34x^4 - 30x^3 + 17x^2 - 6x + 1	\( 3\cdot 47\cdot 103\cdot 11057\cdot 103878739 \)	15T104	Trivial
15.5.77595502265817783.1	x^15 - 3x^13 - 2x^12 + x^11 + 12x^10 + 3x^9 - 15x^8 - 10x^7 - 4x^6 + 20x^5 + 7x^4 - 3x^3 - 7x^2 - 4x + 1	\( -\,3\cdot 13^{3}\cdot 11772948303113 \)	15T104	Trivial
15.1.426781883555301359.1	x^15 - x - 1	\( -\,52489\cdot 418511\cdot 19428121 \)	15T104	Trivial
15.1.449005897206417391.1	x^15 + x - 1	\( -\,7334881\cdot 61215157711 \)	15T104	Trivial
15.5.1094025140357425839.1	x^15 - 4x^14 + 9x^13 - 7x^12 - 10x^11 + 31x^10 - 21x^9 - 32x^8 + 45x^7 + 13x^6 - 35x^5 - 2x^4 + 12x^3 - 3x^2 - 5x - 1	\( -\,3^{2}\cdot 121558348928602871 \)	15T104	Trivial
15.1.2195519179260604096.1	x^15 - 2x^14 + 5x^12 - 8x^11 + 2x^10 + 9x^9 - 11x^8 + 11x^6 - 7x^5 - 3x^4 + 7x^3 - x^2 - 2x + 1	\( -\,2^{6}\cdot 34304987175946939 \)	15T104	Trivial
15.3.6653718481802353153.1	x^15 - 2x^14 + 4x^13 - 6x^12 + 7x^11 - 7x^10 + 5x^9 - 3x^8 - x^7 + 4x^6 - 5x^5 + 4x^4 - 3x^3 + x - 1	\( 33479\cdot 37871\cdot 69401\cdot 75617 \)	15T104	Trivial
15.3.7749103974898680572.1	x^15 - 2x^14 + 5x^12 - 8x^11 + 2x^10 + 9x^9 - 10x^8 + 11x^6 - 7x^5 - 3x^4 + 7x^3 - 2x^2 - 2x + 1	\( 2^{2}\cdot 62896103\cdot 30801208681 \)	15T104	Trivial
15.1.364556133550265927663.1	x^15 + 2x - 1	\( -\,999381407\cdot 364781785009 \)	15T104	Trivial (GRH)
15.1.1429495135340114931712.1	x^15 - 5x^12 + 10x^9 - 10x^6 + 5x^3 - 2x - 1	\( -\,2^{12}\cdot 13\cdot 103\cdot 13063\cdot 14747\cdot 1352993 \)	15T104	Trivial (GRH)
15.1.2035979007135456888031.1	x^15 + 4x - 3	\( -\,443\cdot 4103689\cdot 1119940962053 \)	15T104	Trivial
15.1.2157731614659885068288.1	x^15 - 5x^12 + 10x^9 - 10x^6 + 5x^3 + 2x - 1	\( -\,2^{12}\cdot 11\cdot 37\cdot 3659\cdot 353737138331 \)	15T104	Trivial (GRH)
15.1.6446217020680229863424.1	x^15 - 4x - 4	\( -\,2^{14}\cdot 17\cdot 71\cdot 325970060545673 \)	15T104	Trivial
15.1.6810335260340114931712.1	x^15 - 2x - 2	\( -\,2^{14}\cdot 6737\cdot 61699551243839 \)	15T104	Trivial
15.1.7174442387993174441984.1	x^15 - x - 2	\( -\,2^{15}\cdot 17\cdot 12879212122287839 \)	15T104	Trivial
15.1.7174453499321776927151.1	x^15 - x - 4	\( -\,349\cdot 20557173350492197499 \)	15T104	Trivial
15.1.7538571739659885068288.1	x^15 + 2x - 2	\( -\,2^{14}\cdot 415522027\cdot 1107324941 \)	15T104	Trivial
15.1.7902689979319770136576.1	x^15 + 4x - 4	\( -\,2^{14}\cdot 802609\cdot 600967491871 \)	15T104	Trivial
15.5.8365026531535674375871.1	x^15 - x^14 - x^13 - x^12 - x^11 + 6x^10 - 3x^9 + 5x^8 - 8x^7 + 4x^6 - x^5 + x^4 + x^3 - 2x^2 + 3x - 1	\( -\,61\cdot 443437\cdot 309247046331703 \)	15T104	Trivial (GRH)
15.7.13331179272517323570872.1	x^15 - 2x^14 - 12x^13 + 21x^12 + 59x^11 - 84x^10 - 150x^9 + 160x^8 + 204x^7 - 150x^6 - 140x^5 + 67x^4 + 44x^3 - 13x^2 - 4x + 1	\( 2^{3}\cdot 4373\cdot 411967\cdot 924989228549 \)	15T104	Trivial
15.5.13659290627591033588456.1	x^15 - x^14 - 6x^13 + 5x^12 + 13x^11 - 8x^10 - 15x^9 + 11x^8 + 7x^7 - 16x^6 - x^5 + 17x^4 + 2x^3 - 7x^2 - x + 1	\( -\,2^{3}\cdot 1999922317\cdot 853738824721 \)	15T104	Trivial (GRH)
15.1.28697636207890791071744.1	x^15 - 4x - 8	\( -\,2^{16}\cdot 11\cdot 39808288862597089 \)	15T104	Trivial
15.1.54003103318694043828224.1	x^15 - 4x - 6	\( -\,2^{14}\cdot 71\cdot 661\cdot 70232636190181 \)	15T104	Trivial (GRH)
15.1.114791967168436835713024.1	x^15 + 4x - 8	\( -\,2^{18}\cdot 79\cdot 439\cdot 12626412250891 \)	15T104	Trivial (GRH)
15.3.159444714629406813829137.1	x^15 - 3x - 1	\( 3^{15}\cdot 45736039\cdot 242958869 \)	15T104	Trivial (GRH)
15.1.159445590417187575547887.1	x^15 + 3x - 1	\( -\,3^{16}\cdot 41\cdot 89\cdot 1015076033903 \)	15T104	Trivial (GRH)
15.1.166619606023297194688512.1	x^15 + 3x - 2	\( -\,2^{15}\cdot 3^{16}\cdot 118123441829 \)	15T104	Trivial (GRH)
15.7.307896452502425414887424.1	x^15 - x^14 - 11x^13 + 8x^12 + 48x^11 - 21x^10 - 108x^9 + 17x^8 + 137x^7 + 6x^6 - 99x^5 - 8x^4 + 38x^3 - 6x + 1	\( 2^{11}\cdot 11\cdot 13667278608949991783 \)	15T104	Trivial (GRH)
15.9.893591792459039867256832.1	x^15 - x^14 - 10x^13 + 6x^12 + 38x^11 - 6x^10 - 67x^9 - 25x^8 + 52x^7 + 62x^6 - 10x^5 - 46x^4 - 5x^3 + 13x^2 + x - 1	\( -\,2^{14}\cdot 83\cdot 181\cdot 10301\cdot 53681\cdot 6565421 \)	15T104	Trivial (GRH)
15.1.1616097445411156999918839.1	x^15 - 9x - 9	\( -\,3^{16}\cdot 67\cdot 257\cdot 2180316504061 \)	15T104	Trivial (GRH)
15.1.1934987750457751389295863.1	x^15 - 3x - 3	\( -\,3^{15}\cdot 11\cdot 19\cdot 3246601\cdot 198739501 \)	15T104	Trivial (GRH)
15.1.2094068784741388698916087.1	x^15 - 2x - 3	\( -\,19\cdot 739\cdot 317189\cdot 470191513156163 \)	15T104	Trivial (GRH)
15.1.2094432891869041758426359.1	x^15 - x - 3	\( -\,11\cdot 53\cdot 3592509248488922398673 \)	15T104	Trivial (GRH)
15.1.2094432914093055409542391.1	x^15 + x - 3	\( -\,5636003\cdot 371616713847216797 \)	15T104	Trivial (GRH)
15.1.2253878055504345778672887.1	x^15 + 3x - 3	\( -\,3^{15}\cdot 23\cdot 4003\cdot 314407\cdot 5426327 \)	15T104	Trivial (GRH)
15.1.2572768360550940168049911.1	x^15 + 9x - 9	\( -\,3^{16}\cdot 136904431\cdot 436559161 \)	15T104	Trivial (GRH)
15.1.3227080209313179726837607.1	x^15 + 7x - 4	\( -\,1281803\cdot 2517610123640824469 \)	15T104	Trivial (GRH)
15.1.4701021936735526123046875.1	x^15 - 5x - 8	\( -\,5^{13}\cdot 11\cdot 157\cdot 8231\cdot 270917639 \)	15T104	Trivial (GRH)
15.1.5052348896313519954868247.1	x^15 + 2x - 5	\( -\,13\cdot 388642222793347688836019 \)	15T104	Trivial (GRH)
15.3.11924252023675113917661184.1	x^15 - 4x - 2	\( 2^{14}\cdot 289397\cdot 2514879509564333 \)	15T104	Trivial (GRH)
15.3.11931426039281223536801809.1	x^15 - 4x - 1	\( 317\cdot 63716613109\cdot 590718277553 \)	15T104	Trivial (GRH)