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 21 matches)

Label	Polynomial	Discriminant	Galois group	Class group
15.3.10735931625000000000000.1	x^15 - 5x^11 - 4x^10 - 50x^7 - 80x^6 - 32x^5 - 125x^3 - 300x^2 - 240x - 64	\( 2^{12}\cdot 3\cdot 5^{15}\cdot 31^{5} \)	15T102	Trivial (GRH)
15.1.14658125312000000000000000.1	x^15 + 25x^7 - 40x^6 + 16x^5 - 125x^3 + 300x^2 - 240x + 64	\( -\,2^{24}\cdot 5^{15}\cdot 31^{5} \)	15T102	Trivial (GRH)
15.3.140144361632125000000000000.1	x^15 + 15x^11 - 12x^10 - 50x^7 + 80x^6 - 32x^5 - 125x^3 + 300x^2 - 240x + 64	\( 2^{12}\cdot 5^{15}\cdot 257^{5} \)	15T102	Trivial (GRH)
15.5.11502677381403375000000000000.1	x^15 + 15x^13 - 60x^12 + 100x^11 - 554x^10 + 1575x^9 - 2040x^8 + 4485x^7 - 9800x^6 - 852x^5 + 34650x^4 - 49635x^3 + 26290x^2 - 3560x - 696	\( -\,2^{12}\cdot 3^{8}\cdot 5^{15}\cdot 107^{5} \)	15T102	Trivial (GRH)
15.1.223055728022691840000000000000.1	x^15 + 100x^7 - 160x^6 + 64x^5 + 125x^3 - 300x^2 + 240x - 64	\( -\,2^{25}\cdot 3\cdot 5^{13}\cdot 283^{5} \)	15T102	$[2]$ (GRH)
15.5.430145543444459125122090139648000000.1	x^15 - 54x^13 - 432x^12 - 2132x^11 - 3400x^10 + 10602x^9 + 14904x^8 - 4484x^7 - 118584x^6 + 179240x^5 + 64080x^4 - 206200x^3 + 23200x^2 + 56000x - 16000	\( -\,2^{24}\cdot 5^{6}\cdot 37^{5}\cdot 683^{2}\cdot 225223^{2} \)	15T102	Trivial (GRH)
15.3.708775186466216358380486589441400000.1	x^15 - 36x^13 - 144x^12 + 1114x^11 + 23004x^10 + 96111x^9 + 16110x^8 - 531618x^7 - 1453352x^6 + 436965x^5 + 1457910x^4 + 666875x^3 - 349200x^2 - 339500x - 97000	\( 2^{6}\cdot 5^{5}\cdot 17^{2}\cdot 23^{7}\cdot 97^{4}\cdot 101^{2}\cdot 1997^{2} \)	15T102	Trivial (GRH)
15.7.69334557885208174528044608269101670400000.1	x^15 - 189x^13 - 72x^12 + 7403x^11 - 35100x^10 - 177453x^9 + 1097784x^8 + 375236x^7 - 10195764x^6 + 14540540x^5 + 5350680x^4 - 17217700x^3 + 1937200x^2 + 4676000x - 1336000	\( 2^{16}\cdot 5^{5}\cdot 37^{5}\cdot 67^{2}\cdot 167^{4}\cdot 1182491^{2} \)	15T102	Trivial (GRH)
15.9.236400461395948294457915703984996352000000.1	x^15 + 9x^13 - 792x^12 - 2395x^11 + 95676x^10 - 483381x^9 + 225648x^8 + 4223644x^7 - 8858444x^6 - 4794300x^5 + 25180920x^4 - 13571300x^3 - 5876000x^2 + 3164000x + 904000	\( -\,2^{20}\cdot 5^{6}\cdot 37^{5}\cdot 113^{4}\cdot 139^{2}\cdot 257003^{2} \)	15T102	Trivial (GRH)
15.3.500551203745655641831493145752502272000000.1	x^15 - 486x^13 - 2736x^12 + 32968x^11 + 67760x^10 - 1330002x^9 + 5932512x^8 + 7178496x^7 - 280438208x^6 + 804741760x^5 + 592611840x^4 - 3813875200x^3 + 858214400x^2 + 4143104000x - 2367488000	\( 2^{24}\cdot 5^{6}\cdot 17^{4}\cdot 29\cdot 37^{5}\cdot 311^{2}\cdot 342841^{2} \)	15T102	Trivial (GRH)
15.7.1971910983137006508480742693889540096000000.1	x^15 + 144x^13 - 2520x^12 - 1742x^11 - 60688x^10 + 458730x^9 + 1573056x^8 + 7145208x^7 - 71519792x^6 + 82469440x^5 + 135668160x^4 - 221720800x^3 - 39766400x^2 + 129472000x - 36992000	\( 2^{21}\cdot 5^{6}\cdot 13^{2}\cdot 17^{4}\cdot 37^{5}\cdot 247955177^{2} \)	15T102	Trivial (GRH)
15.5.1165185270593545081708137982665622113856000000.1	x^15 - 216x^13 - 936x^12 + 23904x^11 + 21856x^10 - 1351089x^9 - 316710x^8 + 13736612x^7 - 35086868x^6 - 10495935x^5 + 34914690x^4 - 15970625x^3 - 8362800x^2 + 8130500x - 2323000	\( -\,2^{12}\cdot 5^{6}\cdot 7^{2}\cdot 23^{9}\cdot 101^{4}\cdot 167\cdot 937^{2}\cdot 3677^{2} \)	15T102	Trivial (GRH)
15.9.6381262105849605201341604346805613756416000000.1	x^15 - 99x^13 - 396x^12 - 3868x^11 - 27974x^10 + 97245x^9 + 2044656x^8 + 10660124x^7 + 28900022x^6 + 46578665x^5 + 46949760x^4 + 29930225x^3 + 11744850x^2 + 2593500x + 247000	\( -\,2^{24}\cdot 5^{6}\cdot 13^{4}\cdot 17\cdot 19^{4}\cdot 37^{5}\cdot 74483599^{2} \)	15T102	Trivial (GRH)
15.11.37185061201306863596258469574643558678528000000.1	x^15 - 720x^13 - 7416x^12 + 77582x^11 + 1097648x^10 - 5022270x^9 - 46796256x^8 + 189147496x^7 + 426992368x^6 - 1799651680x^5 - 146822400x^4 + 4945060000x^3 - 5522153600x^2 + 2283904000x - 326272000	\( 2^{21}\cdot 5^{6}\cdot 13\cdot 37^{5}\cdot 293^{2}\cdot 2549^{4}\cdot 18637^{2} \)	15T102	Trivial (GRH)
15.11.4322632523817045420539159292758206089739264000000.1	x^15 - 549x^13 - 2448x^12 + 72493x^11 + 467900x^10 - 2905263x^9 - 21874464x^8 + 5458056x^7 + 214275644x^6 + 311384340x^5 - 113966280x^4 - 366726700x^3 - 41261200x^2 + 99596000x + 28456000	\( 2^{16}\cdot 5^{6}\cdot 37^{5}\cdot 67\cdot 79^{2}\cdot 3557^{4}\cdot 953647^{2} \)	15T102	Trivial (GRH)
15.7.209861185704489525754484343252978976463040512000000.1	x^15 - 405x^13 - 1332x^12 + 36049x^11 + 100486x^10 - 2560086x^9 - 217332x^8 + 184136684x^7 - 836759048x^6 - 741890240x^5 + 7849238400x^4 - 5671808000x^3 - 16999884800x^2 + 26105856000x - 9945088000	\( 2^{18}\cdot 5^{6}\cdot 7^{2}\cdot 13^{2}\cdot 23\cdot 229^{5}\cdot 607^{4}\cdot 1773841^{2} \)	15T102	Trivial (GRH)
15.9.672560372209647616583874741225333544667034419200000.1	x^15 + 522x^13 - 5256x^12 + 90798x^11 - 1156208x^10 + 8741070x^9 - 58030848x^8 + 185704640x^7 + 7128368x^6 - 1113803840x^5 + 1484167680x^4 + 433160800x^3 - 1125382400x^2 + 222848000	\( -\,2^{21}\cdot 5^{5}\cdot 37^{5}\cdot 1741^{4}\cdot 10433^{2}\cdot 1216507^{2} \)	15T102	Trivial (GRH)
15.9.17517842124064884881429616734159236380876841984000000.1	x^15 + 639x^13 - 6552x^12 + 106045x^11 - 1415004x^10 + 9994509x^9 - 54899712x^8 + 193325164x^7 - 284112164x^6 - 102417300x^5 + 624620520x^4 - 336640300x^3 - 145756000x^2 + 78484000x + 22424000	\( -\,2^{16}\cdot 5^{6}\cdot 17^{2}\cdot 37^{6}\cdot 2803^{4}\cdot 4003^{2}\cdot 152723^{2} \)	15T102	Trivial (GRH)
15.5.63587282469726653922176018224241933346768105472000000.1	x^15 - 1386x^13 - 11088x^12 + 616072x^11 + 10189792x^10 - 36042840x^9 - 2150494272x^8 - 22831399776x^7 - 124100912256x^6 - 400169331840x^5 - 806742097920x^4 - 1028587686400x^3 - 807251404800x^2 - 356514816000x - 67907584000	\( -\,2^{18}\cdot 5^{6}\cdot 23^{5}\cdot 59^{4}\cdot 149\cdot 281^{4}\cdot 9133^{2}\cdot 50683^{2} \)	15T102	Trivial (GRH)
15.15.107019657496813016739558827186067295629990920192000000.1	x^15 - 1386x^13 - 11088x^12 + 591772x^11 + 9800992x^10 - 27856440x^9 - 1905031872x^8 - 20335308576x^7 - 110614717056x^6 - 356718963840x^5 - 719153233920x^4 - 916912806400x^3 - 719607244800x^2 - 317807616000x - 60534784000	\( 2^{21}\cdot 5^{6}\cdot 19^{2}\cdot 37^{5}\cdot 67\cdot 1277^{2}\cdot 5003^{2}\cdot 14779^{4} \)	15T102	Trivial (GRH)
15.15.192088820668994844315798629752765566154819292680192000000.1	x^15 - 1449x^13 - 5364x^12 + 494981x^11 + 1241310x^10 - 49569282x^9 - 129545388x^8 + 1541051052x^7 + 4909046392x^6 - 2890123600x^5 - 19343665440x^4 - 7245012800x^3 + 18916572800x^2 + 14524608000x + 2766592000	\( 2^{18}\cdot 5^{6}\cdot 101^{4}\cdot 107^{4}\cdot 193\cdot 229^{5}\cdot 9337^{2}\cdot 18013^{2} \)	15T102	Trivial (GRH)