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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.15551992186695249786376953125.1	x^20 - 8x^19 + 41x^18 - 158x^17 + 523x^16 - 1476x^15 + 3797x^14 - 8748x^13 + 18790x^12 - 36406x^11 + 65251x^10 - 103368x^9 + 147375x^8 - 177441x^7 + 182542x^6 - 142143x^5 + 86332x^4 - 29086x^3 + 5691x^2 - 649x + 269	\( 5^{16}\cdot 269^{7} \)	20T375	Trivial (GRH)
20.6.83510262074750967216189850187.2	x^20 - 4x^19 + 17x^18 - 46x^17 + 89x^16 - 153x^15 + 127x^14 - 28x^13 - 311x^12 + 869x^11 - 1643x^10 + 2610x^9 - 2876x^8 + 1444x^7 + 1909x^6 - 5117x^5 + 5180x^4 - 1169x^3 - 1298x^2 + 519x + 53	\( -\,13^{10}\cdot 347^{7} \)	20T375	Trivial (GRH)
20.0.1585066937048382272465996314821.1	x^20 - 10x^19 + 31x^18 - 30x^17 + 204x^16 - 1356x^15 + 1788x^14 + 5046x^13 - 7719x^12 - 22606x^11 + 6799x^10 + 135932x^9 + 30141x^8 - 628017x^7 + 36765x^6 + 1558050x^5 - 209409x^4 - 2238513x^3 + 177178x^2 + 1358483x + 600301	\( 3^{19}\cdot 223^{9} \)	20T375	$[2]$ (GRH)
20.6.14113234290632913459536084681603.1	x^20 - 3x^19 + 19x^18 - 46x^17 + 70x^16 - 27x^15 - 888x^14 + 993x^13 - 1961x^12 - 6403x^11 + 23782x^10 + 3687x^9 + 8298x^8 + 116976x^7 - 63278x^6 + 60723x^5 + 141149x^4 - 29505x^3 + 16845x^2 + 57338x + 13913	\( -\,13^{12}\cdot 347^{7} \)	20T375	Trivial (GRH)
20.6.14113234290632913459536084681603.2	x^20 - 3x^19 - 10x^18 + 63x^17 - 79x^16 - 241x^15 + 862x^14 - 415x^13 - 2979x^12 + 7740x^11 - 6505x^10 - 5961x^9 + 31475x^8 - 59822x^7 + 72856x^6 - 44088x^5 - 28829x^4 + 50946x^3 - 102634x^2 + 7671x + 59959	\( -\,13^{12}\cdot 347^{7} \)	20T375	Trivial (GRH)
20.0.33422412447112238125305245466624.1	x^20 - 15x^18 - 177x^16 + 459x^14 + 25977x^12 + 114117x^10 + 186858x^8 + 950139x^6 + 7627938x^4 + 6415041x^2 + 33268701	\( 2^{20}\cdot 3^{19}\cdot 223^{7} \)	20T375	$[2]$ (GRH)
20.0.33422412447112238125305245466624.2	x^20 + 3x^18 - 75x^16 - 378x^14 + 4140x^12 + 28782x^10 - 76851x^8 - 843600x^6 + 433512x^4 + 15217074x^2 + 33268701	\( 2^{20}\cdot 3^{19}\cdot 223^{7} \)	20T375	$[2]$ (GRH)
20.0.33422412447112238125305245466624.3	x^20 - 21x^18 + 120x^16 + 1530x^14 - 17268x^12 - 61185x^10 + 1963395x^8 - 12188478x^6 + 35870442x^4 - 52812198x^2 + 33268701	\( 2^{20}\cdot 3^{19}\cdot 223^{7} \)	20T375	$[2]$ (GRH)
20.0.45014308264858198791680908203125.1	x^20 - 3x^19 + 32x^18 - 69x^17 + 423x^16 - 710x^15 + 3340x^14 - 4419x^13 + 20397x^12 - 19773x^11 + 101911x^10 - 78690x^9 + 410478x^8 - 275664x^7 + 1342246x^6 - 738184x^5 + 3056061x^4 - 1278310x^3 + 4404481x^2 - 869298x + 2624639	\( 5^{14}\cdot 269^{9} \)	20T375	$[2]$ (GRH)
20.4.652297830366246329600000000000000.2	x^20 - 125x^16 + 335x^14 - 6895x^12 - 99921x^10 + 116830x^8 - 1623110x^6 + 2578365x^4 + 19537470x^2 + 19465109	\( 2^{20}\cdot 5^{14}\cdot 269^{7} \)	20T375	Trivial (GRH)
20.4.652297830366246329600000000000000.3	x^20 - 34x^18 + 380x^16 - 1190x^14 + 273x^12 + 10624x^10 - 325823x^8 + 458070x^6 + 4696740x^4 + 5861241x^2 + 19465109	\( 2^{20}\cdot 5^{14}\cdot 269^{7} \)	20T375	Trivial (GRH)
20.8.1767246164450779958943837335205078125.1	x^20 - 3x^19 - x^18 + 109x^17 - 612x^16 + 1068x^15 + 2220x^14 - 21632x^13 + 59993x^12 - 51366x^11 - 121445x^10 + 585829x^9 - 1248062x^8 + 1649663x^7 - 1840394x^6 + 1693891x^5 - 903700x^4 + 468496x^3 - 193979x^2 - 389432x + 542881	\( 5^{14}\cdot 6029^{7} \)	20T375	Trivial (GRH)
20.6.7393103457599271381703858996552825547.1	x^20 - 4x^19 - 8x^18 + 76x^17 - 518x^16 + 1026x^15 - 236x^14 - 76948x^13 + 312014x^12 - 499338x^11 + 873214x^10 + 14896738x^9 - 13876331x^8 + 40552439x^7 + 1297915x^6 - 7431976x^5 + 933901288x^4 - 2029101662x^3 - 352647068x^2 + 1802762076x - 4831544171	\( -\,13^{10}\cdot 97^{4}\cdot 347^{7} \)	20T375	$[2]$ (GRH)
20.0.44181154111269498973595933380126953125.1	x^20 - x^19 + 82x^18 - 56x^17 + 2786x^16 - 1336x^15 + 50567x^14 - 24462x^13 + 520328x^12 - 470435x^11 + 2904154x^10 - 7038910x^9 + 7706052x^8 - 61891709x^7 + 23769237x^6 - 275793293x^5 + 334834464x^4 - 534644577x^3 + 2425731912x^2 - 466191748x + 5938372789	\( 5^{16}\cdot 6029^{7} \)	20T375	$[2, 55382]$ (GRH)
20.8.44181154111269498973595933380126953125.1	x^20 - x^19 + 2x^18 - 327x^16 + 281x^15 - 1971x^14 + 4102x^13 + 15220x^12 + 33873x^11 + 105428x^10 + 85897x^9 - 552589x^8 - 1305690x^7 - 3713896x^6 - 9627805x^5 + 977675x^4 - 16163815x^3 + 19666195x^2 + 5616100x - 176155	\( 5^{16}\cdot 6029^{7} \)	20T375	Trivial (GRH)
20.0.1853091914135141046229493177600000000000000.1	x^20 + 244x^18 + 22695x^16 + 1103580x^14 + 31752023x^12 + 570295881x^10 + 6479901642x^8 + 45584687570x^6 + 185406068875x^4 + 369631364129x^2 + 219147162389	\( 2^{20}\cdot 5^{14}\cdot 6029^{7} \)	20T375	$[2, 6976916]$ (GRH)
20.12.1853091914135141046229493177600000000000000.1	x^20 - 23x^18 - 5347x^16 + 168742x^14 + 5882811x^12 - 229221570x^10 - 51334460x^8 + 42893457655x^6 - 221238827475x^4 - 919625677300x^2 + 5478679059725	\( 2^{20}\cdot 5^{14}\cdot 6029^{7} \)	20T375	Trivial (GRH)
20.16.1853091914135141046229493177600000000000000.1	x^20 - 181x^18 + 9050x^16 + 26505x^14 - 13030762x^12 + 325190591x^10 - 2468969743x^8 - 3026975115x^6 + 81314178075x^4 - 245027537181x^2 + 219147162389	\( 2^{20}\cdot 5^{14}\cdot 6029^{7} \)	20T375	Trivial (GRH)
20.4.1853091914135141046229493177600000000000000.1	x^20 + 112x^18 + 2719x^16 - 64063x^14 - 3748581x^12 - 52761509x^10 - 35132954x^8 + 5778316372x^6 + 55307809241x^4 + 195992950672x^2 + 219147162389	\( 2^{20}\cdot 5^{14}\cdot 6029^{7} \)	20T375	$[2]$ (GRH)
20.12.1853091914135141046229493177600000000000000.2	x^20 - 47x^18 - 3496x^16 + 153703x^14 + 548734x^12 - 60076371x^10 + 155401241x^8 + 5433257403x^6 - 12756465679x^4 - 82402822547x^2 + 219147162389	\( 2^{20}\cdot 5^{14}\cdot 6029^{7} \)	20T375	Trivial (GRH)
20.16.1853091914135141046229493177600000000000000.2	x^20 - 195x^18 + 13530x^16 - 345305x^14 - 2379505x^12 + 292323434x^10 - 5351558415x^8 + 33836784760x^6 - 16049740610x^4 - 353855967135x^2 + 219147162389	\( 2^{20}\cdot 5^{14}\cdot 6029^{7} \)	20T375	Trivial (GRH)
20.20.1853091914135141046229493177600000000000000.2	x^20 - 244x^18 + 22695x^16 - 1103580x^14 + 31752023x^12 - 570295881x^10 + 6479901642x^8 - 45584687570x^6 + 185406068875x^4 - 369631364129x^2 + 219147162389	\( 2^{20}\cdot 5^{14}\cdot 6029^{7} \)	20T375	Trivial (GRH)
20.4.1853091914135141046229493177600000000000000.2	x^20 + 103x^18 - 3522x^16 - 668642x^14 - 24058174x^12 - 220957380x^10 + 4607526225x^8 + 121116031230x^6 + 1051048984525x^4 + 3980198089500x^2 + 5478679059725	\( 2^{20}\cdot 5^{14}\cdot 6029^{7} \)	20T375	$[2]$ (GRH)
20.20.67357743345283894401969497023167161600000000000000.1	x^20 - 1321x^18 + 667370x^16 - 176674750x^14 + 27660219998x^12 - 2699562590419x^10 + 166763466367942x^8 - 6421922396464750x^6 + 146252241763546930x^4 - 1745355717739174201x^2 + 7965745361278941149	\( 2^{20}\cdot 5^{14}\cdot 6029^{9} \)	20T375	Trivial (GRH)