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 58)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.26870230840579837578125.1	x^20 - x^19 - 3x^18 + 7x^17 + x^16 - 20x^15 + 39x^14 - 55x^13 + 84x^12 - 111x^11 + 109x^10 - 77x^9 + 48x^8 - 44x^7 + 47x^6 - 47x^5 + 39x^4 - 27x^3 + 15x^2 - 5x + 1	\( 5^{7}\cdot 61^{4}\cdot 397^{4} \)	20T790	Trivial (GRH)
20.0.99984128957797575628203125.1	x^20 - 3x^19 + 14x^18 - 42x^17 + 118x^16 - 271x^15 + 620x^14 - 1111x^13 + 2016x^12 - 3054x^11 + 4174x^10 - 5147x^9 + 5378x^8 - 4516x^7 + 3536x^6 - 1447x^5 + 525x^4 + 131x^3 - 270x^2 + 28x + 29	\( 5^{7}\cdot 61^{6}\cdot 397^{4} \)	20T790	$[2]$ (GRH)
20.4.99984128957797575628203125.1	x^20 - 5x^19 + 12x^18 - 8x^17 - 19x^16 + 70x^15 - 76x^14 - 22x^13 + 201x^12 - 167x^11 - 418x^10 + 130x^9 + 68x^8 - 208x^7 + 402x^6 + 891x^5 + 728x^4 + 452x^3 + 267x^2 + 103x + 17	\( 5^{7}\cdot 61^{6}\cdot 397^{4} \)	20T790	Trivial (GRH)
20.4.252822001979015691772578125.1	x^20 - 6x^19 + 6x^18 + 43x^17 - 147x^16 + 72x^15 + 559x^14 - 1247x^13 + 90x^12 + 3099x^11 - 3768x^10 - 1435x^9 + 6025x^8 - 2380x^7 - 3138x^6 + 2215x^5 + 466x^4 - 837x^3 + 582x^2 - 182x + 29	\( 5^{7}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T790	Trivial (GRH)
20.0.2139410662686720000000000000.1	x^20 - 2x^19 + 26x^17 - 42x^16 - 6x^15 + 240x^14 - 248x^13 - 92x^12 + 566x^11 + 104x^10 - 376x^9 + 27x^8 + 436x^7 + 450x^6 + 394x^5 + 398x^4 + 238x^3 + 68x^2 + 12x + 3	\( 2^{30}\cdot 3^{4}\cdot 5^{13}\cdot 67^{4} \)	20T790	Trivial (GRH)
20.4.2139410662686720000000000000.1	x^20 - 4x^18 - 2x^17 + 4x^16 - 6x^15 - 14x^14 + 158x^13 - 84x^12 - 340x^11 + 206x^10 + 442x^9 - 467x^8 - 212x^7 + 788x^6 - 636x^5 + 146x^4 + 26x^3 - 10x^2 + 2x + 1	\( 2^{30}\cdot 3^{4}\cdot 5^{13}\cdot 67^{4} \)	20T790	Trivial (GRH)
20.0.2139410662686720000000000000.2	x^20 + 8x^18 - 4x^17 + 28x^16 - 36x^15 + 50x^14 - 146x^13 + 46x^12 - 306x^11 + 92x^10 - 240x^9 + 443x^8 + 270x^7 + 1008x^6 + 810x^5 + 1070x^4 + 730x^3 + 618x^2 + 210x + 233	\( 2^{30}\cdot 3^{4}\cdot 5^{13}\cdot 67^{4} \)	20T790	Trivial (GRH)
20.4.2139410662686720000000000000.2	x^20 - 2x^19 - 2x^18 + 10x^17 + 6x^16 - 48x^15 - 4x^14 + 148x^13 - 127x^12 - 100x^11 - 40x^10 - 36x^9 + 160x^8 - 16x^7 - 388x^6 - 490x^5 - 218x^4 - 46x^3 - 32x^2 - 18x - 3	\( 2^{30}\cdot 3^{4}\cdot 5^{13}\cdot 67^{4} \)	20T790	Trivial (GRH)
20.8.5932904427446774989593169589.1	x^20 - 11x^18 - 7x^17 + 8x^16 - 12x^15 + 40x^14 + 40x^13 - 4x^12 + 209x^11 + 7x^10 - 91x^9 + 165x^8 - 195x^7 - 145x^6 - 140x^5 + 177x^4 + 131x^3 - 246x^2 - 31x + 61	\( 29^{7}\cdot 61^{4}\cdot 397^{4} \)	20T790	Trivial (GRH)
20.0.260221794079455712378880000000.1	x^20 - 2x^19 - 8x^17 - 12x^16 + 80x^15 + 20x^14 + 8x^13 + 20x^12 - 1152x^11 + 1104x^10 + 128x^9 + 1520x^8 + 1248x^7 - 3280x^6 + 1920x^5 - 1760x^4 - 1792x^3 + 7104x^2 - 5184x + 1184	\( 2^{30}\cdot 5^{7}\cdot 17^{4}\cdot 439^{4} \)	20T790	Trivial (GRH)
20.4.260221794079455712378880000000.1	x^20 - 2x^19 + 8x^18 + 4x^17 + 21x^16 + 16x^14 - 478x^13 + 356x^12 + 1004x^11 - 2356x^10 + 3404x^9 - 3309x^8 + 462x^7 + 3180x^6 - 4178x^5 + 2655x^4 - 972x^3 + 204x^2 - 22x + 1	\( 2^{30}\cdot 5^{7}\cdot 17^{4}\cdot 439^{4} \)	20T790	Trivial (GRH)
20.0.940750669363917389085763203125.1	x^20 - 9x^19 + 53x^18 - 206x^17 + 639x^16 - 1570x^15 + 2901x^14 - 3825x^13 + 1228x^12 + 11873x^11 - 37774x^10 + 95979x^9 - 105853x^8 + 121655x^7 + 217014x^6 - 494918x^5 + 1294797x^4 - 1276229x^3 + 1498784x^2 - 693246x + 438703	\( 5^{7}\cdot 61^{6}\cdot 97^{2}\cdot 397^{4} \)	20T790	$[2, 2]$ (GRH)
20.0.1462323200000000000000000000000.1	x^20 + 5x^18 + 10x^16 + 20x^14 + 35x^12 + 75x^10 + 145x^8 + 190x^6 + 140x^4 + 50x^2 + 5	\( 2^{32}\cdot 5^{23}\cdot 13^{4} \)	20T790	$[4]$ (GRH)
20.4.1462323200000000000000000000000.1	x^20 - 5x^18 + 10x^16 - 20x^14 + 35x^12 - 75x^10 + 145x^8 - 190x^6 + 140x^4 - 50x^2 + 5	\( 2^{32}\cdot 5^{23}\cdot 13^{4} \)	20T790	$[2]$ (GRH)
20.4.12145567127297495495635986328125.1	x^20 - 5x^18 - 34x^16 + 130x^14 + 409x^12 - 280x^10 - 2215x^8 - 6530x^6 - 7870x^4 - 780x^2 + 45	\( 3^{4}\cdot 5^{15}\cdot 23^{8}\cdot 89^{4} \)	20T790	$[2]$ (GRH)
20.0.15758398580909518097185466328125.1	x^20 - 5x^19 + 33x^18 - 103x^17 + 365x^16 - 1124x^15 + 2209x^14 - 5919x^13 + 10836x^12 - 11224x^11 + 19881x^10 + 32414x^9 - 114921x^8 - 18211x^7 - 200464x^6 - 542786x^5 + 2630440x^4 + 2147907x^3 - 2397578x^2 - 1268571x + 1548289	\( 5^{7}\cdot 61^{6}\cdot 397^{6} \)	20T790	$[2, 2]$ (GRH)
20.4.22076337374529449736276184040669.1	x^20 - 2x^19 + 5x^18 - 14x^17 - 32x^16 + 98x^15 - 488x^14 + 1903x^13 - 5075x^12 + 14339x^11 - 25470x^10 + 38847x^9 - 32979x^8 - 56746x^7 + 162512x^6 - 426217x^5 + 622948x^4 - 501824x^3 + 254803x^2 + 105177x + 8293	\( 29^{7}\cdot 61^{6}\cdot 397^{4} \)	20T790	$[2]$ (GRH)
20.4.22076337374529449736276184040669.2	x^20 - 6x^19 + 28x^18 - 115x^17 + 236x^16 - 872x^15 + 793x^14 - 3049x^13 - 531x^12 + 5303x^11 - 19189x^10 + 93898x^9 - 58075x^8 + 299170x^7 + 28199x^6 + 380724x^5 + 203506x^4 + 282168x^3 + 135251x^2 + 77536x + 3637	\( 29^{7}\cdot 61^{6}\cdot 397^{4} \)	20T790	Trivial (GRH)
20.0.23397171200000000000000000000000.1	x^20 - 10x^18 + 65x^16 - 190x^14 + 470x^12 - 320x^10 + 825x^8 + 6800x^6 - 7860x^4 - 2200x^2 + 3380	\( 2^{36}\cdot 5^{23}\cdot 13^{4} \)	20T790	$[4]$ (GRH)
20.4.23397171200000000000000000000000.1	x^20 + 10x^18 + 65x^16 + 190x^14 + 470x^12 + 320x^10 + 825x^8 - 6800x^6 - 7860x^4 + 2200x^2 + 3380	\( 2^{36}\cdot 5^{23}\cdot 13^{4} \)	20T790	$[2]$ (GRH)
20.12.55822697757846705877082132662901.1	x^20 - 2x^19 - 25x^18 + 53x^17 + 168x^16 - 545x^15 + 514x^14 + 1980x^13 - 11055x^12 + 9429x^11 + 49742x^10 - 112604x^9 - 68969x^8 + 397299x^7 - 97091x^6 - 611602x^5 + 318825x^4 + 405490x^3 - 199654x^2 - 111394x + 21389	\( 29^{7}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T790	Trivial (GRH)
20.8.55822697757846705877082132662901.1	x^20 - 5x^19 - 8x^18 + 129x^17 - 336x^16 - 102x^15 + 2289x^14 - 7155x^13 + 19266x^12 - 40689x^11 + 46980x^10 - 10997x^9 - 75013x^8 + 322775x^7 - 784606x^6 + 1094110x^5 - 1203644x^4 + 1240682x^3 - 401880x^2 - 527389x + 246283	\( 29^{7}\cdot 61^{4}\cdot 97^{2}\cdot 397^{4} \)	20T790	Trivial (GRH)
20.0.93588684800000000000000000000000.1	x^20 - 10x^19 + 50x^18 - 150x^17 + 320x^16 - 704x^15 + 1890x^14 - 4540x^13 + 9250x^12 - 20110x^11 + 47426x^10 - 99340x^9 + 172545x^8 - 258840x^7 + 347590x^6 - 409304x^5 + 400475x^4 - 307840x^3 + 172980x^2 - 61610x + 10201	\( 2^{38}\cdot 5^{23}\cdot 13^{4} \)	20T790	$[2, 4]$ (GRH)
20.12.93588684800000000000000000000000.1	x^20 - 10x^19 + 30x^18 - 10x^17 - 15x^16 - 210x^15 - 640x^14 + 5620x^13 - 9070x^12 - 3800x^11 + 25700x^10 - 23610x^9 - 6545x^8 + 26700x^7 - 17180x^6 - 80x^5 + 4940x^4 - 1800x^3 - 200x^2 + 200x - 20	\( 2^{38}\cdot 5^{23}\cdot 13^{4} \)	20T790	$[2]$ (GRH)
20.4.93588684800000000000000000000000.1	x^20 - 10x^18 - 95x^16 - 10x^14 - 1030x^12 + 2140x^10 + 2105x^8 - 11100x^6 - 6960x^4 + 4600x^2 + 980	\( 2^{38}\cdot 5^{23}\cdot 13^{4} \)	20T790	$[2, 2]$ (GRH)
20.8.93588684800000000000000000000000.1	x^20 + 10x^18 - 95x^16 + 10x^14 - 1030x^12 - 2140x^10 + 2105x^8 + 11100x^6 - 6960x^4 - 4600x^2 + 980	\( 2^{38}\cdot 5^{23}\cdot 13^{4} \)	20T790	$[4]$ (GRH)
20.0.93588684800000000000000000000000.2	x^20 - 25x^16 + 60x^14 - 145x^12 + 480x^10 - 475x^8 + 380x^6 + 1040x^4 + 400x^2 + 20	\( 2^{38}\cdot 5^{23}\cdot 13^{4} \)	20T790	$[4]$ (GRH)
20.0.274167030311132856320000000000000.1	x^20 - 6x^19 + 22x^18 - 30x^17 + 44x^16 - 30x^15 + 152x^14 - 494x^13 + 653x^12 + 346x^11 + 3920x^10 + 682x^9 + 6983x^8 + 1398x^7 + 82x^6 + 4408x^5 + 4555x^4 - 260x^3 - 726x^2 + 742x + 359	\( 2^{30}\cdot 5^{13}\cdot 3803^{4} \)	20T790	$[2]$ (GRH)
20.12.274167030311132856320000000000000.1	x^20 - 6x^19 + 80x^17 - 159x^16 - 386x^15 + 1378x^14 + 2228x^13 - 13382x^12 + 7190x^11 + 47310x^10 - 88740x^9 + 2755x^8 + 144532x^7 - 145638x^6 + 5538x^5 + 74689x^4 - 43330x^3 + 2546x^2 + 4380x - 985	\( 2^{30}\cdot 5^{13}\cdot 3803^{4} \)	20T790	$[2]$ (GRH)
20.4.274167030311132856320000000000000.1	x^20 - 8x^19 + 24x^18 + 8x^17 - 225x^16 + 368x^15 + 1376x^14 - 7814x^13 + 16911x^12 - 16030x^11 - 8924x^10 + 49930x^9 - 74572x^8 + 60584x^7 - 25416x^6 + 1318x^5 + 2789x^4 - 42x^3 - 450x^2 - 108x + 81	\( 2^{30}\cdot 5^{13}\cdot 3803^{4} \)	20T790	$[2]$ (GRH)
20.8.274167030311132856320000000000000.1	x^20 - 16x^18 + 44x^16 + 670x^14 - 2620x^12 - 20350x^10 + 56925x^8 + 247000x^6 - 250750x^4 - 485000x^2 + 3125	\( 2^{30}\cdot 5^{13}\cdot 3803^{4} \)	20T790	$[2]$ (GRH)
20.4.274167030311132856320000000000000.2	x^20 - 8x^19 + 34x^18 - 84x^17 + 163x^16 - 278x^15 + 628x^14 - 1534x^13 + 2066x^12 + 4628x^11 - 19252x^10 + 2902x^9 + 45115x^8 - 3726x^7 - 52142x^6 - 16278x^5 + 30201x^4 + 13856x^3 - 14638x^2 - 4320x + 3251	\( 2^{30}\cdot 5^{13}\cdot 3803^{4} \)	20T790	$[2]$ (GRH)
20.8.303639178182437387390899658203125.1	x^20 - 4x^19 - 11x^18 + 35x^17 + 180x^16 - 604x^15 - 614x^14 + 5809x^13 - 11255x^12 + 3895x^11 + 25814x^10 - 62181x^9 + 69156x^8 - 31205x^7 - 23235x^6 + 53480x^5 - 48760x^4 + 27675x^3 - 10200x^2 + 2250x - 225	\( 3^{4}\cdot 5^{17}\cdot 23^{8}\cdot 89^{4} \)	20T790	$[2]$ (GRH)
20.0.935079133905458759334789865752701.1	x^20 - 8x^19 + 72x^18 - 371x^17 + 1752x^16 - 6438x^15 + 20690x^14 - 58315x^13 + 148935x^12 - 348786x^11 + 761894x^10 - 1551579x^9 + 2809400x^8 - 3955694x^7 + 4759948x^6 - 6634959x^5 + 12143657x^4 - 20961620x^3 + 33984289x^2 - 30098420x + 35738491	\( 29^{7}\cdot 61^{4}\cdot 397^{6} \)	20T790	$[2]$ (GRH)
20.12.2732752603641936486518096923828125.1	x^20 - x^19 - 18x^18 + 75x^17 + 52x^16 - 901x^15 + 222x^14 + 3752x^13 + 4353x^12 - 20619x^11 - 8024x^10 + 51009x^9 - 16352x^8 - 41697x^7 + 35277x^6 + 1386x^5 - 13758x^4 + 5625x^3 + 567x^2 - 729x + 81	\( 3^{6}\cdot 5^{17}\cdot 23^{8}\cdot 89^{4} \)	20T790	$[2]$ (GRH)
20.8.5952110002907068497920000000000000.1	x^20 - 12x^18 + 64x^16 - 250x^14 + 160x^12 + 2910x^10 - 6975x^8 + 11860x^6 - 11030x^4 + 2800x^2 + 125	\( 2^{30}\cdot 5^{13}\cdot 8209^{4} \)	20T790	Trivial (GRH)
20.0.32579380737071045979144192000000000.1	x^20 + 20x^18 + 194x^16 + 1368x^14 + 5573x^12 + 9162x^10 + 8388x^8 + 17254x^6 + 17180x^4 + 2800x^2 + 125	\( 2^{30}\cdot 3^{4}\cdot 5^{9}\cdot 17^{4}\cdot 1231^{4} \)	20T790	$[2]$ (GRH)
20.12.32579380737071045979144192000000000.1	x^20 - 20x^18 + 194x^16 - 1368x^14 + 5573x^12 - 9162x^10 + 8388x^8 - 17254x^6 + 17180x^4 - 2800x^2 + 125	\( 2^{30}\cdot 3^{4}\cdot 5^{9}\cdot 17^{4}\cdot 1231^{4} \)	20T790	Trivial (GRH)
20.0.43294334715274231808000000000000000.1	x^20 + 36x^18 + 470x^16 + 3528x^14 + 15389x^12 + 35830x^10 + 45420x^8 + 32010x^6 + 11300x^4 + 1300x^2 + 5	\( 2^{30}\cdot 5^{15}\cdot 6029^{4} \)	20T790	$[4]$ (GRH)
20.12.43294334715274231808000000000000000.1	x^20 - 40x^18 + 434x^16 - 1710x^14 + 2779x^12 - 2100x^10 + 2235x^8 - 5640x^6 + 5115x^4 - 1170x^2 + 5	\( 2^{30}\cdot 5^{15}\cdot 6029^{4} \)	20T790	$[2]$ (GRH)
20.4.43294334715274231808000000000000000.1	x^20 - 32x^18 + 470x^16 - 4324x^14 + 26049x^12 - 106790x^10 + 281500x^8 - 470090x^6 + 498240x^4 - 304840x^2 + 85805	\( 2^{30}\cdot 5^{15}\cdot 6029^{4} \)	20T790	$[2]$ (GRH)
20.0.43294334715274231808000000000000000.2	x^20 + 8x^18 + 40x^16 + 166x^14 + 4544x^12 + 30470x^10 + 49065x^8 - 66440x^6 - 88510x^4 + 361500x^2 + 163805	\( 2^{30}\cdot 5^{15}\cdot 6029^{4} \)	20T790	$[4]$ (GRH)
20.4.43294334715274231808000000000000000.2	x^20 - 10x^18 + 71x^16 - 180x^14 + 2559x^12 + 3540x^10 - 20265x^8 - 85370x^6 - 84050x^4 - 29860x^2 + 39605	\( 2^{30}\cdot 5^{15}\cdot 6029^{4} \)	20T790	$[2]$ (GRH)
20.0.43294334715274231808000000000000000.3	x^20 + 16x^18 + 40x^16 + 238x^14 - 976x^12 - 2510x^10 + 17505x^8 + 40620x^6 + 20870x^4 + 2100x^2 + 5	\( 2^{30}\cdot 5^{15}\cdot 6029^{4} \)	20T790	$[4]$ (GRH)
20.4.43294334715274231808000000000000000.3	x^20 + 26x^18 + 193x^16 - 488x^14 - 8606x^12 - 13380x^10 + 8170x^8 - 113960x^6 - 271875x^4 - 26310x^2 + 245	\( 2^{30}\cdot 5^{15}\cdot 6029^{4} \)	20T790	$[2]$ (GRH)
20.0.43294334715274231808000000000000000.4	x^20 - 8x^18 - 40x^16 + 854x^14 - 1776x^12 + 22450x^10 + 44085x^8 - 124860x^6 - 18230x^4 + 479520x^2 + 39605	\( 2^{30}\cdot 5^{15}\cdot 6029^{4} \)	20T790	$[4]$ (GRH)
20.4.43294334715274231808000000000000000.4	x^20 - 4x^18 + 38x^16 - 248x^14 + 1109x^12 - 4250x^10 + 15220x^8 - 59410x^6 - 35160x^4 - 15720x^2 + 845	\( 2^{30}\cdot 5^{15}\cdot 6029^{4} \)	20T790	$[4]$ (GRH)
20.4.43294334715274231808000000000000000.5	x^20 - 32x^18 + 320x^16 - 1014x^14 - 516x^12 - 11690x^10 + 178705x^8 - 686260x^6 + 1435030x^4 - 1609960x^2 + 1156805	\( 2^{30}\cdot 5^{15}\cdot 6029^{4} \)	20T790	$[2]$ (GRH)
20.0.777969330534363511811735552000000000.1	x^20 + 50x^18 + 975x^16 + 9446x^14 + 48249x^12 + 129702x^10 + 179134x^8 + 119926x^6 + 37520x^4 + 4700x^2 + 125	\( 2^{34}\cdot 5^{9}\cdot 7^{4}\cdot 23^{4}\cdot 431^{4} \)	20T790	$[2, 2, 476]$ (GRH)
20.20.777969330534363511811735552000000000.1	x^20 - 50x^18 + 975x^16 - 9446x^14 + 48249x^12 - 129702x^10 + 179134x^8 - 119926x^6 + 37520x^4 - 4700x^2 + 125	\( 2^{34}\cdot 5^{9}\cdot 7^{4}\cdot 23^{4}\cdot 431^{4} \)	20T790	Trivial (GRH)