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 17 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.2.3195114169182285566595267779.2	x^20 - 3x^19 + 4x^18 + 11x^17 - 31x^16 + 51x^15 + 44x^14 - 70x^13 + 323x^12 + 55x^11 + 32x^10 + 444x^9 - 329x^8 + 5x^7 - 38x^6 - 316x^5 + 104x^4 - 257x^3 + 22x^2 - 52x - 23	\( -\,11^{17}\cdot 43^{6} \)	20T326	Trivial (GRH)
20.6.3195114169182285566595267779.2	x^20 - x^19 + 6x^18 + 8x^17 + 10x^16 + 71x^15 - 90x^14 + 8x^13 + 342x^12 - 447x^11 + 100x^10 + 418x^9 - 475x^8 + 37x^7 + 280x^6 - 138x^5 - 69x^4 + 42x^3 + 11x^2 - 4x - 1	\( -\,11^{17}\cdot 43^{6} \)	20T326	Trivial (GRH)
20.2.6965462128295683654948996096.2	x^20 - 4x^19 + 6x^18 - 9x^17 + 39x^16 - 121x^15 + 219x^14 - 244x^13 + 118x^12 + 140x^11 - 517x^10 + 833x^9 - 854x^8 + 492x^7 + 31x^6 - 307x^5 + 220x^4 - 110x^2 + 55x - 11	\( -\,2^{10}\cdot 11^{16}\cdot 23^{6} \)	20T326	Trivial (GRH)
20.6.6965462128295683654948996096.2	x^20 - 7x^19 + 21x^18 - 52x^17 + 122x^16 - 182x^15 + 167x^14 - 130x^13 - 123x^12 + 693x^11 - 897x^10 + 1365x^9 - 2195x^8 + 3272x^7 - 5451x^6 + 5455x^5 - 2486x^4 + 652x^3 - 368x^2 + 176x - 32	\( -\,2^{10}\cdot 11^{16}\cdot 23^{6} \)	20T326	Trivial (GRH)
20.10.4717154733296640478520170220486763971.3	x^20 - 10x^19 + 14x^18 + 124x^17 - 519x^16 - 24x^15 + 4374x^14 - 3205x^13 - 15774x^12 + 3289x^11 + 46166x^10 + 56516x^9 - 229286x^8 - 661698x^7 - 274432x^6 + 772487x^5 + 1089529x^4 + 549299x^3 + 80270x^2 - 15797x - 2333	\( -\,11^{17}\cdot 1451^{6} \)	20T326	Trivial (GRH)
20.0.82270188117030423168911138645967110144.1	x^20 + 80x^18 + 2725x^16 + 52004x^14 + 616265x^12 + 4747128x^10 + 24125607x^8 + 80059320x^6 + 166415810x^4 + 196170128x^2 + 99859859	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	$[2, 2, 3888]$ (GRH)
20.0.82270188117030423168911138645967110144.2	x^20 + 100x^18 + 3758x^16 + 74104x^14 + 870719x^12 + 6447376x^10 + 30638916x^8 + 92413816x^6 + 169077370x^4 + 168727724x^2 + 69135539	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	$[2, 2, 3804]$ (GRH)
20.16.82270188117030423168911138645967110144.3	x^20 - 72x^18 + 1869x^16 - 19680x^14 + 45743x^12 + 384176x^10 - 1191806x^8 + 235796x^6 + 569503x^4 - 116380x^2 + 5819	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	Trivial (GRH)
20.16.82270188117030423168911138645967110144.4	x^20 - 14x^18 - 179x^16 + 3106x^14 - 8942x^12 - 22232x^10 + 126599x^8 - 198858x^6 + 140921x^4 - 46552x^2 + 5819	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	Trivial (GRH)
20.20.82270188117030423168911138645967110144.5	x^20 - 100x^18 + 3439x^16 - 56240x^14 + 502714x^12 - 2665928x^10 + 8710790x^8 - 17539984x^6 + 20849477x^4 - 13011284x^2 + 3078251	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	Trivial (GRH)
20.4.82270188117030423168911138645967110144.5	x^20 + 52x^18 + 327x^16 - 11744x^14 - 223794x^12 - 1672364x^10 - 6309985x^8 - 11830280x^6 - 8707501x^4 + 23276x^2 + 5819	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	$[2, 4]$ (GRH)
20.8.82270188117030423168911138645967110144.5	x^20 + 36x^18 - 520x^16 - 9024x^14 + 74625x^12 + 346116x^10 - 360173x^8 - 1875236x^6 - 1468159x^4 - 186208x^2 + 5819	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	Trivial (GRH)
20.20.82270188117030423168911138645967110144.6	x^20 - 80x^18 + 2736x^16 - 52796x^14 + 635559x^12 - 4959032x^10 + 25114837x^8 - 79828584x^6 + 146183147x^4 - 125992988x^2 + 26121491	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	Trivial (GRH)
20.4.82270188117030423168911138645967110144.6	x^20 + 28x^18 - 980x^16 - 38444x^14 - 374193x^12 - 1268004x^10 - 1825384x^8 - 1130404x^6 - 268686x^4 + 5819	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	$[2, 2]$ (GRH)
20.8.82270188117030423168911138645967110144.6	x^20 - 28x^18 - 639x^16 + 10856x^14 + 168140x^12 + 761608x^10 + 1378531x^8 + 722568x^6 - 273493x^4 - 23276x^2 + 5819	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	Trivial (GRH)
20.12.82270188117030423168911138645967110144.7	x^20 + 8x^18 - 1059x^16 + 4272x^14 + 103137x^12 - 614296x^10 + 921283x^8 + 611248x^6 - 2470292x^4 + 1512940x^2 + 5819	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	Trivial (GRH)
20.12.82270188117030423168911138645967110144.8	x^20 - 60x^18 + 131x^16 + 23816x^14 - 2503x^12 - 506320x^10 + 1283953x^8 - 1009976x^6 + 105754x^4 + 93104x^2 + 5819	\( 2^{40}\cdot 11^{17}\cdot 23^{6} \)	20T326	Trivial (GRH)