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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.10.74824300206301289262147419.1	x^20 - 3x^19 - 4x^18 + 23x^17 + 3x^16 - 108x^15 + 62x^14 + 353x^13 - 538x^12 - 333x^11 + 1385x^10 - 819x^9 - 865x^8 + 1401x^7 - 518x^6 - 210x^5 + 322x^4 - 267x^3 + 152x^2 - 37x + 1	\( -\,11^{17}\cdot 23^{6} \)	20T310	Trivial (GRH)
20.2.74824300206301289262147419.1	x^20 - x^19 + 6x^18 - 6x^17 + 16x^16 - 16x^15 + 15x^14 - 15x^13 + 9x^12 - 31x^11 + 21x^10 - 31x^9 + 9x^8 - 15x^7 + 15x^6 - 16x^5 + 16x^4 - 6x^3 + 6x^2 - x + 1	\( -\,11^{17}\cdot 23^{6} \)	20T310	Trivial (GRH)
20.6.74824300206301289262147419.1	x^20 - 9x^19 + 36x^18 - 90x^17 + 160x^16 - 206x^15 + 183x^14 - 78x^13 - 78x^12 + 212x^11 - 265x^10 + 225x^9 - 136x^8 + 63x^7 - 20x^6 - 8x^5 + 10x^4 - 8x^3 + 9x^2 - x + 1	\( -\,11^{17}\cdot 23^{6} \)	20T310	Trivial (GRH)
20.6.74824300206301289262147419.2	x^20 - 4x^19 + 6x^18 + 3x^17 - 35x^16 + 84x^15 - 97x^14 - 44x^13 + 341x^12 - 545x^11 + 351x^10 + 135x^9 - 275x^8 + 22x^7 + 106x^6 + 7x^5 - 65x^4 + 20x^3 + 2x^2 - 3x + 1	\( -\,11^{17}\cdot 23^{6} \)	20T310	Trivial (GRH)
20.10.39582054809133382019675984651.1	x^20 - 9x^19 + 30x^18 - 22x^17 - 192x^16 + 901x^15 - 2010x^14 + 2181x^13 + 563x^12 - 5693x^11 + 8525x^10 - 5047x^9 - 1525x^8 + 4350x^7 - 2541x^6 + 309x^5 + 284x^4 - 115x^3 + 6x^2 + 4x - 1	\( -\,11^{17}\cdot 23^{8} \)	20T310	Trivial (GRH)
20.2.39582054809133382019675984651.1	x^20 - 7x^19 + 33x^18 - 112x^17 + 304x^16 - 673x^15 + 1289x^14 - 2071x^13 + 3127x^12 - 3988x^11 + 5160x^10 - 5511x^9 + 5961x^8 - 5894x^7 + 5968x^6 - 6441x^5 + 5364x^4 - 613x^3 - 894x^2 + 5795x + 241	\( -\,11^{17}\cdot 23^{8} \)	20T310	$[2]$ (GRH)
20.6.39582054809133382019675984651.1	x^20 - 7x^19 + 18x^18 - 19x^17 + 73x^15 - 389x^14 + 993x^13 - 989x^12 - 639x^11 + 2177x^10 - 290x^9 - 3180x^8 + 1947x^7 + 2739x^6 - 2694x^5 - 1189x^4 + 1376x^3 + 442x^2 - 118x + 1	\( -\,11^{17}\cdot 23^{8} \)	20T310	$[2]$ (GRH)
20.6.39582054809133382019675984651.2	x^20 - 5x^19 + 11x^18 - 25x^17 + 29x^16 + 84x^15 - 157x^14 - 45x^13 - 902x^12 + 3704x^11 - 4597x^10 + 3927x^9 - 8789x^8 + 17281x^7 - 19822x^6 + 14564x^5 - 6820x^4 + 1639x^3 + 22x^2 - 88x + 11	\( -\,11^{17}\cdot 23^{8} \)	20T310	Trivial (GRH)
20.10.295542555810828925413205326764411.1	x^20 - 6x^19 + 11x^18 - 4x^17 - 78x^16 + 483x^15 - 1045x^14 + 401x^13 + 2572x^12 - 8098x^11 + 9973x^10 + 8760x^9 - 32045x^8 + 8528x^7 + 28915x^6 - 10020x^5 - 16808x^4 + 4960x^3 + 7039x^2 - 4245x + 683	\( -\,11^{16}\cdot 1451^{5} \)	20T310	Trivial (GRH)
20.10.295542555810828925413205326764411.2	x^20 - 8x^19 + 30x^18 - 67x^17 + 8x^16 + 546x^15 - 1921x^14 + 3464x^13 - 3077x^12 - 3559x^11 + 20428x^10 - 40810x^9 + 48560x^8 - 42349x^7 + 37707x^6 - 33332x^5 + 15773x^4 + 2101x^3 - 3449x^2 - 112x + 43	\( -\,11^{16}\cdot 1451^{5} \)	20T310	Trivial (GRH)
20.20.2108097156584902878904709960659367677.1	x^20 - 6x^19 - 43x^18 + 292x^17 + 651x^16 - 5652x^15 - 3017x^14 + 55069x^13 - 21081x^12 - 278393x^11 + 287287x^10 + 648233x^9 - 1112755x^8 - 339422x^7 + 1572788x^6 - 665992x^5 - 512025x^4 + 473717x^3 - 97022x^2 - 2652x + 23	\( 11^{16}\cdot 43^{5}\cdot 199^{5} \)	20T310	$[2]$ (GRH)
20.20.2108097156584902878904709960659367677.2	x^20 - 8x^19 - 33x^18 + 347x^17 + 257x^16 - 5846x^15 + 2463x^14 + 48956x^13 - 51892x^12 - 214995x^11 + 334300x^10 + 466727x^9 - 1021695x^8 - 352662x^7 + 1529604x^6 - 241444x^5 - 1034673x^4 + 467149x^3 + 212326x^2 - 161926x + 22307	\( 11^{16}\cdot 43^{5}\cdot 199^{5} \)	20T310	$[2]$ (GRH)
20.12.282119316059236304095781411736743051264.1	x^20 - 14x^18 - 110x^16 + 2320x^14 - 6339x^12 - 34808x^10 + 166327x^8 - 104756x^6 - 170005x^4 + 92186x^2 + 47081	\( 2^{40}\cdot 11^{16}\cdot 89^{5} \)	20T310	$[2]$ (GRH)
20.16.282119316059236304095781411736743051264.1	x^20 - 42x^18 + 659x^16 - 4664x^14 + 11775x^12 + 26484x^10 - 197479x^8 + 264880x^6 + 252478x^4 - 756286x^2 + 399521	\( 2^{40}\cdot 11^{16}\cdot 89^{5} \)	20T310	Trivial (GRH)
20.8.282119316059236304095781411736743051264.1	x^20 + 14x^18 - 242x^16 - 3068x^14 + 14737x^12 + 156886x^10 + 46130x^8 - 447664x^6 - 434830x^4 - 32918x^2 + 47081	\( 2^{40}\cdot 11^{16}\cdot 89^{5} \)	20T310	$[2]$ (GRH)
20.12.282119316059236304095781411736743051264.2	x^20 - 10x^18 - 146x^16 + 1760x^14 + 1167x^12 - 54710x^10 + 81057x^8 + 422400x^6 - 821467x^4 - 372840x^2 + 399521	\( 2^{40}\cdot 11^{16}\cdot 89^{5} \)	20T310	Trivial (GRH)
20.16.282119316059236304095781411736743051264.2	x^20 - 40x^18 + 572x^16 - 3230x^14 + 215x^12 + 73902x^10 - 291135x^8 + 387748x^6 - 126643x^4 - 87702x^2 + 47081	\( 2^{40}\cdot 11^{16}\cdot 89^{5} \)	20T310	Trivial (GRH)
20.8.282119316059236304095781411736743051264.2	x^20 + 18x^18 - 81x^16 - 3058x^14 - 15397x^12 + 7168x^10 + 190798x^8 + 212388x^6 - 576239x^4 - 713046x^2 + 399521	\( 2^{40}\cdot 11^{16}\cdot 89^{5} \)	20T310	$[2]$ (GRH)
20.12.282119316059236304095781411736743051264.3	x^20 - 18x^18 - 59x^16 + 1584x^14 - 1251x^12 - 35350x^10 + 57819x^8 + 237094x^6 - 418708x^4 - 329600x^2 + 399521	\( 2^{40}\cdot 11^{16}\cdot 89^{5} \)	20T310	$[2]$ (GRH)
20.12.282119316059236304095781411736743051264.4	x^20 - 12x^18 - 209x^16 + 2114x^14 + 9440x^12 - 54498x^10 + 29057x^8 + 139058x^6 - 175043x^4 + 4308x^2 + 47081	\( 2^{40}\cdot 11^{16}\cdot 89^{5} \)	20T310	Trivial (GRH)
20.8.34136437243167592795589550820145909202944.1	x^20 - 22x^18 - 693x^16 + 110x^14 + 66660x^12 + 164780x^10 - 1965403x^8 - 6499636x^6 + 14551823x^4 + 63428926x^2 + 48342041	\( 2^{40}\cdot 11^{18}\cdot 89^{5} \)	20T310	$[2, 2]$ (GRH)
20.8.34136437243167592795589550820145909202944.2	x^20 + 66x^18 + 1199x^16 + 396x^14 - 140151x^12 - 702064x^10 + 2648932x^8 + 16052102x^6 - 11841665x^4 - 79682614x^2 + 19911881	\( 2^{40}\cdot 11^{18}\cdot 89^{5} \)	20T310	$[2, 4]$ (GRH)