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 )

Label	Polynomial	Discriminant	Galois group	Class group
10.0.4993045981293568.1	x^10 + 46x^8 + 787x^6 + 6147x^4 + 21091x^2 + 22747	\( -\,2^{10}\cdot 11^{8}\cdot 23^{2}\cdot 43 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$[2, 2, 36]$
10.0.9445893863498752.1	x^10 + 60x^8 + 1165x^6 + 9624x^4 + 34138x^2 + 43033	\( -\,2^{10}\cdot 11^{8}\cdot 23\cdot 1871 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$[2, 72]$ (GRH)
10.0.9445893863498752.2	x^10 + 53x^8 + 1029x^6 + 8978x^4 + 34313x^2 + 43033	\( -\,2^{10}\cdot 11^{8}\cdot 23\cdot 1871 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$[2, 72]$ (GRH)
10.0.9630096522760791.1	x^10 - x^9 + 56x^8 - 56x^7 + 1156x^6 - 1156x^5 + 10781x^4 - 10781x^3 + 45156x^2 - 45156x + 79531	\( -\,3^{5}\cdot 7^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 66]$
10.0.9914423014398139.1	x^10 - 3x^9 + 41x^8 - 81x^7 + 602x^6 - 708x^5 + 4098x^4 - 2272x^3 + 15013x^2 - 2843x + 30725	\( -\,61^{2}\cdot 97\cdot 397^{3}\cdot 439 \)	$C_2 \wr S_5$ (as 10T39)	$[2, 64]$
10.0.11258530353021875.4	x^10 - 3x^9 + 39x^8 - 88x^7 + 730x^6 - 1192x^5 + 7716x^4 - 8217x^3 + 46199x^2 - 23945x + 126611	\( -\,5^{5}\cdot 7^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[110]$
10.0.18775450875101184.1	x^10 + 66x^8 + 1584x^6 + 16632x^4 + 71280x^2 + 85536	\( -\,2^{15}\cdot 3^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 124]$
10.0.19340358336761319.3	x^10 - 3x^9 + 44x^8 - 100x^7 + 910x^6 - 1500x^5 + 10534x^4 - 11333x^3 + 68332x^2 - 35865x + 200509	\( -\,3^{5}\cdot 11^{8}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[220]$
10.0.21950349414400000.4	x^10 - 2x^9 + 43x^8 - 66x^7 + 896x^6 - 1052x^5 + 10707x^4 - 8734x^3 + 72463x^2 - 31666x + 221651	\( -\,2^{15}\cdot 5^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[310]$
10.0.25123244285634975.1	x^10 - 2x^9 + 8x^8 - 14x^7 + 31x^6 - 49x^5 + 93x^4 - 126x^3 + 216x^2 - 162x + 243	\( -\,3^{2}\cdot 5^{2}\cdot 59\cdot 211^{2}\cdot 349^{3} \)	$C_2 \wr S_5$ (as 10T39)	$[114]$
10.0.28312660190713043.1	x^10 - x^9 + 9x^8 - 7x^7 + 41x^6 - 25x^5 + 123x^4 - 63x^3 + 243x^2 - 81x + 243	\( -\,29^{2}\cdot 53^{2}\cdot 97\cdot 433^{2}\cdot 659 \)	$C_2 \wr S_5$ (as 10T39)	$[116]$
10.0.28631509956043776.1	x^10 - 2x^9 + 19x^8 - 76x^7 + 23x^6 - 226x^5 + 1573x^4 + 1072x^3 - 7724x^2 - 2616x + 15924	\( -\,2^{10}\cdot 3^{5}\cdot 163^{5} \)	$D_5$ (as 10T2)	$[22, 22]$
10.0.28851751301753799.1	x^10 - 4x^9 + 26x^8 - 46x^7 + 191x^6 - 86x^5 + 591x^4 + 682x^3 + 1021x^2 + 2244x + 3115	\( -\,3^{5}\cdot 653^{5} \)	$A_5\times C_2$ (as 10T11)	$[3, 42]$
10.0.31512565339032283.3	x^10 - 3x^9 + 49x^8 - 112x^7 + 1110x^6 - 1844x^5 + 13964x^4 - 15153x^3 + 97561x^2 - 51749x + 305293	\( -\,11^{8}\cdot 43^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 10, 10]$
10.0.35987941646972963.1	x^10 - 4x^9 + 11x^8 - 25x^7 + 57x^6 - 106x^5 + 171x^4 - 225x^3 + 297x^2 - 324x + 243	\( -\,23\cdot 109\cdot 857^{2}\cdot 4421^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 56]$
10.0.36754651794468608.1	x^10 - 4x^9 + 33x^8 - 70x^7 + 269x^6 - 416x^5 + 867x^4 - 958x^3 + 1214x^2 - 736x + 584	\( -\,2^{8}\cdot 7^{4}\cdot 11^{5}\cdot 13^{5} \)	$D_{10}$ (as 10T3)	$[110]$ (GRH)
10.0.37367680402046543.1	x^10 + 30x^8 + 373x^6 + 2220x^4 + 5476x^2 + 2063	\( -\,2063^{5} \)	$D_5$ (as 10T2)	$[2, 2, 2, 18]$
10.0.38598883026443567.1	x^10 + 8x^8 - 2x^7 + 31x^6 - 11x^5 + 93x^4 - 18x^3 + 216x^2 + 243	\( -\,241^{2}\cdot 3697^{2}\cdot 48623 \)	$C_2 \wr S_5$ (as 10T39)	$[102]$
10.0.39315232405371887.1	x^10 - 3x^9 + 9x^8 - 20x^7 + 41x^6 - 70x^5 + 123x^4 - 180x^3 + 243x^2 - 243x + 243	\( -\,419^{2}\cdot 2903\cdot 8783^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[103]$
10.0.40581147486860288.1	x^10 + 77x^8 + 2156x^6 + 26411x^4 + 132055x^2 + 184877	\( -\,2^{10}\cdot 7^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 124]$ (GRH)
10.0.46514690461023863.1	x^10 - 2x^9 + 7x^8 - 15x^7 + 34x^6 - 61x^5 + 102x^4 - 135x^3 + 189x^2 - 162x + 243	\( -\,13\cdot 1091\cdot 1810969^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[106]$
10.0.47100103555799631.1	x^10 - 3x^9 + 12x^8 - 27x^7 + 65x^6 - 111x^5 + 195x^4 - 243x^3 + 324x^2 - 243x + 243	\( -\,3\cdot 17^{2}\cdot 12757\cdot 65257^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[120]$
10.0.48265583903159931.1	x^10 - x^9 + 8x^8 - 5x^7 + 32x^6 - 16x^5 + 96x^4 - 45x^3 + 216x^2 - 81x + 243	\( -\,3^{6}\cdot 7^{2}\cdot 11^{4}\cdot 61\cdot 89^{2}\cdot 191 \)	$C_2 \wr S_5$ (as 10T39)	$[146]$
10.0.48364216424306959.3	x^10 - x^9 + 78x^8 - 78x^7 + 2234x^6 - 2234x^5 + 28645x^4 - 28645x^3 + 160700x^2 - 160700x + 345577	\( -\,11^{9}\cdot 29^{5} \)	$C_{10}$ (as 10T1)	$[550]$ (GRH)
10.0.49162139063457167.3	x^10 - 3x^9 + 54x^8 - 124x^7 + 1330x^6 - 2224x^5 + 18066x^4 - 19749x^3 + 135254x^2 - 72389x + 449723	\( -\,11^{8}\cdot 47^{5} \)	$C_{10}$ (as 10T1)	$[275]$ (GRH)
10.0.49513445102501951.1	x^10 - 3x^9 + 11x^8 - 26x^7 + 59x^6 - 106x^5 + 177x^4 - 234x^3 + 297x^2 - 243x + 243	\( -\,31^{2}\cdot 61^{2}\cdot 1567^{2}\cdot 5639 \)	$C_2 \wr S_5$ (as 10T39)	$[102]$
10.0.50575265985138951.1	x^10 - 4x^9 + 13x^8 - 29x^7 + 64x^6 - 111x^5 + 192x^4 - 261x^3 + 351x^2 - 324x + 243	\( -\,3\cdot 7^{2}\cdot 89^{2}\cdot 157\cdot 16633^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 64]$
10.0.51989066519656192.1	x^10 - 4x^9 + 16x^8 - 34x^7 + 21x^6 + 74x^5 + 414x^4 - 168x^3 + 168x^2 - 1120x + 1024	\( -\,2^{8}\cdot 727^{5} \)	$D_{10}$ (as 10T3)	$[143]$
10.0.52154166497894723.1	x^10 - 5x^9 + 16x^8 - 29x^7 + 47x^6 - 43x^5 + 71x^4 - 24x^3 + 99x^2 + 38x + 72	\( -\,2267\cdot 4796437^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[108]$
10.0.53979104674799231.1	x^10 - 2x^9 + 9x^8 - 17x^7 + 44x^6 - 71x^5 + 132x^4 - 153x^3 + 243x^2 - 162x + 243	\( -\,33119\cdot 1276657^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 52]$
10.0.54740593776568887.1	x^10 - 2x^9 - 2x^8 + 4x^7 + 89x^6 - 173x^5 + 75x^4 + 6x^3 + 8x^2 - 6x + 1	\( -\,3^{5}\cdot 11^{4}\cdot 109^{5} \)	$D_5\times C_5$ (as 10T6)	$[132]$
10.0.55242885427637399.1	x^10 - x^9 + 6x^8 - 4x^7 + 21x^6 - 5x^5 + 63x^4 - 36x^3 + 162x^2 - 81x + 243	\( -\,727^{2}\cdot 2027^{2}\cdot 25439 \)	$C_2 \wr S_5$ (as 10T39)	$[116]$
10.0.57034389417011487.1	x^10 - 3x^9 + 7x^8 - 10x^7 + 21x^6 - 34x^5 + 63x^4 - 90x^3 + 189x^2 - 243x + 243	\( -\,3^{2}\cdot 13\cdot 173^{2}\cdot 179\cdot 9539^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[142]$
10.0.58114578958432007.1	x^10 - 3x^9 + 6x^8 - 17x^7 + 35x^6 - 55x^5 + 105x^4 - 153x^3 + 162x^2 - 243x + 243	\( -\,11^{2}\cdot 1607\cdot 546691^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[110]$
10.0.60344817717557475.1	x^10 + 2x^8 - 5x^7 + 12x^6 - 7x^5 + 36x^4 - 45x^3 + 54x^2 + 243	\( -\,3^{8}\cdot 5^{2}\cdot 23^{2}\cdot 47\cdot 157\cdot 307^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[138]$
10.0.61173988183846719.1	x^10 - 3x^9 + 8x^8 - 17x^7 + 39x^6 - 67x^5 + 117x^4 - 153x^3 + 216x^2 - 243x + 243	\( -\,3^{6}\cdot 12479\cdot 82003^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[106]$
10.0.62234340016148027.1	x^10 - x^9 + 8x^8 - 4x^7 + 30x^6 - 7x^5 + 90x^4 - 36x^3 + 216x^2 - 81x + 243	\( -\,7^{2}\cdot 13\cdot 53^{2}\cdot 71\cdot 22133^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 70]$
10.0.63529312977857975.1	x^10 - 3x^9 + 10x^8 - 25x^7 + 55x^6 - 95x^5 + 165x^4 - 225x^3 + 270x^2 - 243x + 243	\( -\,5^{2}\cdot 16631\cdot 390893^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[114]$
10.0.63789194356505600.1	x^10 - 2x^9 + 3x^8 - 2x^7 + 2x^6 + 10x^5 + 6x^4 - 18x^3 + 81x^2 - 162x + 243	\( -\,2^{10}\cdot 5^{2}\cdot 839\cdot 54497^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[104]$
10.0.64009367101492424.1	x^10 + 7x^8 - x^7 + 25x^6 - 8x^5 + 75x^4 - 9x^3 + 189x^2 + 243	\( -\,2^{3}\cdot 199^{2}\cdot 4513\cdot 6691^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 52]$
10.0.64024396763274499.1	x^10 - 3x^9 + 17x^8 - 36x^7 + 198x^6 - 294x^5 + 1455x^4 - 1341x^3 + 6437x^2 - 2826x + 13249	\( -\,19^{5}\cdot 401^{4} \)	$D_{10}$ (as 10T3)	$[2, 58]$
10.0.66647608526448099.1	x^10 + 3x^8 - x^7 + 17x^6 - 2x^5 + 51x^4 - 9x^3 + 81x^2 + 243	\( -\,3^{2}\cdot 241^{2}\cdot 3659\cdot 5903^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[127]$
10.0.67569098939773383.1	x^10 - 2x^9 + 10x^8 - 16x^7 + 49x^6 - 63x^5 + 147x^4 - 144x^3 + 270x^2 - 162x + 243	\( -\,3\cdot 17^{2}\cdot 18301\cdot 65257^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[128]$
10.0.67875840501030167.1	x^10 - 2x^9 + 8x^8 - 14x^7 + 39x^6 - 59x^5 + 117x^4 - 126x^3 + 216x^2 - 162x + 243	\( -\,97\cdot 311\cdot 557^{2}\cdot 2693^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[124]$
10.0.72734340569594783.1	x^10 - 3x^9 + 11x^8 - 24x^7 + 57x^6 - 94x^5 + 171x^4 - 216x^3 + 297x^2 - 243x + 243	\( -\,8087\cdot 2998997^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[108]$
10.0.73959226721104131.3	x^10 - 3x^9 + 59x^8 - 136x^7 + 1570x^6 - 2640x^5 + 22900x^4 - 25193x^3 + 182899x^2 - 98649x + 644071	\( -\,3^{5}\cdot 11^{8}\cdot 17^{5} \)	$C_{10}$ (as 10T1)	$[710]$ (GRH)
10.0.76323004483946747.1	x^10 - 2x^9 + 9x^8 - 13x^7 + 37x^6 - 46x^5 + 111x^4 - 117x^3 + 243x^2 - 162x + 243	\( -\,17^{2}\cdot 269^{2}\cdot 617^{2}\cdot 9587 \)	$C_2 \wr S_5$ (as 10T39)	$[109]$
10.0.77547890020179719.1	x^10 - 2x^9 + 9x^8 - 17x^7 + 44x^6 - 65x^5 + 132x^4 - 153x^3 + 243x^2 - 162x + 243	\( -\,7^{2}\cdot 433^{2}\cdot 487^{2}\cdot 35591 \)	$C_2 \wr S_5$ (as 10T39)	$[188]$
10.0.78500682315625383.1	x^10 - x^9 + 3x^8 - x^6 + 22x^5 - 3x^4 + 81x^2 - 81x + 243	\( -\,3^{2}\cdot 11^{2}\cdot 31^{2}\cdot 863\cdot 9323^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[104]$
10.0.80927385004882719.1	x^10 - x^9 + 6x^8 - 5x^7 + 23x^6 - 9x^5 + 69x^4 - 45x^3 + 162x^2 - 81x + 243	\( -\,3^{9}\cdot 37\cdot 109^{2}\cdot 197^{2}\cdot 241 \)	$C_2 \wr S_5$ (as 10T39)	$[2, 70]$

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