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 200)

Label	Polynomial	Discriminant	Galois group	Class group
10.2.268435456000000.1	x^10 - 4x^9 - 2x^8 + 16x^7 + 4x^6 + 16x^5 - 88x^4 - 96x^3 + 196x^2 + 176x - 232	\( 2^{34}\cdot 5^{6} \)	$M_{10}$ (as 10T31)	Trivial
10.2.570630428688384.3	x^10 - 12x^8 + 30x^6 - 48x^5 - 24x^4 + 96x^3 - 129x^2 + 80x - 36	\( 2^{30}\cdot 3^{12} \)	$M_{10}$ (as 10T31)	Trivial
10.2.1014454095446016.1	x^10 - 2x^9 + 9x^8 - 54x^2 + 108x - 54	\( 2^{34}\cdot 3^{10} \)	$M_{10}$ (as 10T31)	Trivial
10.2.1014454095446016.2	x^10 - 2x^9 + 3x^8 + 12x^6 - 24x^5 - 12x^4 + 36x^2 - 8x - 20	\( 2^{34}\cdot 3^{10} \)	$M_{10}$ (as 10T31)	Trivial
10.2.3243658447265625.1	x^10 - 5x^9 + 15x^8 - 15x^7 + 15x^6 - 96x^5 + 345x^4 - 510x^3 - 45x^2 + 170x - 52	\( 3^{12}\cdot 5^{14} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.3783403212890625.1	x^10 - 5x^9 + 135x^6 - 360x^5 + 405x^4 - 270x^3 + 135x^2 - 45x + 9	\( 3^{18}\cdot 5^{10} \)	$M_{10}$ (as 10T31)	Trivial
10.2.5572562780160000.7	x^10 - x^9 - 6x^8 + 12x^7 + 72x^4 - 72x^3 + 36x^2 - 36x - 72	\( 2^{24}\cdot 3^{12}\cdot 5^{4} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.6499837226778624.1	x^10 - 4x^9 + 24x^7 - 42x^6 + 84x^4 - 120x^3 - 162x^2 + 296x - 320	\( 2^{24}\cdot 3^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.6499837226778624.2	x^10 - 4x^9 + 24x^7 - 60x^6 + 156x^4 - 120x^3 - 207x^2 + 428x - 236	\( 2^{24}\cdot 3^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.6499837226778624.4	x^10 - 4x^9 - 24x^7 + 96x^6 - 24x^4 - 48x^3 + 36x^2 + 16x + 80	\( 2^{24}\cdot 3^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.6499837226778624.5	x^10 - x^9 + 9x^8 + 12x^7 + 6x^6 + 126x^5 - 42x^4 + 276x^3 + 45x^2 + 79x + 101	\( 2^{24}\cdot 3^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.9130086859014144.7	x^10 - 2x^9 + 9x^8 - 288x^2 + 576x - 288	\( 2^{34}\cdot 3^{12} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.9130086859014144.12	x^10 - 4x^9 + 12x^8 - 36x^6 + 144x^5 - 48x^4 + 324x^2 + 240x + 48	\( 2^{34}\cdot 3^{12} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.9130086859014144.15	x^10 - 4x^9 + 12x^8 - 96x^6 + 144x^5 + 120x^4 - 528x^3 + 798x^2 - 856x + 184	\( 2^{34}\cdot 3^{12} \)	$M_{10}$ (as 10T31)	$[4]$ (GRH)
10.2.9130086859014144.19	x^10 - 2x^9 + 3x^8 - 48x^6 + 96x^5 - 48x^4 + 576x^2 - 640x + 704	\( 2^{34}\cdot 3^{12} \)	$M_{10}$ (as 10T31)	Trivial
10.2.12961461825709056.1	x^10 - 2x^9 + 3x^8 + 6x^7 + 6x^6 - 144x^5 + 102x^4 + 78x^3 - 555x^2 - 546x - 249	\( 2^{10}\cdot 3^{10}\cdot 11^{8} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.13271040000000000.3	x^10 + 5x^8 - 40x^7 + 40x^6 - 24x^5 + 140x^4 - 80x^3 - 20x^2 - 80x - 12	\( 2^{24}\cdot 3^{4}\cdot 5^{10} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.15479341056000000.16	x^10 - 4x^9 + 12x^8 + 6x^6 - 12x^4 - 120x^3 - 66x^2 + 104x + 88	\( 2^{24}\cdot 3^{10}\cdot 5^{6} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.18226538222455809.1	x^10 - 5x^9 + 9x^8 + 3x^7 - 60x^6 + 126x^5 - 105x^4 + 219x^3 - 423x^2 + 505x - 302	\( 3^{18}\cdot 19^{6} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.27422596920508416.1	x^10 - 4x^9 - 3x^8 + 48x^7 - 42x^6 - 96x^5 + 60x^4 + 456x^3 - 195x^2 - 68x + 35	\( 2^{18}\cdot 3^{10}\cdot 11^{6} \)	$M_{10}$ (as 10T31)	Trivial
10.2.79101562500000000.2	x^10 - 5x^8 - 90x^6 - 240x^5 + 190x^4 + 600x^3 - 95x^2 - 600x - 261	\( 2^{8}\cdot 3^{4}\cdot 5^{18} \)	$M_{10}$ (as 10T31)	Trivial
10.2.92264062500000000.6	x^10 - 5x^9 + 30x^7 - 15x^6 - 81x^5 - 90x^4 + 360x^3 - 360	\( 2^{8}\cdot 3^{10}\cdot 5^{14} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.102400000000000000.4	x^10 - 5x^8 - 20x^7 - 5x^6 + 4x^5 + 375x^4 + 340x^3 - 565x^2 - 3160x + 2729	\( 2^{24}\cdot 5^{14} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.113507926962890625.1	x^10 - 30x^7 + 15x^6 - 15x^5 + 90x^4 - 585x^3 - 1485x^2 - 1485x + 54	\( 3^{8}\cdot 5^{10}\cdot 11^{6} \)	$M_{10}$ (as 10T31)	Trivial
10.2.119439360000000000.22	x^10 - 5x^9 + 110x^6 - 102x^5 - 100x^4 - 60x^3 - 450x^2 - 270x - 48	\( 2^{24}\cdot 3^{6}\cdot 5^{10} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.163716748799901696.1	x^10 - 4x^9 + 2x^8 + 56x^7 - 194x^6 + 560x^5 - 1008x^4 + 1512x^3 - 1977x^2 + 1228x - 582	\( 2^{34}\cdot 3^{4}\cdot 7^{6} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.195689447424000000.4	x^10 - 4x^9 - 14x^8 + 32x^7 + 36x^6 - 192x^5 + 112x^4 + 80x^3 - 2x^2 + 8x + 12	\( 2^{34}\cdot 3^{6}\cdot 5^{6} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.195689447424000000.20	x^10 - 4x^9 - 6x^8 + 24x^7 + 42x^6 - 48x^5 + 72x^4 - 1128x^3 - 1005x^2 + 11740x - 13630	\( 2^{34}\cdot 3^{6}\cdot 5^{6} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.225254058837890625.1	x^10 - 5x^9 - 45x^7 - 90x^6 - 261x^5 - 420x^4 - 180x^3 - 75x^2 - 30x - 12	\( 3^{10}\cdot 5^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.225254058837890625.4	x^10 - 5x^9 - 15x^8 + 90x^7 - 45x^6 - 66x^5 + 150x^4 - 150x^2 + 200x - 85	\( 3^{10}\cdot 5^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.270633809240653824.1	x^10 + 10x^8 - 48x^7 - 92x^6 - 528x^5 - 688x^4 - 816x^3 - 430x^2 - 288x - 796	\( 2^{34}\cdot 3^{8}\cdot 7^{4} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.393379840000000000.1	x^10 - 10x^8 + 75x^6 - 60x^5 - 450x^4 + 420x^3 + 985x^2 - 540x + 296	\( 2^{24}\cdot 5^{10}\cdot 7^{4} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.415989582513831936.1	x^10 - 4x^9 + 18x^8 - 90x^6 + 504x^5 - 540x^4 + 720x^3 + 990x^2 + 120x - 732	\( 2^{30}\cdot 3^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.739537035580145664.1	x^10 - 2x^9 + 9x^8 - 648x^2 + 1296x - 648	\( 2^{34}\cdot 3^{16} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.739537035580145664.2	x^10 - 2x^9 - 9x^8 + 24x^7 + 6x^6 - 36x^5 - 150x^4 + 552x^3 - 387x^2 - 514x + 587	\( 2^{34}\cdot 3^{16} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.830376562500000000.11	x^10 - 5x^9 + 30x^7 + 45x^6 - 111x^5 - 210x^4 + 1200x^3 + 3300x^2 + 4750x + 1450	\( 2^{8}\cdot 3^{12}\cdot 5^{14} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.1048970301636870144.2	x^10 - 4x^9 + 24x^8 - 72x^7 + 180x^6 - 384x^5 + 372x^4 - 216x^3 - 639x^2 + 332x - 620	\( 2^{24}\cdot 3^{12}\cdot 7^{6} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.1191560814085640625.1	x^10 - 2x^9 + 36x^8 + 9x^7 + 270x^6 + 783x^5 + 1251x^4 + 972x^3 + 1323x^2 - 3330x - 4653	\( 3^{16}\cdot 5^{6}\cdot 11^{6} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.1386703172671635456.1	x^10 - 2x^9 - 5x^8 - 32x^7 + 108x^6 - 216x^5 + 4x^4 + 640x^3 + 904x^2 + 208x + 72	\( 2^{30}\cdot 3^{6}\cdot 11^{6} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.1473450739199115264.1	x^10 - 2x^9 + 5x^8 + 40x^7 - 182x^6 + 420x^5 - 518x^4 - 152x^3 - 109x^2 + 514x - 305	\( 2^{34}\cdot 3^{6}\cdot 7^{6} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.1696058545166015625.4	x^10 - 5x^9 + 15x^8 + 30x^7 - 165x^6 + 363x^5 - 150x^4 - 720x^3 + 870x^2 + 235x - 938	\( 3^{10}\cdot 5^{12}\cdot 7^{6} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.1721868840000000000.2	x^10 + 45x^6 - 36x^5 + 360x^4 - 1080x^3 + 1305x^2 - 780x + 180	\( 2^{12}\cdot 3^{16}\cdot 5^{10} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.1779985907461265625.1	x^10 - 12x^8 + 117x^6 - 495x^5 - 162x^4 + 495x^3 - 2538x^2 - 3960x - 1431	\( 3^{12}\cdot 5^{6}\cdot 11^{8} \)	$M_{10}$ (as 10T31)	$[5]$ (GRH)
10.2.2027286529541015625.1	x^10 - 5x^9 + 30x^7 - 15x^6 + 39x^5 + 480x^4 - 3780x^3 + 5625x^2 + 3345x - 8472	\( 3^{12}\cdot 5^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.2027286529541015625.3	x^10 - 5x^9 + 30x^7 - 15x^6 + 99x^5 - 420x^4 + 120x^3 + 1125x^2 - 4355x + 5188	\( 3^{12}\cdot 5^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.2027286529541015625.4	x^10 - 75x^7 - 150x^6 - 645x^5 + 4500x^2 - 4125x + 6975	\( 3^{12}\cdot 5^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.2027286529541015625.5	x^10 - 5x^9 - 15x^8 + 90x^7 + 105x^6 - 606x^5 - 750x^4 + 2025x^3 + 4350x^2 - 5600x - 4655	\( 3^{12}\cdot 5^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.2027286529541015625.6	x^10 - 5x^9 + 30x^7 - 90x^6 - 51x^5 + 855x^4 + 495x^3 - 3300x^2 - 5405x - 2447	\( 3^{12}\cdot 5^{18} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.2344726562500000000.1	x^10 - 30x^8 - 50x^7 + 160x^6 + 670x^5 + 1740x^4 + 2700x^3 + 1080x^2 + 1944	\( 2^{8}\cdot 5^{18}\cdot 7^{4} \)	$M_{10}$ (as 10T31)	Trivial (GRH)
10.2.2364627008056640625.1	x^10 - 75x^7 + 198x^5 + 165x^4 + 2430x^3 - 225x^2 + 3650x - 1035	\( 3^{18}\cdot 5^{14} \)	$M_{10}$ (as 10T31)	Trivial (GRH)