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
16.6.6226566414068750000.1	x^16 - 3x^15 + 4x^14 - 8x^13 - 2x^12 + 38x^11 - 58x^10 + 51x^9 - 17x^8 - 33x^7 + 62x^6 - 80x^5 + 66x^4 - 30x^3 + 10x^2 - x - 1	\( -\,2^{4}\cdot 5^{8}\cdot 251^{5} \)	16T1675	Trivial
16.2.9729010021982421875.1	x^16 - 5x^15 + 15x^14 - 27x^13 + 35x^12 - 27x^11 + 26x^10 - 13x^9 + 53x^8 - 50x^7 + 99x^6 - 41x^5 + 38x^4 + 19x^3 - 4x^2 + 6x - 1	\( -\,5^{10}\cdot 251^{5} \)	16T1675	Trivial
16.6.9729010021982421875.1	x^16 - 7x^15 + 18x^14 - 18x^13 - 7x^12 + 36x^11 - 35x^10 + 21x^9 - 24x^8 + 42x^7 - 55x^6 + 38x^5 - 7x^4 - 11x^3 + 12x^2 - 6x + 1	\( -\,5^{10}\cdot 251^{5} \)	16T1675	Trivial
16.2.1594001002001600000000.1	x^16 - 5x^14 - 19x^12 + 86x^10 + 118x^8 - 442x^6 - 959x^4 - 753x^2 - 251	\( -\,2^{12}\cdot 5^{8}\cdot 251^{5} \)	16T1675	Trivial
16.0.10098465517192226985994092544.1	x^16 + 28x^14 + 322x^12 + 1960x^10 + 6778x^8 + 13268x^6 + 13728x^4 + 6168x^2 + 514	\( 2^{53}\cdot 257^{5} \)	16T1675	$[2, 270]$ (GRH)
16.16.10098465517192226985994092544.1	x^16 - 28x^14 + 314x^12 - 1836x^10 + 6034x^8 - 11076x^6 + 10452x^4 - 4112x^2 + 514	\( 2^{53}\cdot 257^{5} \)	16T1675	Trivial (GRH)
16.0.10098465517192226985994092544.2	x^16 + 28x^14 + 314x^12 + 1836x^10 + 6034x^8 + 11076x^6 + 10452x^4 + 4112x^2 + 514	\( 2^{53}\cdot 257^{5} \)	16T1675	$[2, 318]$ (GRH)
16.16.10098465517192226985994092544.2	x^16 - 28x^14 + 322x^12 - 1960x^10 + 6778x^8 - 13268x^6 + 13728x^4 - 6168x^2 + 514	\( 2^{53}\cdot 257^{5} \)	16T1675	Trivial (GRH)
16.12.669002270083080728394108412888785769293.1	x^16 - 2x^15 - 87x^14 + 210x^13 + 609x^12 - 361x^11 + 119099x^10 - 394416x^9 - 3864589x^8 + 11770693x^7 + 45769170x^6 - 136010120x^5 - 196639436x^4 + 701260374x^3 - 10433250x^2 - 1333911191x + 1096054873	\( 3^{8}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[48]$ (GRH)
16.4.669002270083080728394108412888785769293.1	x^16 - 2x^15 + 57x^14 + 31x^13 - 202x^12 + 4150x^11 - 49354x^10 + 46333x^9 - 210018x^8 - 23935x^7 + 8525768x^6 - 23633591x^5 + 71298922x^4 - 184526648x^3 + 232361572x^2 - 125645924x + 205891711	\( 3^{8}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[2, 48]$ (GRH)
16.12.669002270083080728394108412888785769293.2	x^16 - 78x^14 - 49x^13 + 943x^12 + 2329x^11 + 35406x^10 - 58366x^9 - 834951x^8 + 936994x^7 + 5070510x^6 - 8440364x^5 - 4438837x^4 + 26735463x^3 - 23034358x^2 - 7770217x + 11794897	\( 3^{8}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[48]$ (GRH)
16.4.669002270083080728394108412888785769293.2	x^16 + 48x^14 - 2664x^12 - 136830x^10 - 690838x^8 + 36489216x^6 + 506855805x^4 + 1581795462x^2 + 122603533	\( 3^{8}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[2, 48]$ (GRH)
16.0.5215553034727934460124227765005778951509.1	x^16 - 4x^15 - 32x^14 + 145x^13 + 1429x^12 + 3357x^11 - 25164x^10 - 107121x^9 + 79776x^8 - 1059869x^7 + 41589315x^6 + 74545252x^5 + 1059195894x^4 + 1301275602x^3 + 20404848082x^2 + 5295191495x + 153463978421	\( 149^{9}\cdot 331^{8} \)	16T1675	$[2, 2, 300]$ (GRH)
16.0.5215553034727934460124227765005778951509.2	x^16 - 6x^15 + 99x^14 - 616x^13 + 5369x^12 - 23796x^11 + 170050x^10 - 549695x^9 + 4065355x^8 - 14810136x^7 + 10311242x^6 + 138905845x^5 + 1881736663x^4 + 886766664x^3 + 402208164x^2 - 3217639232x + 25172218864	\( 149^{9}\cdot 331^{8} \)	16T1675	$[2, 2, 300]$ (GRH)
16.8.6021020430747726555546975715999071923637.1	x^16 - 8x^15 + 72x^14 - 220x^13 - 2660x^12 + 26877x^11 - 202403x^10 + 477846x^9 + 1234105x^8 - 15197529x^7 + 75430919x^6 - 41505565x^5 - 301240263x^4 + 2074151994x^3 - 1983832568x^2 - 3995172348x + 4653510391	\( 3^{10}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[2, 48]$ (GRH)
16.8.6021020430747726555546975715999071923637.2	x^16 - 6x^15 + 11x^14 - 65x^13 - 2257x^12 + 15255x^11 - 46642x^10 - 38121x^9 + 2494561x^8 - 8559267x^7 + 10820944x^6 + 89342780x^5 - 512361357x^4 + 634416836x^3 + 770369830x^2 - 2443995613x + 1729288237	\( 3^{10}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[2, 48]$ (GRH)
16.12.43843732772164778616036288947079464176386048.1	x^16 - 305x^14 + 28234x^12 - 615347x^10 - 17210403x^8 + 256834865x^6 + 699456118x^4 - 3008559853x^2 + 17826133	\( 2^{16}\cdot 3^{8}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[48]$ (GRH)
16.4.43843732772164778616036288947079464176386048.1	x^16 - 53x^14 - 7553x^12 + 22063x^10 + 12434364x^8 + 280462457x^6 + 2060129785x^4 + 4785170858x^2 + 3379364677	\( 2^{16}\cdot 3^{8}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[2, 2, 48]$ (GRH)
16.8.43843732772164778616036288947079464176386048.1	x^16 - 137x^14 + 2120x^12 + 225613x^10 - 2409767x^8 - 86396905x^6 + 63138950x^4 + 3934885019x^2 + 3379364677	\( 2^{16}\cdot 3^{8}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[96]$ (GRH)
16.12.43843732772164778616036288947079464176386048.2	x^16 + 49x^14 - 8561x^12 + 37450x^10 + 4217877x^8 - 55975156x^6 + 240378148x^4 - 347055202x^2 + 122603533	\( 2^{16}\cdot 3^{8}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[48]$ (GRH)
16.4.43843732772164778616036288947079464176386048.2	x^16 + 166x^14 + 3088x^12 - 280730x^10 - 1100037x^8 + 52895846x^6 + 550192699x^4 + 1888648151x^2 + 2087205133	\( 2^{16}\cdot 3^{8}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[2, 2, 48]$ (GRH)
16.8.43843732772164778616036288947079464176386048.2	x^16 + 16x^14 - 4339x^12 + 65683x^10 + 1424734x^8 - 22392589x^6 - 80164555x^4 + 630712667x^2 + 2087205133	\( 2^{16}\cdot 3^{8}\cdot 13^{9}\cdot 1327^{8} \)	16T1675	$[96]$ (GRH)