Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 25 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.12.103745853703303712158203125.1	x^20 - x^19 - 5x^18 + 7x^17 - 13x^16 - 18x^15 + 90x^14 - 28x^13 - 89x^12 + 219x^11 - 175x^10 - 400x^9 + 452x^8 + 355x^7 - 406x^6 - 186x^5 + 178x^4 + 61x^3 - 34x^2 - 10x + 1	\( 5^{13}\cdot 419^{2}\cdot 695771^{2} \)	20T1039	Trivial (GRH)
20.0.109683542324480000000000000.1	x^20 + 7x^18 + 23x^16 + 62x^14 + 101x^12 + 120x^10 + 80x^8 + 50x^6 + 75x^4 + 125x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 199^{2}\cdot 1471^{2} \)	20T1039	Trivial (GRH)
20.0.226342912585206153564453125.1	x^20 - 4x^19 + 8x^18 - 19x^17 + 47x^16 - 104x^15 + 119x^14 + 17x^13 + 217x^12 - 500x^11 - 970x^10 + 1294x^9 + 2215x^8 - 1524x^7 - 4142x^6 + 1597x^5 + 4773x^4 - 1202x^3 - 3418x^2 + 595x + 1439	\( 5^{13}\cdot 199^{2}\cdot 1471^{4} \)	20T1039	Trivial (GRH)
20.4.341095197764547393798828125.1	x^20 - 3x^19 - 7x^18 + 30x^17 - 4x^16 - 59x^15 + 55x^14 - 313x^13 + 892x^12 + 23x^11 - 2694x^10 + 2135x^9 + 3089x^8 - 4537x^7 - 1344x^6 + 4751x^5 - 623x^4 - 2729x^3 + 1015x^2 + 682x - 359	\( 5^{15}\cdot 97^{2}\cdot 1039^{2}\cdot 1049^{2} \)	20T1039	Trivial (GRH)
20.4.1520519664538880000000000000.1	x^20 + 2x^18 - 15x^16 - 26x^14 + 84x^12 + 165x^10 - 195x^8 - 575x^6 - 225x^4 + 250x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 1039^{2}\cdot 1049^{2} \)	20T1039	Trivial (GRH)
20.8.1520519664538880000000000000.1	x^20 - x^18 - 3x^16 - 9x^14 + 86x^12 - 160x^10 - 10x^8 - 700x^6 + 1350x^4 - 750x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 1039^{2}\cdot 1049^{2} \)	20T1039	Trivial (GRH)
20.4.1520519664538880000000000000.2	x^20 - 9x^18 + 20x^16 - 2x^14 - 91x^12 + 205x^10 - 365x^8 + 175x^6 + 375x^4 - 375x^2 + 125	\( 2^{20}\cdot 5^{13}\cdot 1039^{2}\cdot 1049^{2} \)	20T1039	Trivial (GRH)
20.4.1565392407210041309814453125.1	x^20 - 3x^19 + 3x^18 + 7x^17 - 59x^16 + 57x^15 + 80x^14 - 12x^13 + 261x^12 - 697x^11 - 343x^10 - 66x^9 + 425x^8 + 3217x^7 - 1369x^6 - 1504x^5 - 2086x^4 + 9x^3 + 2565x^2 - 450x + 89	\( 5^{13}\cdot 1039^{4}\cdot 1049^{2} \)	20T1039	Trivial (GRH)
20.4.2508817920032000000000000000.2	x^20 - 10x^16 - 50x^12 + 125x^10 + 1250x^8 - 3125x^6 - 5625x^4 + 3125	\( 2^{20}\cdot 5^{15}\cdot 280001^{2} \)	20T1039	Trivial (GRH)
20.4.2508817920032000000000000000.3	x^20 - 5x^18 + 25x^16 - 100x^14 - 50x^12 + 250x^10 + 1375x^8 - 1250x^6 - 3125x^4 - 3125x^2 + 3125	\( 2^{20}\cdot 5^{15}\cdot 280001^{2} \)	20T1039	Trivial (GRH)
20.4.188410691650467891200000000000.1	x^20 + 15x^18 + 96x^16 + 342x^14 + 741x^12 + 996x^10 + 792x^8 + 292x^6 - 29x^4 - 40x^2 + 5	\( 2^{20}\cdot 5^{11}\cdot 60662149^{2} \)	20T1039	Trivial (GRH)
20.8.217426936208300406768798828125.1	x^20 - 4x^19 - x^18 + 51x^17 - 182x^16 + 338x^15 - 414x^14 + 252x^13 + 401x^12 - 1448x^11 + 2059x^10 - 1763x^9 + 2525x^8 - 3465x^7 + 3209x^6 - 4624x^5 + 3745x^4 - 2041x^3 + 1307x^2 - 46x - 79	\( 5^{15}\cdot 97^{2}\cdot 27517559^{2} \)	20T1039	Trivial (GRH)
20.12.976144737494384627696533203125.1	x^20 - 4x^19 - 7x^18 + 13x^17 + 92x^16 - 30x^15 - 440x^14 + 117x^13 + 1004x^12 - 766x^11 - 1008x^10 + 2003x^9 - 186x^8 - 1124x^7 + 1591x^6 - 1264x^5 - 1927x^4 + 720x^3 + 607x^2 - 10x - 1	\( 5^{13}\cdot 97^{2}\cdot 419^{2}\cdot 695771^{2} \)	20T1039	Trivial (GRH)
20.8.14728777159439278684044189453125.1	x^20 - 5x^19 - 24x^18 + 94x^17 + 316x^16 - 527x^15 - 2449x^14 + 241x^13 + 8088x^12 + 1094x^11 - 4294x^10 + 30738x^9 + 13527x^8 - 70159x^7 - 81531x^6 + 172477x^5 + 311280x^4 - 349102x^3 - 259484x^2 + 366509x + 141791	\( 5^{13}\cdot 97^{2}\cdot 1039^{4}\cdot 1049^{2} \)	20T1039	Trivial (GRH)
20.0.15013659868612228667344970703125.1	x^20 - 3x^19 + 4x^18 - 4x^17 - 82x^16 - 72x^15 + 121x^14 + 1790x^13 + 5367x^12 + 19115x^11 + 56651x^10 + 113482x^9 + 217288x^8 + 331696x^7 + 452704x^6 + 634779x^5 + 824178x^4 + 1595619x^3 + 2792880x^2 + 3799228x + 3079229	\( 5^{13}\cdot 97^{2}\cdot 1039^{2}\cdot 1049^{4} \)	20T1039	Trivial (GRH)
20.0.15013659868612228667344970703125.2	x^20 - 2x^19 + 22x^18 - 27x^17 + 54x^16 + 58x^15 - 816x^14 + 2216x^13 - 3887x^12 + 1165x^11 + 21460x^10 - 82331x^9 + 243515x^8 - 209120x^7 - 69140x^6 + 1208576x^5 - 1135731x^4 + 359049x^3 + 3568744x^2 - 4233714x + 4326689	\( 5^{13}\cdot 97^{2}\cdot 1039^{2}\cdot 1049^{4} \)	20T1039	$[2]$ (GRH)
20.20.18213725822005703010206298828125.1	x^20 - x^19 - 35x^18 + 21x^17 + 470x^16 - 203x^15 - 3217x^14 + 1178x^13 + 12340x^12 - 4086x^11 - 27187x^10 + 7734x^9 + 33940x^8 - 7178x^7 - 22623x^6 + 2714x^5 + 7041x^4 - 340x^3 - 845x^2 + 25	\( 5^{13}\cdot 419^{4}\cdot 695771^{2} \)	20T1039	Trivial (GRH)
20.8.24403618437359615692413330078125.1	x^20 - x^19 - 26x^18 - 6x^17 + 216x^16 + 115x^15 - 760x^14 + 29x^13 + 1667x^12 + 883x^11 - 3171x^10 - 12637x^9 - 14173x^8 - 231x^7 + 18000x^6 + 29732x^5 + 21334x^4 + 2464x^3 - 9048x^2 - 11078x - 5429	\( 5^{15}\cdot 97^{2}\cdot 419^{2}\cdot 695771^{2} \)	20T1039	Trivial (GRH)
20.8.455343145550142575255157470703125.1	x^20 - 4x^19 - 3x^18 - 4x^17 - 50x^16 + 68x^15 + 412x^14 + 980x^13 + 3744x^12 + 6397x^11 + 13632x^10 + 29987x^9 + 22346x^8 + 43229x^7 + 91210x^6 + 20653x^5 + 12935x^4 + 111707x^3 + 57603x^2 - 10493x - 29	\( 5^{15}\cdot 419^{4}\cdot 695771^{2} \)	20T1039	$[2]$ (GRH)
20.12.171372946259251659623031065673828125.1	x^20 - 3x^19 - 30x^18 + 101x^17 + 159x^16 - 923x^15 + 1411x^14 - 755x^13 - 4153x^12 + 31035x^11 - 62649x^10 + 14499x^9 + 60948x^8 - 305712x^7 + 408264x^6 - 547740x^5 - 821616x^4 + 1875378x^3 + 406400x^2 - 366925x + 21731	\( 5^{13}\cdot 97^{2}\cdot 419^{4}\cdot 695771^{2} \)	20T1039	$[2]$ (GRH)
20.12.3197619919037143226174828028564453125.1	x^20 - 8x^19 + 20x^18 + 43x^17 - 637x^16 + 1823x^15 - 611x^14 + 11122x^13 - 21862x^12 - 436971x^11 + 1581758x^10 + 1374098x^9 - 13942971x^8 + 12201676x^7 + 41873506x^6 - 80519029x^5 - 23286812x^4 + 149491890x^3 - 68689262x^2 - 69482714x + 49341221	\( 5^{13}\cdot 419^{6}\cdot 695771^{2} \)	20T1039	Trivial (GRH)
20.8.3197619919037143226174828028564453125.1	x^20 + 20x^18 - 71x^17 - 497x^16 - 224x^15 - 6543x^14 + 22634x^13 + 13881x^12 + 84798x^11 + 214863x^10 - 1198093x^9 + 2844358x^8 - 5483095x^7 + 21372876x^6 - 24683413x^5 - 8610893x^4 + 19084901x^3 - 49913465x^2 + 45658124x - 11257231	\( 5^{13}\cdot 419^{6}\cdot 695771^{2} \)	20T1039	Trivial (GRH)
20.8.4284323656481291490575776641845703125.1	x^20 - 2x^19 - 7x^18 - 43x^17 - 29x^16 - 648x^15 - 640x^14 + 22872x^13 + 23645x^12 + 102939x^11 - 257213x^10 - 1369808x^9 + 1210580x^8 - 4911960x^7 + 9713821x^6 + 30158869x^5 - 47374562x^4 - 2328854x^3 + 2610644x^2 - 41632095x + 94715791	\( 5^{15}\cdot 97^{2}\cdot 419^{4}\cdot 695771^{2} \)	20T1039	$[2]$ (GRH)
20.4.4168598900368303957126361907200000000000000000000.1	x^20 - 5080x^12 - 17552x^10 + 840350x^4 + 4033680x^2 + 3764768	\( 2^{87}\cdot 5^{20}\cdot 7^{10} \)	20T1039	Trivial (GRH)
20.4.10008805959784297801060394939187200000000000000000000.1	x^20 - 10360x^12 - 36400x^10 + 840350x^4 + 4033680x^2 + 3764768	\( 2^{87}\cdot 5^{20}\cdot 7^{14} \)	20T1039	Trivial (GRH)