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 56)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.622079687467809991455078125.2	x^20 - x^19 + x^18 + 2x^17 - 8x^16 + 28x^15 - 4x^14 - 51x^13 + 128x^12 - 101x^11 + 101x^10 + 230x^9 - 620x^8 + 785x^7 + 269x^6 - 980x^5 + 955x^4 + 245x^3 - 135x^2 + 315x + 145	\( 5^{14}\cdot 269^{7} \)	20T796	Trivial (GRH)
20.0.672090982065037264479584256.1	x^20 - 9x^18 + 27x^16 - 9x^14 - 120x^12 + 288x^10 - 276x^8 - 159x^6 + 1065x^4 - 1338x^2 + 669	\( 2^{20}\cdot 3^{19}\cdot 223^{5} \)	20T796	Trivial (GRH)
20.0.672090982065037264479584256.2	x^20 - 18x^18 + 135x^16 - 534x^14 + 1152x^12 - 1245x^10 + 621x^8 - 828x^6 + 1722x^4 - 1338x^2 + 669	\( 2^{20}\cdot 3^{19}\cdot 223^{5} \)	20T796	Trivial (GRH)
20.0.9014494415033600000000000000.1	x^20 + 10x^18 + 35x^16 + 45x^14 + 20x^12 + 161x^10 + 400x^8 - 80x^6 - 310x^4 + 270x^2 + 269	\( 2^{20}\cdot 5^{14}\cdot 269^{5} \)	20T796	Trivial (GRH)
20.4.9014494415033600000000000000.1	x^20 - 9x^18 + 23x^16 + 4x^14 - 108x^12 + 146x^10 - 62x^8 - 181x^6 + 937x^4 - 689x^2 + 269	\( 2^{20}\cdot 5^{14}\cdot 269^{5} \)	20T796	Trivial (GRH)
20.4.9014494415033600000000000000.2	x^20 - 12x^18 + 66x^16 - 218x^14 + 437x^12 - 435x^10 + 32x^8 + 129x^6 + 403x^4 - 677x^2 + 269	\( 2^{20}\cdot 5^{14}\cdot 269^{5} \)	20T796	Trivial (GRH)
20.12.48619051277337287286376953125.1	x^20 - 15x^18 - 15x^17 + 94x^16 + 180x^15 - 263x^14 - 855x^13 + 121x^12 + 2040x^11 + 1025x^10 - 2480x^9 - 2535x^8 + 1150x^7 + 2309x^6 + 275x^5 - 673x^4 - 195x^3 + 51x^2 + 15x - 1	\( 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.8.48619051277337287286376953125.1	x^20 - 2x^19 + 27x^17 - 61x^16 + 41x^15 + 195x^14 - 522x^13 + 484x^12 + 401x^11 - 1595x^10 + 1728x^9 - 325x^8 - 1383x^7 + 1759x^6 - 989x^5 + 155x^4 + 48x^3 - 106x^2 - 24x - 1	\( 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.10.83510262074750967216189850187.1	x^20 - 5x^19 + 7x^18 - 2x^17 - 42x^16 + 307x^15 - 536x^14 - 501x^13 + 1645x^12 + 230x^11 - 687x^10 - 4221x^9 + 5682x^8 - 1785x^7 - 1628x^6 + 6629x^5 - 7057x^4 + 881x^3 + 1774x^2 - 684x + 53	\( -\,13^{10}\cdot 347^{7} \)	20T796	Trivial (GRH)
20.12.1215476281933432182159423828125.1	x^20 - 21x^18 - 14x^17 + 166x^16 + 224x^15 - 504x^14 - 1152x^13 - 480x^12 + 1459x^11 + 5985x^10 + 5146x^9 - 8287x^8 - 14875x^7 - 8496x^6 + 4504x^5 + 20746x^4 + 10984x^3 - 7016x^2 - 1452x + 181	\( 5^{16}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.8.1215476281933432182159423828125.1	x^20 - 4x^19 + 10x^18 + 11x^17 - 77x^16 + 205x^15 - 22x^14 - 581x^13 + 1350x^12 - 431x^11 - 2827x^10 + 3671x^9 - 428x^8 - 6778x^7 + 3448x^6 + 4645x^5 - 970x^4 - 551x^3 - 733x^2 - 215x + 251	\( 5^{16}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.2.14113234290632913459536084681603.1	x^20 - 5x^19 + 18x^18 - 20x^17 - 73x^16 + 625x^15 - 2261x^14 + 5613x^13 - 12106x^12 + 22404x^11 - 49524x^10 + 92168x^9 - 154411x^8 + 167166x^7 - 227470x^6 + 215582x^5 - 163122x^4 + 52247x^3 - 104799x^2 - 52719x - 12143	\( -\,13^{12}\cdot 347^{7} \)	20T796	$[2, 2]$ (GRH)
20.10.785748055861331850537130300409483.1	x^20 - 7x^19 + 6x^18 + 76x^17 - 310x^16 + 628x^15 - 1590x^14 - 4464x^13 + 48529x^12 - 44206x^11 - 148199x^10 + 118185x^9 - 541338x^8 + 1589249x^7 + 1429417x^6 - 4418610x^5 + 2876572x^4 - 4250894x^3 + 2270690x^2 - 308835x + 154547	\( -\,13^{10}\cdot 97^{2}\cdot 347^{7} \)	20T796	Trivial (GRH)
20.2.785748055861331850537130300409483.1	x^20 - 4x^19 + 33x^18 - 86x^17 + 274x^16 - 292x^15 - 1125x^14 + 4757x^13 - 27523x^12 + 36977x^11 - 116322x^10 - 99930x^9 + 354518x^8 - 2208621x^7 + 4299577x^6 - 8938579x^5 + 10789583x^4 - 11186429x^3 + 6073672x^2 - 500979x - 1444031	\( -\,13^{10}\cdot 97^{2}\cdot 347^{7} \)	20T796	Trivial (GRH)
20.6.785748055861331850537130300409483.1	x^20 - 6x^19 + 36x^18 - 113x^17 + 242x^16 + 173x^15 - 3651x^14 + 12031x^13 - 20751x^12 - 15033x^11 + 122424x^10 - 178945x^9 - 158699x^8 + 1093654x^7 - 1521385x^6 - 32234x^5 + 1545640x^4 - 2061817x^3 + 4345303x^2 - 3835220x + 729661	\( -\,13^{10}\cdot 97^{2}\cdot 347^{7} \)	20T796	Trivial (GRH)
20.6.785748055861331850537130300409483.2	x^20 - 9x^19 + 8x^18 + 218x^17 - 1287x^16 + 2647x^15 + 5893x^14 - 47747x^13 + 80856x^12 + 127471x^11 - 645738x^10 + 573446x^9 + 1056435x^8 - 2570439x^7 + 1152018x^6 + 1100891x^5 + 720336x^4 - 3458400x^3 - 176876x^2 + 5057872x - 3073379	\( -\,13^{10}\cdot 97^{2}\cdot 347^{7} \)	20T796	Trivial (GRH)
20.6.785748055861331850537130300409483.3	x^20 - 7x^19 + 15x^18 + 40x^17 - 214x^16 - 98x^15 + 1415x^14 - 490x^13 - 7101x^12 + 6806x^11 + 13020x^10 + 8727x^9 + 14292x^8 - 171479x^7 + 80199x^6 + 777200x^5 - 353620x^4 - 2059358x^3 - 1818712x^2 - 1209234x - 564811	\( -\,13^{10}\cdot 97^{2}\cdot 347^{7} \)	20T796	Trivial (GRH)
20.6.785748055861331850537130300409483.4	x^20 - 5x^19 - 9x^18 + 99x^17 - 266x^16 + 246x^15 + 1037x^14 - 6171x^13 + 12565x^12 - 4754x^11 - 36867x^10 + 81703x^9 - 75794x^8 - 57441x^7 - 94946x^6 + 601986x^5 - 1223688x^4 - 256048x^3 - 143581x^2 + 3058945x - 999623	\( -\,13^{10}\cdot 97^{2}\cdot 347^{7} \)	20T796	Trivial (GRH)
20.6.785748055861331850537130300409483.5	x^20 - 6x^19 + 5x^18 + 19x^17 - 49x^16 - 71x^15 - 546x^14 + 6146x^13 - 12271x^12 + 12828x^11 + 42877x^10 + 30308x^9 - 29854x^8 - 41335x^7 + 894721x^6 + 1040532x^5 + 303069x^4 - 864833x^3 - 1855645x^2 - 125280x - 47837	\( -\,13^{10}\cdot 97^{2}\cdot 347^{7} \)	20T796	Trivial (GRH)
20.6.785748055861331850537130300409483.6	x^20 - x^19 - x^18 + 14x^17 - 197x^16 - 119x^15 + 1395x^14 - 188x^13 - 165x^12 + 11695x^11 - 18629x^10 - 22238x^9 - 31665x^8 - 141925x^7 + 243060x^6 + 206790x^5 - 463938x^4 + 1292806x^3 + 1358059x^2 - 1792952x - 1237531	\( -\,13^{10}\cdot 97^{2}\cdot 347^{7} \)	20T796	Trivial (GRH)
20.12.50980770312185223353600000000000000.1	x^20 - 16x^18 + 12x^16 + 508x^14 - 1140x^12 - 4146x^10 + 12018x^8 + 2169x^6 - 17649x^4 + 2125x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.16.50980770312185223353600000000000000.1	x^20 - 42x^18 + 606x^16 - 3753x^14 + 9282x^12 + 1685x^10 - 44008x^8 + 46029x^6 + 30253x^4 - 45337x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.20.50980770312185223353600000000000000.1	x^20 - 50x^18 + 1039x^16 - 11588x^14 + 74646x^12 - 277800x^10 + 565705x^8 - 571621x^6 + 288157x^4 - 68639x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.4.50980770312185223353600000000000000.1	x^20 + 30x^18 + 224x^16 - 78x^14 - 6034x^12 - 20580x^10 - 19000x^8 + 21029x^6 + 51062x^4 + 31636x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.8.50980770312185223353600000000000000.1	x^20 + 20x^18 - 115x^16 - 4060x^14 - 21055x^12 + 4104x^10 + 179540x^8 + 39970x^6 - 447345x^4 + 165540x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.12.50980770312185223353600000000000000.2	x^20 - 33x^18 + 232x^16 + 586x^14 - 5297x^12 - 6325x^10 + 27773x^8 + 32103x^6 - 21966x^4 - 17058x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.16.50980770312185223353600000000000000.2	x^20 - 26x^18 + 150x^16 + 1180x^14 - 17532x^12 + 83681x^10 - 198783x^8 + 248260x^6 - 149215x^4 + 26254x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.20.50980770312185223353600000000000000.2	x^20 - 43x^18 + 756x^16 - 7147x^14 + 39982x^12 - 136710x^10 + 284442x^8 - 347809x^6 + 232878x^4 - 72348x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.4.50980770312185223353600000000000000.2	x^20 + 34x^18 + 319x^16 - 106x^14 - 12321x^12 - 34544x^10 + 34097x^8 + 197102x^6 + 209787x^4 + 74827x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.8.50980770312185223353600000000000000.2	x^20 + 15x^18 - 161x^16 - 2362x^14 - 5199x^12 + 14160x^10 + 37645x^8 - 27874x^6 - 48653x^4 - 2946x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.12.50980770312185223353600000000000000.3	x^20 - 20x^18 + 9x^16 + 1372x^14 - 3334x^12 - 23645x^10 + 61845x^8 + 64844x^6 - 109628x^4 - 36174x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.16.50980770312185223353600000000000000.3	x^20 - 29x^18 + 203x^16 + 364x^14 - 8933x^12 + 29746x^10 - 2902x^8 - 135171x^6 + 192397x^4 - 68654x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.4.50980770312185223353600000000000000.3	x^20 + 50x^18 + 945x^16 + 8440x^14 + 36175x^12 + 61089x^10 - 10420x^8 - 101145x^6 - 19700x^4 + 21585x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.8.50980770312185223353600000000000000.3	x^20 - 5x^18 - 276x^16 - 1338x^14 + 3611x^12 + 27960x^10 + 6015x^8 - 91126x^6 + 17662x^4 + 33596x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.12.50980770312185223353600000000000000.4	x^20 - 16x^18 - 96x^16 + 1956x^14 - 566x^12 - 45135x^10 + 105556x^8 + 3486x^6 - 102061x^4 - 6029x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.16.50980770312185223353600000000000000.4	x^20 - 21x^18 - 9x^16 + 3669x^14 - 39816x^12 + 190615x^10 - 444739x^8 + 431154x^6 - 48614x^4 - 35264x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.4.50980770312185223353600000000000000.4	x^20 + 26x^18 + 16x^16 - 2429x^14 - 8031x^12 + 39565x^10 + 229036x^8 + 370646x^6 + 245821x^4 + 66319x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.8.50980770312185223353600000000000000.4	x^20 - 5x^18 - 240x^16 - 970x^14 + 3460x^12 + 24564x^10 + 22395x^8 - 67490x^6 - 100745x^4 - 1570x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.12.50980770312185223353600000000000000.5	x^20 - 23x^18 + 134x^16 + 197x^14 - 2741x^12 + 3011x^10 + 10361x^8 - 16933x^6 - 8629x^4 + 14252x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.16.50980770312185223353600000000000000.5	x^20 - 18x^18 - 28x^16 + 2511x^14 - 20147x^12 + 69665x^10 - 122732x^8 + 109223x^6 - 36831x^4 - 7678x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.4.50980770312185223353600000000000000.5	x^20 + 38x^18 + 503x^16 + 2233x^14 - 5587x^12 - 69801x^10 - 126389x^8 + 135831x^6 + 354316x^4 + 89701x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.8.50980770312185223353600000000000000.5	x^20 - 16x^18 - 22x^16 + 986x^14 - 23x^12 - 16121x^10 - 23812x^8 + 21406x^6 + 60507x^4 + 36174x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.12.50980770312185223353600000000000000.6	x^20 + 13x^18 - 102x^16 - 1712x^14 - 2977x^12 + 16319x^10 + 7011x^8 - 65989x^6 + 77556x^4 - 36174x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.16.50980770312185223353600000000000000.6	x^20 - 24x^18 + 174x^16 + 34x^14 - 5676x^12 + 21615x^10 - 3359x^8 - 125086x^6 + 242159x^4 - 143206x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.4.50980770312185223353600000000000000.6	x^20 + 30x^18 + 319x^16 + 1284x^14 - 918x^12 - 24776x^10 - 83135x^8 - 122357x^6 - 77317x^4 - 8681x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.8.50980770312185223353600000000000000.6	x^20 + 16x^18 - 26x^16 - 1126x^14 - 1996x^12 + 8180x^10 + 17206x^8 - 10781x^6 - 24541x^4 + 6029x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	$[2]$ (GRH)
20.12.50980770312185223353600000000000000.7	x^20 - 19x^18 + 11x^16 + 1406x^14 - 5976x^12 - 5350x^10 + 34111x^8 - 1314x^6 - 31879x^4 + 1299x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.8.50980770312185223353600000000000000.7	x^20 + 9x^18 - 197x^16 - 1999x^14 + 4570x^12 + 67830x^10 + 16874x^8 - 605797x^6 - 800669x^4 + 60290x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.12.50980770312185223353600000000000000.8	x^20 - x^18 - 164x^16 + 249x^14 + 8439x^12 - 20030x^10 - 124489x^8 + 508854x^6 - 513694x^4 + 54261x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)
20.8.50980770312185223353600000000000000.8	x^20 + 10x^18 - 176x^16 - 1969x^14 + 767x^12 + 33926x^10 - 3000x^8 - 60538x^6 + 793x^4 + 24116x^2 + 6029	\( 2^{20}\cdot 5^{14}\cdot 6029^{5} \)	20T796	Trivial (GRH)