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 62)

Label	Polynomial	Discriminant	Galois group	Class group
16.8.12849417078227563094777.1	x^16 - 4x^15 - x^14 + 21x^13 + x^12 - 89x^11 - 69x^10 + 429x^9 + x^8 - 769x^7 + 237x^6 + 667x^5 + 69x^4 - 191x^3 - 69x^2 + 4x + 1	\( 17^{15}\cdot 67^{2} \)	16T1223	Trivial (GRH)
16.8.12849417078227563094777.2	x^16 - 3x^15 - 8x^14 + 7x^13 + 64x^12 - 22x^11 - 104x^10 + 6x^9 + 33x^8 - 48x^7 - 60x^6 - 24x^5 + 4x^4 + 39x^3 + 36x^2 + 11x + 1	\( 17^{15}\cdot 67^{2} \)	16T1223	Trivial (GRH)
16.12.187591757103747287810048.1	x^16 - 17x^14 + 102x^12 - 255x^10 + 221x^8 + 51x^6 - 136x^4 + 17x^2 + 17	\( 2^{16}\cdot 17^{15} \)	16T1223	Trivial (GRH)
16.4.187591757103747287810048.1	x^16 + 17x^14 + 85x^12 + 102x^10 - 153x^8 - 306x^6 + 136x^2 + 17	\( 2^{16}\cdot 17^{15} \)	16T1223	Trivial
16.8.187591757103747287810048.1	x^16 - 34x^12 + 68x^10 + 102x^8 - 238x^6 - 51x^4 + 68x^2 + 17	\( 2^{16}\cdot 17^{15} \)	16T1223	Trivial
16.12.187591757103747287810048.2	x^16 - 17x^14 + 85x^12 - 102x^10 - 153x^8 + 306x^6 - 136x^2 + 17	\( 2^{16}\cdot 17^{15} \)	16T1223	Trivial (GRH)
16.4.187591757103747287810048.2	x^16 + 17x^14 + 102x^12 + 255x^10 + 221x^8 - 51x^6 - 136x^4 - 17x^2 + 17	\( 2^{16}\cdot 17^{15} \)	16T1223	Trivial
16.8.187591757103747287810048.2	x^16 - 17x^12 + 85x^8 - 119x^4 - 34x^2 + 17	\( 2^{16}\cdot 17^{15} \)	16T1223	Trivial
16.12.57681033264163530732453953.1	x^16 - 6x^15 + 2x^14 + 5x^13 + 21x^12 + 588x^11 - 1148x^10 - 2666x^9 + 2396x^8 - 2068x^7 + 37704x^6 + 18372x^5 - 197765x^4 + 22600x^3 + 310514x^2 - 95169x - 110533	\( 17^{15}\cdot 67^{4} \)	16T1223	Trivial (GRH)
16.12.57681033264163530732453953.2	x^16 - 5x^15 - 26x^14 + 181x^13 - 72x^12 - 1068x^11 + 1549x^10 - 758x^9 + 3110x^8 + 2895x^7 - 17586x^6 + 2114x^5 + 8351x^4 + 7222x^3 + 15366x^2 - 11312x - 13633	\( 17^{15}\cdot 67^{4} \)	16T1223	Trivial (GRH)
16.4.57681033264163530732453953.5	x^16 - 3x^15 + 9x^14 + 7x^13 - 38x^12 + 199x^11 - 36x^10 + 397x^9 - 1905x^8 - 3584x^7 - 655x^6 - 5770x^5 + 29839x^4 - 14853x^3 + 48758x^2 - 39480x + 32743	\( 17^{15}\cdot 67^{4} \)	16T1223	$[2, 4]$ (GRH)
16.4.57681033264163530732453953.6	x^16 - 7x^15 + 32x^14 - 105x^13 + 106x^12 - 130x^11 - 1028x^10 + 3779x^9 - 7413x^8 + 17755x^7 - 18375x^6 + 15762x^5 - 18211x^4 - 10206x^3 + 18521x^2 + 31904x + 42127	\( 17^{15}\cdot 67^{4} \)	16T1223	$[2, 2]$ (GRH)
16.0.842099397638721574979305472.1	x^16 + 51x^14 + 1071x^12 + 12104x^10 + 79951x^8 + 310318x^6 + 661946x^4 + 624172x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	16T1223	$[2, 2, 2, 160]$ (GRH)
16.16.842099397638721574979305472.1	x^16 - 51x^14 + 1071x^12 - 12104x^10 + 79951x^8 - 310318x^6 + 661946x^4 - 624172x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	16T1223	Trivial (GRH)
16.0.842099397638721574979305472.2	x^16 + 51x^14 + 986x^12 + 9486x^10 + 49980x^8 + 148869x^6 + 248608x^4 + 216410x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	16T1223	$[2, 2, 2, 132]$ (GRH)
16.16.842099397638721574979305472.2	x^16 - 51x^14 + 986x^12 - 9486x^10 + 49980x^8 - 148869x^6 + 248608x^4 - 216410x^2 + 76313	\( 2^{16}\cdot 17^{15}\cdot 67^{2} \)	16T1223	Trivial (GRH)
16.12.1990160951113654976376799232.1	x^16 - 17x^14 - 374x^12 + 4811x^10 + 24599x^8 - 358819x^6 + 866694x^4 - 709155x^2 + 180353	\( 2^{16}\cdot 17^{15}\cdot 103^{2} \)	16T1223	Trivial (GRH)
16.4.1990160951113654976376799232.1	x^16 + 34x^14 + 238x^12 - 3332x^10 - 52088x^8 - 196180x^6 - 11747x^4 + 749428x^2 + 180353	\( 2^{16}\cdot 17^{15}\cdot 103^{2} \)	16T1223	$[2, 2]$ (GRH)
16.8.1990160951113654976376799232.1	x^16 - 306x^12 + 1156x^10 + 10251x^8 - 31824x^6 - 99603x^4 + 194361x^2 + 180353	\( 2^{16}\cdot 17^{15}\cdot 103^{2} \)	16T1223	$[2]$ (GRH)
16.12.1990160951113654976376799232.2	x^16 - 34x^14 + 238x^12 + 3332x^10 - 52088x^8 + 196180x^6 - 11747x^4 - 749428x^2 + 180353	\( 2^{16}\cdot 17^{15}\cdot 103^{2} \)	16T1223	Trivial (GRH)
16.4.1990160951113654976376799232.2	x^16 + 34x^14 + 357x^12 + 374x^10 - 14501x^8 - 66538x^6 + 31977x^4 + 465766x^2 + 180353	\( 2^{16}\cdot 17^{15}\cdot 103^{2} \)	16T1223	$[2, 2]$ (GRH)
16.8.1990160951113654976376799232.2	x^16 + 34x^14 + 85x^12 - 2125x^10 - 3196x^8 + 39899x^6 - 21471x^4 - 152337x^2 + 180353	\( 2^{16}\cdot 17^{15}\cdot 103^{2} \)	16T1223	Trivial (GRH)
16.8.1990160951113654976376799232.3	x^16 - 17x^14 - 272x^12 + 3927x^10 + 21947x^8 - 179979x^6 - 147594x^4 + 520047x^2 + 180353	\( 2^{16}\cdot 17^{15}\cdot 103^{2} \)	16T1223	$[2]$ (GRH)
16.8.1990160951113654976376799232.4	x^16 - 17x^14 - 119x^12 + 2363x^10 + 2006x^8 - 68629x^6 - 11985x^4 + 527051x^2 + 180353	\( 2^{16}\cdot 17^{15}\cdot 103^{2} \)	16T1223	Trivial (GRH)
16.0.5687391518377022952405204992.1	x^16 - 16x^14 + 64x^12 + 128x^10 - 1048x^8 - 1088x^6 + 11424x^4 + 75272	\( 2^{79}\cdot 97^{2} \)	16T1223	Trivial (GRH)
16.0.5687391518377022952405204992.2	x^16 + 24x^12 - 432x^10 + 516x^8 - 6176x^6 + 63264x^4 - 27936x^2 + 18818	\( 2^{79}\cdot 97^{2} \)	16T1223	Trivial (GRH)
16.8.31236842166910780816202985728.1	x^16 - 5x^15 + 8x^14 - 91x^13 - 242x^12 + 768x^11 - 3636x^10 + 14151x^9 + 65279x^8 - 3888x^7 + 258154x^6 - 85776x^5 - 3147512x^4 - 3724040x^3 - 6494240x^2 - 14923984x - 7366864	\( 2^{8}\cdot 17^{15}\cdot 6529^{2} \)	16T1223	$[2]$ (GRH)
16.8.31236842166910780816202985728.2	x^16 - 3x^15 - 8x^14 + 58x^13 - 514x^12 + 1270x^11 - 325x^10 - 4635x^9 + 65772x^8 - 166563x^7 - 166320x^6 + 1031825x^5 - 130335x^4 - 2529391x^3 - 4525330x^2 + 8481940x + 4029307	\( 2^{8}\cdot 17^{15}\cdot 6529^{2} \)	16T1223	$[2]$ (GRH)
16.8.258930158322830089457985795017.8	x^16 - 6x^15 + 19x^14 - 80x^13 - 1169x^12 + 1642x^11 + 6995x^10 + 44662x^9 + 256954x^8 + 526530x^7 + 1144659x^6 + 1017904x^5 - 478367x^4 - 1128470x^3 - 16468792x^2 - 5820344x + 22064131	\( 17^{15}\cdot 67^{6} \)	16T1223	$[2, 2]$ (GRH)
16.8.258930158322830089457985795017.9	x^16 - 2x^15 - 13x^14 + 9x^13 - 817x^12 + 461x^11 + 5657x^10 + 17212x^9 + 235026x^8 + 272440x^7 - 255115x^6 - 7489970x^5 - 22529999x^4 - 33994711x^3 - 28965335x^2 + 34884977x + 27895267	\( 17^{15}\cdot 67^{6} \)	16T1223	$[2, 4]$ (GRH)
16.12.330335765244944607776060014592.1	x^16 - 34x^14 - 629x^12 + 36788x^10 - 438872x^8 + 1065322x^6 + 6336206x^4 - 28920638x^2 + 29935793	\( 2^{16}\cdot 17^{15}\cdot 1327^{2} \)	16T1223	Trivial (GRH)
16.4.330335765244944607776060014592.1	x^16 - 1683x^12 - 34408x^10 - 188122x^8 + 509150x^6 + 8293467x^4 + 27567098x^2 + 29935793	\( 2^{16}\cdot 17^{15}\cdot 1327^{2} \)	16T1223	$[2, 2]$ (GRH)
16.8.330335765244944607776060014592.1	x^16 + 17x^14 - 663x^12 - 6443x^10 + 163166x^8 + 419169x^6 - 14410713x^4 + 40944585x^2 + 29935793	\( 2^{16}\cdot 17^{15}\cdot 1327^{2} \)	16T1223	$[2, 2]$ (GRH)
16.12.330335765244944607776060014592.2	x^16 - 51x^14 + 544x^12 + 8568x^10 - 179197x^8 + 591158x^6 + 4162654x^4 - 25333757x^2 + 29935793	\( 2^{16}\cdot 17^{15}\cdot 1327^{2} \)	16T1223	Trivial (GRH)
16.4.330335765244944607776060014592.2	x^16 + 51x^14 + 544x^12 - 8568x^10 - 179197x^8 - 591158x^6 + 4162654x^4 + 25333757x^2 + 29935793	\( 2^{16}\cdot 17^{15}\cdot 1327^{2} \)	16T1223	$[2, 4]$ (GRH)
16.8.330335765244944607776060014592.2	x^16 - 578x^12 + 1088x^10 + 95183x^8 - 387056x^6 - 3813202x^4 + 15159648x^2 + 29935793	\( 2^{16}\cdot 17^{15}\cdot 1327^{2} \)	16T1223	Trivial (GRH)
16.8.330335765244944607776060014592.3	x^16 - 578x^12 - 1088x^10 + 95183x^8 + 387056x^6 - 3813202x^4 - 15159648x^2 + 29935793	\( 2^{16}\cdot 17^{15}\cdot 1327^{2} \)	16T1223	$[2]$ (GRH)
16.8.330335765244944607776060014592.4	x^16 + 34x^14 - 1071x^12 - 2856x^10 + 128146x^8 + 191318x^6 - 4900420x^4 - 9565016x^2 + 29935793	\( 2^{16}\cdot 17^{15}\cdot 1327^{2} \)	16T1223	Trivial (GRH)
16.12.2356327674777993305467029827040553.1	x^16 - 6x^15 - 68x^14 + 410x^13 + 1313x^12 - 11454x^11 + 5874x^10 + 186897x^9 - 398494x^8 - 1609224x^7 + 4265765x^6 + 4925652x^5 - 20020144x^4 + 8333545x^3 + 38229184x^2 - 43213225x + 9590257	\( 61^{2}\cdot 97^{15} \)	16T1223	$[2]$ (GRH)
16.8.2356327674777993305467029827040553.3	x^16 - 7x^15 + 26x^14 + 149x^13 - 1244x^12 + 860x^11 + 3461x^10 - 11172x^9 + 47818x^8 - 144545x^7 + 224890x^6 - 376128x^5 + 1214523x^4 - 876464x^3 - 1124560x^2 + 313014x + 119309	\( 61^{2}\cdot 97^{15} \)	16T1223	$[2]$ (GRH)
16.4.8767895277848913089642817986417897713.4	x^16 - x^15 - 45x^14 + x^13 - 1290x^12 + 1891x^11 + 18570x^10 - 10925x^9 + 1273077x^8 + 2235206x^7 + 9623711x^6 + 16338438x^5 + 250869331x^4 + 134079573x^3 + 956191714x^2 + 725765798x + 9255611219	\( 61^{4}\cdot 97^{15} \)	16T1223	$[2, 4]$ (GRH)
16.8.8767895277848913089642817986417897713.4	x^16 - 6x^15 - 68x^14 + 507x^13 - 1597x^12 - 7768x^11 + 50397x^10 - 78689x^9 + 2148726x^8 - 3895029x^7 + 12299693x^6 - 42398902x^5 - 45938641x^4 + 50586939x^3 - 125389252x^2 - 9553740x + 85935077	\( 61^{4}\cdot 97^{15} \)	16T1223	$[2]$ (GRH)
16.4.8767895277848913089642817986417897713.5	x^16 - 6x^15 + 126x^14 - 1045x^13 + 6648x^12 - 16304x^11 - 128956x^10 + 416011x^9 - 557186x^8 + 3674172x^7 - 55725340x^6 + 495788623x^5 - 1308728873x^4 + 1495727762x^3 + 2585237336x^2 - 7816045840x + 9682157008	\( 61^{4}\cdot 97^{15} \)	16T1223	$[2, 4]$ (GRH)
16.8.8767895277848913089642817986417897713.6	x^16 - 4x^15 + 56x^14 - 518x^13 - 2574x^12 - 5750x^11 - 114969x^10 + 325596x^9 + 111047x^8 - 1411152x^7 + 22961073x^6 - 18436972x^5 + 104056579x^4 - 54294058x^3 - 612399080x^2 + 499997728x + 186691984	\( 61^{4}\cdot 97^{15} \)	16T1223	$[4]$ (GRH)
16.12.1274602568003244304847660149105336749401.1	x^16 - 5x^15 - 233x^14 + 1346x^13 + 18632x^12 - 140131x^11 - 678393x^10 + 7483195x^9 + 16528758x^8 - 200346915x^7 - 387385807x^6 + 2180463570x^5 + 5102097565x^4 - 2559956558x^3 - 10822844427x^2 - 5205126238x + 20892667	\( 31^{10}\cdot 41^{15} \)	16T1223	Trivial (GRH)
16.8.1274602568003244304847660149105336749401.1	x^16 - 4x^15 - 54x^14 + 104x^13 - 2893x^12 + 34380x^11 - 39845x^10 - 133478x^9 + 1972610x^8 - 21748618x^7 + 76888174x^6 - 263187800x^5 + 548662862x^4 - 199051862x^3 + 2355411513x^2 + 388958406x - 1486289473	\( 31^{10}\cdot 41^{15} \)	16T1223	$[2]$ (GRH)
16.12.1274602568003244304847660149105336749401.2	x^16 - 6x^15 + 63x^14 - 100x^13 - 5859x^12 + 30525x^11 - 35277x^10 - 472409x^9 + 5199015x^8 - 6540911x^7 - 64725915x^6 + 118654269x^5 + 202450036x^4 - 244482346x^3 - 286455995x^2 + 18504933x + 26094979	\( 31^{10}\cdot 41^{15} \)	16T1223	Trivial (GRH)
16.4.1274602568003244304847660149105336749401.2	x^16 - 6x^15 + 104x^14 - 510x^13 - 611x^12 - 7359x^11 - 242491x^10 + 222254x^9 - 4451483x^8 + 15418771x^7 - 50674969x^6 + 19815774x^5 - 8721981x^4 + 576210513x^3 - 2009102852x^2 + 1790386599x - 209580401	\( 31^{10}\cdot 41^{15} \)	16T1223	$[2, 6]$ (GRH)
16.8.1274602568003244304847660149105336749401.2	x^16 - x^15 - 234x^14 - 475x^13 + 22314x^12 + 94770x^11 - 1157237x^10 - 5440409x^9 + 27762331x^8 + 177151636x^7 - 416803896x^6 - 2264266519x^5 + 3143223321x^4 + 4277390699x^3 - 10350960621x^2 + 35090087210x + 118357793	\( 31^{10}\cdot 41^{15} \)	16T1223	$[2]$ (GRH)
16.8.1274602568003244304847660149105336749401.3	x^16 - 2x^15 + 7x^14 - 69x^13 - 2054x^12 + 7086x^11 - 25901x^10 + 173122x^9 + 421736x^8 - 3978878x^7 + 23881913x^6 - 69734673x^5 + 259011770x^4 - 719804582x^3 - 1870281267x^2 + 1118219916x + 1688997251	\( 31^{10}\cdot 41^{15} \)	16T1223	$[2]$ (GRH)