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 44 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.10.10672332302001983204197.1	x^18 - 6x^17 + 7x^16 + 21x^15 - 49x^14 - 5x^13 + 87x^12 - 97x^11 + 63x^10 + 116x^9 - 329x^8 + 93x^7 + 293x^6 - 176x^5 - 84x^4 + 59x^3 + 12x^2 - 6x - 1	\( 19^{16}\cdot 37 \)	18T460	Trivial
18.6.32593879733141191947953.1	x^18 - 7x^17 + 16x^16 - 11x^15 - 15x^14 + 42x^13 - 42x^12 + 16x^11 + 12x^10 - 23x^9 + 12x^8 + 16x^7 - 42x^6 + 42x^5 - 15x^4 - 11x^3 + 16x^2 - 7x + 1	\( 19^{16}\cdot 113 \)	18T460	Trivial
18.8.43554653448710796319831.1	x^18 - 2x^17 - 5x^16 + 8x^15 + 7x^14 - 14x^13 - x^12 - x^11 + 23x^10 + 34x^9 - 64x^8 - 9x^7 + 11x^6 - 13x^5 + 48x^4 - 20x^3 - 10x^2 + 7x - 1	\( -\,19^{16}\cdot 151 \)	18T460	Trivial
18.8.55092309991415643027071.1	x^18 - 2x^17 - 4x^16 + 21x^15 - 42x^14 + 47x^13 - 17x^12 - 45x^11 + 110x^10 - 137x^9 + 110x^8 - 45x^7 - 17x^6 + 47x^5 - 42x^4 + 21x^3 - 4x^2 - 2x + 1	\( -\,19^{16}\cdot 191 \)	18T460	Trivial
18.4.6904998999395283133115459.1	x^18 - 9x^17 + 53x^16 - 220x^15 + 722x^14 - 1918x^13 + 4249x^12 - 7918x^11 + 12511x^10 - 16762x^9 + 18979x^8 - 18008x^7 + 14106x^6 - 8921x^5 + 4389x^4 - 1584x^3 + 375x^2 - 45x + 1	\( -\,19^{16}\cdot 37\cdot 647 \)	18T460	Trivial
18.14.14610422921440715006545693.1	x^18 - 5x^17 - 2x^16 + 33x^15 + 15x^14 - 104x^13 - 297x^12 + 691x^11 + 676x^10 - 2335x^9 + 1040x^8 + 1412x^7 - 1939x^6 + 962x^5 + 320x^4 - 738x^3 + 262x^2 + 8x - 1	\( 19^{16}\cdot 37^{3} \)	18T460	Trivial (GRH)
18.2.14610422921440715006545693.1	x^18 - 2x^17 + 2x^16 - 15x^15 + 31x^14 - 27x^13 + 57x^12 - 70x^11 - 13x^10 + 74x^9 - 370x^8 + 612x^7 - 684x^6 + 1071x^5 - 1148x^4 + 1581x^3 - 1580x^2 + 898x - 647	\( 19^{16}\cdot 37^{3} \)	18T460	$[2]$
18.10.14610422921440715006545693.3	x^18 - 2x^17 - 9x^16 + 32x^15 + 5x^14 - 140x^13 + 154x^12 + 102x^11 - 378x^10 + 418x^9 - 92x^8 - 635x^7 + 705x^6 + 303x^5 - 307x^4 + 13x^3 + 34x^2 - 14x + 1	\( 19^{16}\cdot 37^{3} \)	18T460	Trivial
18.6.14610422921440715006545693.3	x^18 - 7x^17 + 22x^16 - 23x^15 - 64x^14 + 338x^13 - 776x^12 + 1199x^11 - 1401x^10 + 1351x^9 - 1081x^8 + 584x^7 + 35x^6 - 424x^5 + 391x^4 - 213x^3 + 81x^2 - 11x - 1	\( 19^{16}\cdot 37^{3} \)	18T460	Trivial
18.10.14610422921440715006545693.4	x^18 - 9x^17 + 41x^16 - 124x^15 + 237x^14 - 203x^13 - 214x^12 + 933x^11 - 1341x^10 + 798x^9 + 433x^8 - 1301x^7 + 1181x^6 - 496x^5 + 11x^4 + 80x^3 - 26x^2 - x + 1	\( 19^{16}\cdot 37^{3} \)	18T460	Trivial
18.10.14610422921440715006545693.5	x^18 - 3x^17 - 4x^16 + 14x^15 - 16x^14 + 82x^13 - 73x^12 - 194x^11 + 161x^10 + 103x^9 - 27x^8 + 211x^7 - 309x^6 + 372x^5 - 672x^4 + 79x^3 + 312x^2 - 37x - 37	\( 19^{16}\cdot 37^{3} \)	18T460	Trivial
18.8.24782597812316443105983839.1	x^18 - 9x^17 + 44x^16 - 148x^15 + 370x^14 - 714x^13 + 1071x^12 - 1226x^11 + 1003x^10 - 450x^9 - 126x^8 + 404x^7 - 324x^6 + 97x^5 + 40x^4 - 48x^3 + 12x^2 + 3x - 1	\( -\,19^{16}\cdot 151\cdot 569 \)	18T460	Trivial (GRH)
18.16.75613185918270483380568064.1	x^18 - 14x^16 + 66x^14 - 134x^12 + 91x^10 + 78x^8 - 159x^6 + 87x^4 - 18x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T460	Trivial (GRH)
18.4.75613185918270483380568064.2	x^18 + 9x^16 + 17x^14 - 49x^12 - 178x^10 - 83x^8 + 160x^6 + 131x^4 + 28x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T460	Trivial
18.8.75613185918270483380568064.3	x^18 + 4x^16 - 14x^14 - 49x^12 + 37x^10 + 160x^8 + 65x^6 - 41x^4 - 13x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T460	Trivial
18.12.75613185918270483380568064.4	x^18 - 8x^16 + x^14 + 69x^12 - 54x^10 - 123x^8 + 151x^6 - 34x^4 - 3x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T460	Trivial (GRH)
18.8.75613185918270483380568064.4	x^18 + 5x^16 - 10x^14 - 58x^12 - 4x^10 + 116x^8 + 50x^6 - 46x^4 - 18x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T460	Trivial (GRH)
18.12.75613185918270483380568064.5	x^18 - 14x^16 + 66x^14 - 115x^12 - 4x^10 + 211x^8 - 159x^6 - 27x^4 + 39x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T460	Trivial (GRH)
18.8.75613185918270483380568064.5	x^18 + 4x^16 - 14x^14 - 49x^12 + 56x^10 + 103x^8 - 49x^6 - 22x^4 + 6x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T460	Trivial (GRH)
18.8.75613185918270483380568064.6	x^18 + 6x^16 - 3x^14 - 68x^12 - 68x^10 + 151x^8 + 198x^6 - 33x^4 - 34x^2 + 1	\( -\,2^{18}\cdot 19^{16} \)	18T460	Trivial
18.14.138500625111351088464218089.1	x^18 - 9x^17 + 26x^16 - 4x^15 - 118x^14 + 182x^13 + 91x^12 - 442x^11 + 247x^10 + 338x^9 - 494x^8 + 52x^7 + 300x^6 - 179x^5 - 42x^4 + 72x^3 - 12x^2 - 9x + 1	\( 19^{16}\cdot 480169 \)	18T460	Trivial (GRH)
18.16.258151783382020583032356864.1	x^18 - 9x^16 + 9x^14 + 96x^12 - 333x^10 + 450x^8 - 306x^6 + 108x^4 - 18x^2 + 1	\( -\,2^{18}\cdot 3^{44} \)	18T460	Trivial (GRH)
18.2.342520060884797108186970777.1	x^18 - 9x^17 + 54x^16 - 228x^15 + 765x^14 - 2079x^13 + 4725x^12 - 9045x^11 + 14715x^10 - 20335x^9 + 23805x^8 - 23409x^7 + 19059x^6 - 12573x^5 + 6480x^4 - 2466x^3 + 621x^2 - 81x + 1	\( 3^{45}\cdot 269\cdot 431 \)	18T460	$[10]$
18.10.416191250312479879983411857.1	x^18 - 3x^17 - 12x^16 + 67x^15 - 78x^14 - 268x^13 + 818x^12 - 404x^11 - 919x^10 + 1400x^9 - 167x^8 - 750x^7 - 425x^6 + 201x^5 + 713x^4 - 61x^3 - 253x^2 - 10x + 37	\( 19^{16}\cdot 113^{3} \)	18T460	Trivial (GRH)
18.6.419572475355251585492511741.1	x^18 - 9x^17 + 45x^16 - 156x^15 + 405x^14 - 819x^13 + 1302x^12 - 1611x^11 + 1485x^10 - 880x^9 + 99x^8 + 423x^7 - 474x^6 + 225x^5 - 63x^3 + 27x^2 - 3	\( 3^{44}\cdot 426061 \)	18T460	Trivial
18.10.774455350146061749097070592.1	x^18 - 18x^14 + 3x^12 + 72x^10 - 27x^8 - 81x^6 + 54x^4 - 3	\( 2^{18}\cdot 3^{45} \)	18T460	Trivial (GRH)
18.0.2797687878976007885081018368.1	x^18 + 21x^16 + 177x^14 + 780x^12 + 1970x^10 + 2950x^8 + 2615x^6 + 1323x^4 + 349x^2 + 37	\( -\,2^{18}\cdot 19^{16}\cdot 37 \)	18T460	$[50]$ (GRH)
18.10.2797687878976007885081018368.1	x^18 - 15x^16 + 62x^14 - 11x^12 - 286x^10 + 122x^8 + 369x^6 - 22x^4 - 146x^2 - 37	\( 2^{18}\cdot 19^{16}\cdot 37 \)	18T460	Trivial (GRH)
18.18.2797687878976007885081018368.1	x^18 - 21x^16 + 177x^14 - 780x^12 + 1970x^10 - 2950x^8 + 2615x^6 - 1323x^4 + 349x^2 - 37	\( 2^{18}\cdot 19^{16}\cdot 37 \)	18T460	Trivial (GRH)
18.6.2797687878976007885081018368.1	x^18 + 4x^16 - 14x^14 - 87x^12 - 96x^10 + 103x^8 + 217x^6 + 35x^4 - 89x^2 - 37	\( 2^{18}\cdot 19^{16}\cdot 37 \)	18T460	Trivial (GRH)
18.6.2797687878976007885081018368.2	x^18 + x^16 - 46x^14 - 159x^12 - 55x^10 + 300x^8 + 265x^6 - 86x^4 - 147x^2 - 37	\( 2^{18}\cdot 19^{16}\cdot 37 \)	18T460	Trivial (GRH)
18.18.16656540065306762851345570381.1	x^18 - 9x^17 + 17x^16 + 68x^15 - 254x^14 - 126x^13 + 1281x^12 - 302x^11 - 3449x^10 + 1614x^9 + 5643x^8 - 2584x^7 - 5814x^6 + 1615x^5 + 3553x^4 - 969x^2 - 285x - 19	\( 19^{16}\cdot 229\cdot 252169 \)	18T460	Trivial (GRH)
18.0.102359054154765255044328108199.1	x^18 - 9x^17 + 62x^16 - 292x^15 + 1146x^14 - 3626x^13 + 9891x^12 - 22842x^11 + 46111x^10 - 80086x^9 + 121818x^8 - 159244x^7 + 180716x^6 - 173115x^5 + 140578x^4 - 91800x^3 + 48036x^2 - 17345x + 4181	\( -\,19^{17}\cdot 37\cdot 151\cdot 3343 \)	18T460	$[2, 2, 76]$ (GRH)
18.12.103514451522112291747997679616.1	x^18 - 31x^16 + 349x^14 - 1679x^12 + 2503x^10 + 4896x^8 - 15410x^6 + 4376x^4 + 7807x^2 + 1369	\( -\,2^{18}\cdot 19^{16}\cdot 37^{2} \)	18T460	Trivial (GRH)
18.4.103514451522112291747997679616.1	x^18 + 26x^16 + 197x^14 + 373x^12 - 1183x^10 - 4433x^8 - 1920x^6 + 5459x^4 + 5698x^2 + 1369	\( -\,2^{18}\cdot 19^{16}\cdot 37^{2} \)	18T460	Trivial (GRH)
18.8.103514451522112291747997679616.1	x^18 - 10x^16 - 97x^14 + 236x^12 + 1855x^10 - 957x^8 - 7630x^6 + 891x^4 + 8103x^2 + 1369	\( -\,2^{18}\cdot 19^{16}\cdot 37^{2} \)	18T460	Trivial (GRH)
18.12.103514451522112291747997679616.2	x^18 - 13x^16 + 16x^14 + 255x^12 - 581x^10 - 894x^8 + 2592x^6 + 252x^4 - 2960x^2 + 1369	\( -\,2^{18}\cdot 19^{16}\cdot 37^{2} \)	18T460	Trivial (GRH)
18.4.103514451522112291747997679616.2	x^18 + 16x^16 + 42x^14 - 229x^12 - 1282x^10 - 1517x^8 + 2387x^6 + 7316x^4 + 5920x^2 + 1369	\( -\,2^{18}\cdot 19^{16}\cdot 37^{2} \)	18T460	$[2]$ (GRH)
18.12.103514451522112291747997679616.3	x^18 - 29x^16 + 264x^14 - 657x^12 - 1964x^10 + 9740x^8 - 5483x^6 - 9464x^4 + 5994x^2 + 1369	\( -\,2^{18}\cdot 19^{16}\cdot 37^{2} \)	18T460	Trivial (GRH)
18.12.103514451522112291747997679616.4	x^18 - 22x^16 + 118x^14 + 265x^12 - 3923x^10 + 10738x^8 - 8576x^6 - 3723x^4 + 4514x^2 + 1369	\( -\,2^{18}\cdot 19^{16}\cdot 37^{2} \)	18T460	Trivial (GRH)
18.10.3830034706318154794675914145792.1	x^18 + 7x^16 - 221x^14 - 2401x^12 - 2190x^10 + 29064x^8 + 6003x^6 - 133089x^4 + 153328x^2 - 50653	\( 2^{18}\cdot 19^{16}\cdot 37^{3} \)	18T460	Trivial (GRH)
18.14.3830034706318154794675914145792.1	x^18 - 34x^16 + 290x^14 + 1129x^12 - 24549x^10 + 99948x^8 - 140877x^6 + 9250x^4 + 112258x^2 - 50653	\( 2^{18}\cdot 19^{16}\cdot 37^{3} \)	18T460	Trivial (GRH)
18.6.3830034706318154794675914145792.1	x^18 + 9x^16 - 97x^14 - 1645x^12 - 8120x^10 - 13896x^8 + 10648x^6 + 52799x^4 + 12321x^2 - 50653	\( 2^{18}\cdot 19^{16}\cdot 37^{3} \)	18T460	$[6]$ (GRH)
18.14.3830034706318154794675914145792.2	x^18 - 40x^16 + 595x^14 - 3953x^12 + 10140x^10 + 4441x^8 - 58622x^6 + 59496x^4 + 35594x^2 - 50653	\( 2^{18}\cdot 19^{16}\cdot 37^{3} \)	18T460	Trivial (GRH)