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 419)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.9095120158391.1	x^14 - 7x^13 + 25x^12 - 59x^11 + 103x^10 - 141x^9 + 159x^8 - 153x^7 + 129x^6 - 95x^5 + 58x^4 - 27x^3 + 10x^2 - 3x + 1	\( -\,71^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.1789940649848551.1	x^14 - 4x^13 + 6x^12 - 2x^11 - 9x^10 + 19x^9 - 16x^8 - 5x^7 + 25x^6 - 22x^5 + 41x^4 - 60x^3 + 23x^2 + 3x + 9	\( -\,151^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.11398895185373143.1	x^14 - 7x^13 + 21x^12 - 35x^11 + 42x^10 - 56x^9 + 77x^8 - 71x^7 + 49x^6 - 49x^5 + 35x^4 + 14x^2 - 21x + 9	\( -\,7^{19} \)	$D_{7}$ (as 14T2)	Trivial
14.0.21235828992734375.1	x^14 - 2x^13 - 5x^12 + 12x^11 - 10x^10 - 7x^9 + 55x^8 - 28x^7 + 65x^6 - 2x^5 + 106x^4 - 70x^3 + 50x^2 + 25x + 25	\( -\,5^{7}\cdot 43^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.27424204663190047.1	x^14 - 2x^13 - x^12 + 16x^11 - 21x^10 - 7x^9 + 55x^8 - 46x^7 + 6x^6 - 23x^5 + 110x^4 - 134x^3 + 55x^2 - 9x + 9	\( -\,223^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.62764785704439251.1	x^14 - 4x^13 + 2x^12 + 28x^11 - 74x^10 + 22x^9 + 190x^8 - 326x^7 + 154x^6 + 148x^5 - 198x^4 + 42x^3 + 81x^2 - 6x + 4	\( -\,251^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.160388518974780383.1	x^14 - 6x^13 + 25x^12 - 68x^11 + 149x^10 - 219x^9 + 279x^8 - 193x^7 + 254x^6 + 10x^5 + 158x^4 + 341x^3 + 334x^2 + 135x + 25	\( -\,7^{7}\cdot 41^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.1397131555718611831.1	x^14 - 2x^13 - 7x^12 + 15x^11 + 28x^10 - 76x^9 - 28x^8 + 78x^7 - 136x^6 + 188x^5 + 421x^4 + 342x^3 + 995x^2 + 391x + 391	\( -\,17^{7}\cdot 23^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.1756586560892125184.1	x^14 - 4x^13 + 10x^12 - 14x^11 + 54x^10 - 66x^9 + 68x^8 + 134x^7 + 369x^6 - 90x^5 + 194x^4 - 56x^3 + 264x^2 + 96x + 64	\( -\,2^{14}\cdot 101^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.2762745569510280911.1	x^14 + 6x^12 + 65x^10 + 50x^8 + 430x^6 + 575x^4 + 895x^2 + 431	\( -\,431^{7} \)	$D_{7}$ (as 14T2)	$[3]$
14.0.3565764541089561663.1	x^14 - 4x^13 + 4x^12 - 5x^11 + 26x^10 - 14x^9 + 55x^8 - 379x^7 + 1252x^6 - 2247x^5 + 2859x^4 - 2493x^3 + 1674x^2 - 729x + 729	\( -\,3^{7}\cdot 149^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.4561072096211304367.1	x^14 - 4x^13 + 4x^12 - 5x^11 + 10x^10 + 57x^9 - 30x^8 - 429x^7 + 173x^6 + 1021x^5 + 107x^4 - 1546x^3 - 373x^2 + 798x + 441	\( -\,463^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.4844156483581198523.1	x^14 - 2x^13 + 3x^12 - 26x^11 + 34x^10 - 32x^9 + 155x^8 - 114x^7 + 1066x^6 - 736x^5 + 879x^4 - 250x^3 + 117x^2 - 6x + 4	\( -\,467^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.6496848334417832983.1	x^14 - 4x^13 + 6x^12 + 7x^11 - 49x^10 + 108x^9 + 18x^8 - 594x^7 + 725x^6 + 226x^5 - 327x^4 - 391x^3 - 230x^2 + 504x + 441	\( -\,487^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.8146590668153303687.1	x^14 - 4x^13 - 2x^12 + 21x^11 + 22x^10 - 101x^9 + 29x^8 - 40x^7 + 73x^6 - 222x^5 - 475x^4 + 867x^3 + 2445x^2 + 2446x + 1403	\( -\,503^{7} \)	$D_{7}$ (as 14T2)	$[3]$
14.0.9098007718612700671.1	x^14 - 6x^12 + 59x^10 - 284x^8 + 1027x^6 - 1306x^4 + 2445x^2 + 511	\( -\,7^{7}\cdot 73^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.12545167784987734375.1	x^14 + 6x^12 - 85x^10 + 355x^8 - 695x^6 + 1091x^4 - 609x^2 + 535	\( -\,5^{7}\cdot 107^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.12710233464526340096.1	x^14 - 2x^13 + 3x^12 - 32x^11 + 95x^10 - 138x^9 + 293x^8 - 932x^7 + 1612x^6 - 776x^5 + 868x^4 - 2384x^3 + 1840x^2 - 640x + 256	\( -\,2^{21}\cdot 67^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.19186974916023370183.1	x^14 + x^12 + 45x^10 + 59x^8 - 51x^6 - 95x^4 + 58x^2 + 63	\( -\,7^{7}\cdot 13^{12} \)	$D_{7}$ (as 14T2)	Trivial
14.14.21292697885552828353.1	x^14 - 2x^13 - 25x^12 + 69x^11 + 161x^10 - 632x^9 - 147x^8 + 2146x^7 - 1171x^6 - 2669x^5 + 2682x^4 + 667x^3 - 1466x^2 + 336x + 49	\( 577^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.24014121782394769283.1	x^14 + 12x^12 + 48x^10 - 114x^8 - 1080x^6 + 1232x^4 + 3953x^2 + 2348	\( -\,587^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.26713070983635746816.1	x^14 + 8x^12 + 66x^10 + 212x^8 + 673x^6 + 2684x^4 + 4804x^2 + 2384	\( -\,2^{14}\cdot 149^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.48859625810781274112.1	x^14 - 4x^13 + 10x^12 - 12x^11 - 72x^10 + 40x^9 + 470x^8 + 148x^7 - 877x^6 - 1148x^5 + 280x^4 + 1264x^3 + 1756x^2 + 880x + 400	\( -\,2^{21}\cdot 13^{12} \)	$D_{7}$ (as 14T2)	Trivial (GRH)
14.0.75987588324579688448.1	x^14 - 4x^13 + 24x^11 - 2x^10 - 80x^9 - 92x^8 + 432x^7 + 1005x^6 - 796x^5 - 2308x^4 + 328x^3 + 3076x^2 - 1920x + 400	\( -\,2^{14}\cdot 173^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.84856922099409044287.1	x^14 - 4x^13 + 24x^12 - 32x^11 + 137x^10 - 54x^9 + 637x^8 - 148x^7 + 2542x^6 - 702x^5 + 4247x^4 - 755x^3 + 2028x^2 - 175x + 25	\( -\,19^{7}\cdot 37^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.125003362773881021207.1	x^14 - 2x^13 + 15x^12 + 8x^11 + 80x^10 + 108x^9 + 519x^8 + 608x^7 + 2679x^6 + 1744x^5 + 3438x^4 + 1127x^3 + 1067x^2 + 170x + 25	\( -\,743^{7} \)	$D_{7}$ (as 14T2)	$[3]$
14.0.222902399220465737943.1	x^14 - 2x^13 - 5x^12 + 35x^11 + 5x^10 - 193x^9 + 415x^8 + 241x^7 - 440x^6 - 357x^5 + 3537x^4 - 639x^3 + 2781x^2 + 7209x + 7587	\( -\,3^{7}\cdot 269^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.230752268637185668771.1	x^14 + 2x^12 - 18x^11 - 35x^10 - 36x^9 + 101x^8 + 270x^7 + 542x^6 - 216x^5 + 2641x^4 + 144x^3 - 5380x^2 - 1008x + 3568	\( -\,811^{7} \)	$D_{7}$ (as 14T2)	Trivial (GRH)
14.0.264568763060045171603.1	x^14 - 2x^13 + 7x^12 - 40x^11 + 113x^10 - 226x^9 + 473x^8 - 1232x^7 + 1863x^6 - 410x^5 + 557x^4 - 3056x^3 + 3828x^2 - 1600x + 400	\( -\,827^{7} \)	$D_{7}$ (as 14T2)	Trivial (GRH)
14.0.273657381125642667711.1	x^14 - 6x^13 + 21x^12 - 63x^11 + 72x^10 + 162x^9 - 578x^8 + 876x^7 - 510x^6 - 2556x^5 + 7677x^4 - 8370x^3 + 4195x^2 - 1707x + 867	\( -\,3^{7}\cdot 277^{7} \)	$D_{7}$ (as 14T2)	$[4]$
14.0.345105711415338434419.1	x^14 - 2x^13 + 5x^12 - 28x^11 + 48x^10 - 108x^9 + 470x^8 - 868x^7 + 1374x^6 - 3956x^5 + 9920x^4 - 21684x^3 + 41785x^2 - 50890x + 26237	\( -\,859^{7} \)	$D_{7}$ (as 14T2)	Trivial (GRH)
14.0.356513163590850929567.1	x^14 - 6x^13 + 19x^12 - 70x^11 + 212x^10 - 467x^9 + 1126x^8 - 2393x^7 + 5781x^6 - 11969x^5 + 20359x^4 - 32768x^3 + 36718x^2 - 35471x + 26759	\( -\,863^{7} \)	$D_{7}$ (as 14T2)	$[3]$
14.0.454013768754343191251.1	x^14 - 7x^13 + 38x^12 - 137x^11 + 412x^10 - 971x^9 + 2060x^8 - 3635x^7 + 5352x^6 - 6205x^5 + 5518x^4 - 3595x^3 + 1565x^2 - 396x + 44	\( -\,11^{7}\cdot 13^{12} \)	$D_{7}$ (as 14T2)	Trivial (GRH)
14.0.474589190351997996299.1	x^14 + 4x^12 + 40x^10 + 54x^8 + 288x^6 + 3272x^4 + 7273x^2 + 3596	\( -\,29^{7}\cdot 31^{7} \)	$D_{7}$ (as 14T2)	$[2]$
14.0.624714053801881484375.1	x^14 + 16x^12 - 70x^10 + 15x^8 + 95x^6 + 101x^4 + 166x^2 + 935	\( -\,5^{7}\cdot 11^{7}\cdot 17^{7} \)	$D_{7}$ (as 14T2)	$[2, 2]$ (GRH)
14.0.890538686357276796875.1	x^14 - 7x^13 + 14x^12 + 7x^11 - 21x^10 - 126x^9 + 7x^8 + 471x^7 + 1274x^6 - 287x^5 - 3171x^4 - 1498x^3 + 2576x^2 + 1960x + 400	\( -\,5^{7}\cdot 7^{19} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.14.1064726745878753869969.1	x^14 - 4x^13 - 28x^12 + 91x^11 + 271x^10 - 620x^9 - 1144x^8 + 1365x^7 + 2396x^6 - 620x^5 - 1817x^4 - 337x^3 + 266x^2 + 70x + 1	\( 1009^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.1238256615687209381111.1	x^14 + 10x^12 + 31x^10 - 28x^8 - 281x^6 + 3950x^4 + 29709x^2 + 50519	\( -\,1031^{7} \)	$D_{7}$ (as 14T2)	$[5]$
14.0.1887551606348838984375.1	x^14 - 4x^13 + 7x^11 - 22x^10 + 186x^9 - 223x^8 - 743x^7 + 2916x^6 - 4381x^5 + 7159x^4 - 13533x^3 + 15756x^2 + 3285x + 9855	\( -\,3^{7}\cdot 5^{7}\cdot 73^{7} \)	$D_{7}$ (as 14T2)	$[2, 2]$ (GRH)
14.0.2102487927340409028608.1	x^14 + 24x^12 + 250x^10 + 1396x^8 + 4297x^6 + 11020x^4 - 5052x^2 + 4448	\( -\,2^{21}\cdot 139^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.2877782737305190278467.1	x^14 - 10x^12 + 183x^10 + 193x^8 + 163x^6 - 1427x^4 + 1122x^2 + 1163	\( -\,1163^{7} \)	$D_{7}$ (as 14T2)	Trivial (GRH)
14.0.3019244372533000260091.1	x^14 - 16x^12 - 36x^11 + 96x^10 + 336x^9 + 310x^8 - 780x^7 - 2544x^6 - 5028x^5 + 1208x^4 + 8688x^3 + 18961x^2 + 21780x + 50256	\( -\,1171^{7} \)	$D_{7}$ (as 14T2)	Trivial (GRH)
14.0.3819521878148762839571.1	x^14 + 14x^12 - 105x^10 + 313x^8 - 77x^6 - 539x^4 + 834x^2 + 1211	\( -\,7^{7}\cdot 173^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.3980696262723902109375.1	x^14 - 5x^13 + 14x^12 - 21x^11 - 8x^10 - 97x^9 + 1051x^8 - 2083x^7 + 193x^6 + 1359x^5 + 3281x^4 - 1841x^3 - 4601x^2 - 4737x + 10869	\( -\,3^{7}\cdot 5^{7}\cdot 13^{12} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)
14.0.4092467123737598613047.1	x^14 + 20x^12 - 42x^10 - 17x^8 - 497x^6 + 673x^4 + 762x^2 + 1223	\( -\,1223^{7} \)	$D_{7}$ (as 14T2)	$[5]$
14.0.5796901408038404767744.2	x^14 - 7x^12 + 50x^10 - 238x^8 + 1369x^6 - 1935x^4 + 4212x^2 + 26244	\( -\,2^{14}\cdot 29^{12} \)	$D_{7}$ (as 14T2)	$[7]$ (GRH)
14.0.6656084731100035682271.1	x^14 - 4x^13 + 16x^12 - 23x^11 - 52x^10 + 412x^9 - 689x^8 - 10x^7 + 2020x^6 - 2313x^5 + 4557x^4 - 10242x^3 + 12078x^2 + 2079x + 3969	\( -\,3^{7}\cdot 19^{7}\cdot 23^{7} \)	$D_{7}$ (as 14T2)	$[2, 2]$ (GRH)
14.0.7557338235665775234375.1	x^14 - 4x^13 - 4x^12 + 17x^11 + 2x^10 + 104x^9 + 187x^8 - 1569x^7 + 5418x^6 - 6741x^5 + 9963x^4 + 10557x^3 + 5454x^2 - 729x + 729	\( -\,3^{7}\cdot 5^{7}\cdot 89^{7} \)	$D_{7}$ (as 14T2)	$[2, 2]$ (GRH)
14.0.8784167171490938568704.1	x^14 - 2x^13 + 11x^12 - 48x^11 + 143x^10 - 338x^9 + 693x^8 - 1660x^7 + 2148x^6 + 184x^5 - 44x^4 - 3728x^3 + 7904x^2 - 4352x + 1024	\( -\,2^{14}\cdot 11^{7}\cdot 31^{7} \)	$D_{7}$ (as 14T2)	$[2, 2]$ (GRH)
14.0.10332321900000132284416.1	x^14 - 4x^13 - 18x^12 + 16x^11 + 117x^10 + 244x^9 + 1256x^8 + 2992x^7 + 2740x^6 + 2960x^5 + 10400x^4 + 13632x^3 + 4928x^2 + 3072x + 9216	\( -\,2^{14}\cdot 349^{7} \)	$D_{7}$ (as 14T2)	$[2]$ (GRH)