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 53)

Label	Polynomial	Discriminant	Galois group	Class group
14.10.51074220604765625.1	x^14 - x^13 - 6x^12 + 5x^11 + 14x^10 - 19x^9 - 2x^8 + 42x^7 - 35x^6 - 44x^5 + 40x^4 + 19x^3 - 12x^2 - 2x + 1	\( 5^{7}\cdot 859\cdot 761059399 \)	14T61	Trivial
14.10.61162027905113369.1	x^14 - x^13 - 9x^12 + 4x^11 + 15x^10 - 6x^9 + 17x^8 - 16x^7 - 41x^6 + 54x^5 - 6x^4 - 27x^3 + 23x^2 - 8x + 1	\( 13^{2}\cdot 53^{2}\cdot 2729\cdot 6871^{2} \)	14T57	Trivial
14.10.81799439172384353.1	x^14 - 4x^13 - 2x^12 + 26x^11 - 21x^10 - 59x^9 + 86x^8 + 63x^7 - 114x^6 - 49x^5 + 61x^4 + 30x^3 - 9x^2 - 7x - 1	\( 7^{2}\cdot 17^{7}\cdot 2017^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.10.87169416344387584.1	x^14 - 8x^12 + 22x^10 - 23x^8 + 7x^6 - 5x^4 + 6x^2 - 1	\( 2^{14}\cdot 107^{2}\cdot 21557^{2} \)	14T55	Trivial
14.10.91965715396182016.1	x^14 - 7x^12 + 20x^10 - 35x^8 + 44x^6 - 33x^4 + 10x^2 - 1	\( 2^{14}\cdot 23^{2}\cdot 239^{2}\cdot 431^{2} \)	14T55	Trivial
14.10.150223723038203125.1	x^14 - 2x^13 - 10x^12 + 23x^11 + 31x^10 - 96x^9 - 18x^8 + 176x^7 - 64x^6 - 133x^5 + 99x^4 + 21x^3 - 37x^2 + 11x - 1	\( 5^{7}\cdot 44959\cdot 42769271 \)	14T61	Trivial
14.10.185977177463008369.1	x^14 - 7x^13 + 15x^12 - 42x^10 + 54x^9 - 10x^8 - 34x^7 + 33x^6 - 9x^5 - 6x^4 + 12x^3 - 2x^2 - 5x - 1	\( 17^{4}\cdot 23^{2}\cdot 64879^{2} \)	14T55	Trivial
14.10.214655123975078125.1	x^14 - 3x^13 - 4x^12 + 21x^11 - 6x^10 - 50x^9 + 45x^8 + 46x^7 - 70x^6 - 10x^5 + 46x^4 - 4x^3 - 13x^2 + x + 1	\( 5^{7}\cdot 2747585586881 \)	14T61	Trivial
14.10.298720649203203125.1	x^14 - 12x^12 - x^11 + 54x^10 + 8x^9 - 116x^8 - 22x^7 + 127x^6 + 25x^5 - 69x^4 - 11x^3 + 15x^2 + x - 1	\( 5^{7}\cdot 31\cdot 79\cdot 1561300249 \)	14T61	Trivial
14.10.340421892311181409.1	x^14 - 7x^13 + 14x^12 - 16x^10 - 14x^9 + 9x^8 + 71x^7 - 64x^6 - 9x^5 + 14x^4 - 5x^3 + 10x^2 - 6x + 1	\( 17^{2}\cdot 23^{4}\cdot 64879^{2} \)	14T55	Trivial
14.10.415656167718828125.1	x^14 - 9x^12 - 4x^11 + 16x^10 + 36x^9 + 8x^8 - 64x^7 - 11x^6 + 40x^5 - 13x^4 - 7x^3 + 10x^2 - x - 1	\( 5^{7}\cdot 107^{2}\cdot 21557^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.10.890650137908152453.1	x^14 - 6x^13 + 10x^12 + 3x^11 - 24x^10 + 42x^9 - 94x^8 + 136x^7 - 52x^6 - 88x^5 + 109x^4 - 23x^3 - 24x^2 + 10x - 1	\( 13^{3}\cdot 71^{2}\cdot 283583^{2} \)	14T57	Trivial
14.10.1070170257679431581.1	x^14 - 6x^13 + 6x^12 + 26x^11 - 61x^10 + 22x^9 + 47x^8 - 69x^7 + 47x^6 + 22x^5 - 61x^4 + 26x^3 + 6x^2 - 6x + 1	\( 29\cdot 577^{6} \)	14T38	Trivial
14.10.1365389639108240293.1	x^14 - 2x^13 - x^12 + 9x^11 - 4x^10 - 14x^9 - 46x^8 - 10x^7 + 174x^6 + 31x^5 - 191x^4 + 6x^3 + 68x^2 - 17x + 1	\( 37\cdot 577^{6} \)	14T38	Trivial
14.10.1569388010932621673.1	x^14 - x^13 - 3x^12 + 4x^11 - 9x^10 - 3x^9 + 31x^8 - 8x^7 + 20x^6 + 24x^5 - 121x^4 - 28x^3 + 106x^2 + 13x - 25	\( 2621\cdot 5261\cdot 113813822033 \)	14T63	Trivial
14.10.2065365078342175169.1	x^14 - 2x^13 - 10x^12 + 19x^11 + 37x^10 - 64x^9 - 68x^8 + 95x^7 + 68x^6 - 64x^5 - 37x^4 + 19x^3 + 10x^2 - 2x - 1	\( 7^{2}\cdot 17^{5}\cdot 2017^{2}\cdot 7297 \)	14T57	Trivial
14.10.3161612016871142273.1	x^14 - 4x^13 - 6x^12 + 28x^11 + 29x^10 - 61x^9 - 215x^8 + 237x^7 + 347x^6 - 324x^5 - 202x^4 + 139x^3 + 47x^2 - 14x - 1	\( 17^{5}\cdot 23^{2}\cdot 64879^{2} \)	14T57	Trivial
14.10.6236509432683584041.1	x^14 - 5x^13 + 5x^12 + 8x^11 - 26x^10 + 54x^9 - 23x^8 - 117x^7 + 142x^6 + 5x^5 - 162x^4 + 73x^3 + 85x^2 - 8x - 7	\( 13^{2}\cdot 577^{6} \)	14T28	Trivial
14.10.6236509432683584041.2	x^14 - 4x^13 - 7x^12 + 40x^11 + 18x^10 - 161x^9 - 34x^8 + 320x^7 + 85x^6 - 295x^5 - 122x^4 + 81x^3 + 40x^2 - 2x - 1	\( 13^{2}\cdot 577^{6} \)	14T28	Trivial
14.10.6642679726469111153.1	x^14 - 5x^13 - 2x^12 + 42x^11 - 27x^10 - 134x^9 + 127x^8 + 207x^7 - 211x^6 - 163x^5 + 150x^4 + 62x^3 - 40x^2 - 9x + 1	\( 126173\cdot 52647394660261 \)	14T63	Trivial
14.10.9524221049139396608.1	x^14 - 2x^13 - 8x^12 + 8x^11 + 39x^10 + 6x^9 - 139x^8 - 72x^7 + 279x^6 + 186x^5 - 223x^4 - 208x^3 - 10x^2 + 20x + 1	\( 2^{15}\cdot 4129^{4} \)	14T51	Trivial
14.10.13025427850756358144.1	x^14 - x^13 - 10x^12 + 5x^11 + 77x^10 - 56x^9 - 309x^8 + 293x^7 + 550x^6 - 549x^5 - 389x^4 + 352x^3 + 60x^2 - 36x - 4	\( 2^{20}\cdot 29\cdot 809^{4} \)	14T51	Trivial
14.10.14953489656814350625.1	x^14 - 5x^13 - 4x^12 + 47x^11 - 20x^10 - 119x^9 + 17x^8 + 191x^7 + 17x^6 - 119x^5 - 20x^4 + 47x^3 - 4x^2 - 5x + 1	\( 5^{4}\cdot 12437^{4} \)	14T50	Trivial
14.10.16230381662628806656.1	x^14 - 9x^12 + 20x^10 + 17x^8 - 71x^6 + x^4 + 26x^2 - 1	\( 2^{16}\cdot 3967^{4} \)	14T50	Trivial
14.10.21292697885552828353.1	x^14 - 2x^13 - 6x^12 + 12x^11 - 2x^10 + 20x^9 - x^8 - 120x^7 + 92x^6 + 130x^5 - 146x^4 - 68x^3 + 50x^2 + 16x - 1	\( 577^{7} \)	14T27	Trivial
14.10.95794555555546517504.1	x^14 - 7x^13 + 12x^12 + 17x^11 - 85x^10 + 166x^9 - 263x^8 + 151x^7 + 355x^6 - 756x^5 + 679x^4 - 165x^3 - 386x^2 + 205x + 101	\( 2^{12}\cdot 29\cdot 73^{8} \)	14T44	Trivial
14.10.137633950666927456949.1	x^14 - 7x^13 + 20x^12 - 29x^11 + 8x^10 + 59x^9 - 121x^8 + 97x^7 + 9x^6 - 100x^5 + 77x^4 - 23x^2 + 9x - 1	\( 29^{12}\cdot 389 \)	$C_2 \wr C_7$ (as 14T29)	Trivial
14.10.171769547892704100352.1	x^14 - 19x^12 + 93x^10 - 75x^8 - 181x^6 + 59x^4 + 59x^2 - 13	\( 2^{14}\cdot 13\cdot 73^{8} \)	14T44	Trivial
14.10.532317447138820708825.1	x^14 - 2x^13 - 18x^12 + 32x^11 + 124x^10 - 200x^9 - 403x^8 + 592x^7 + 654x^6 - 503x^5 - 407x^4 - 1451x^3 - 1189x^2 + 1642x + 1055	\( 5^{2}\cdot 577^{7} \)	14T27	Trivial
14.10.772735640087899996445.1	x^14 - 7x^13 + 6x^12 + 55x^11 - 168x^10 + 169x^9 + 182x^8 - 851x^7 + 1059x^6 - 394x^5 - 318x^4 + 416x^3 - 185x^2 + 35x - 2	\( 5\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.10.824550655859252425804.1	x^14 - 2x^13 + 8x^12 - 42x^11 - 7x^10 + 267x^9 - 253x^8 - 293x^7 + 433x^6 + 58x^5 - 257x^4 + 38x^3 + 65x^2 - 6x - 2	\( 2^{2}\cdot 149^{4}\cdot 211^{5} \)	14T56	Trivial
14.10.824550655859252425804.2	x^14 - 3x^13 - 19x^12 + 52x^11 + 138x^10 - 313x^9 - 494x^8 + 820x^7 + 854x^6 - 1067x^5 - 385x^4 + 559x^3 - 127x^2 - 138x + 16	\( 2^{2}\cdot 149^{4}\cdot 211^{5} \)	14T56	Trivial
14.10.1000402691469045597184.1	x^14 - 5x^12 - 24x^10 + 127x^8 - 147x^6 + 51x^4 + 5x^2 - 4	\( 2^{10}\cdot 149^{4}\cdot 211^{4} \)	14T53	Trivial
14.10.1000402691469045597184.2	x^14 - 4x^13 - x^12 + 4x^11 + 94x^10 - 214x^9 - 117x^8 + 592x^7 - 97x^6 - 564x^5 + 171x^4 + 204x^3 - 71x^2 - 22x + 8	\( 2^{10}\cdot 149^{4}\cdot 211^{4} \)	14T53	Trivial
14.10.1738292029888469398433.1	x^14 - 3x^13 - 19x^12 + 72x^11 + 44x^10 - 382x^9 + 244x^8 + 594x^7 - 937x^6 - 59x^5 + 1020x^4 - 424x^3 - 328x^2 + 193x - 17	\( 17^{3}\cdot 29^{12} \)	$C_2 \wr C_7$ (as 14T29)	Trivial
14.10.1854565536210959991468.1	x^14 - 13x^12 + 45x^10 - 49x^8 - 5x^6 + 24x^4 - 2x^2 - 3	\( 2^{2}\cdot 3\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.10.3382538789271711514624.1	x^14 - 2x^12 - 44x^10 + 164x^8 - 4x^6 - 356x^4 + 232x^2 - 4	\( 2^{22}\cdot 73^{8} \)	14T35	Trivial
14.10.3382538789271711514624.2	x^14 - 11x^12 - 15x^10 + 109x^8 + 19x^6 - 97x^4 + 27x^2 - 1	\( 2^{22}\cdot 73^{8} \)	14T35	Trivial
14.10.8162357716043213196457.1	x^14 - 6x^13 - 2x^12 + 53x^11 - 52x^10 + 134x^9 - 408x^8 - 966x^7 + 2454x^6 - 2033x^5 + 6188x^4 - 2867x^3 - 4228x^2 + 1130x - 59	\( 71^{3}\cdot 283583^{3} \)	14T54	Trivial (GRH)
14.10.8162357716043213196457.2	x^14 - 3x^13 - 2x^12 - 17x^11 + 49x^10 + 63x^9 - 626x^8 + 2779x^7 + 427x^6 - 12220x^5 + 6108x^4 + 6963x^3 - 4068x^2 - 286x + 173	\( 71^{3}\cdot 283583^{3} \)	14T54	Trivial (GRH)
14.10.29550964508103979773361.1	x^14 - 6x^13 + 3x^12 + 62x^11 - 194x^10 - 85x^9 + 1031x^8 - 550x^7 - 841x^6 + 754x^5 - 2204x^4 + 1276x^3 + 2494x^2 - 1479x - 29	\( 17^{4}\cdot 29^{12} \)	$C_2^3:F_8$ (as 14T21)	Trivial
14.10.29550964508103979773361.2	x^14 - x^13 - 19x^12 + 42x^11 + 51x^10 - 260x^9 + 332x^8 - 56x^7 - 390x^6 + 494x^5 - 428x^4 + 245x^3 + 367x^2 - 378x - 1	\( 17^{4}\cdot 29^{12} \)	$C_2^3:F_8$ (as 14T21)	Trivial
14.10.112664856324815819481681.1	x^14 - 17x^12 - 19x^11 + 48x^10 + 289x^9 + 318x^8 - 1066x^7 - 1710x^6 + 16x^5 + 2662x^4 + 1302x^3 - 491x^2 - 252x - 9	\( 3^{6}\cdot 7^{8}\cdot 173^{6} \)	14T41	Trivial
14.10.633025036360007677087744.1	x^14 - 19x^12 + 105x^10 - 27x^8 - 1109x^6 + 1903x^4 + 171x^2 - 1	\( 2^{12}\cdot 7^{8}\cdot 173^{6} \)	14T41	Trivial (GRH)
14.10.19491020144193136770330813.1	x^14 - x^13 - 24x^12 + 27x^11 - 22x^10 - 52x^9 + 2263x^8 - 5418x^7 - 7121x^6 + 37648x^5 - 26576x^4 - 42261x^3 + 63553x^2 - 19692x - 2020	\( 3^{6}\cdot 7^{8}\cdot 173^{7} \)	14T40	$[2]$ (GRH)
14.10.109513331290281328136179712.1	x^14 - 31x^12 + 108x^10 + 2686x^8 - 10226x^6 - 47024x^4 + 208269x^2 - 177152	\( 2^{12}\cdot 7^{8}\cdot 173^{7} \)	14T40	$[2]$ (GRH)
14.10.1273417700659086943252185088.1	x^14 - 4x^13 - 17x^12 + 78x^11 + 149x^10 - 812x^9 - 2150x^8 + 84x^7 + 4571x^6 + 3596x^5 - 1113x^4 - 1794x^3 - 193x^2 + 100x + 16	\( 2^{16}\cdot 13^{7}\cdot 17597207^{2} \)	14T52	Trivial (GRH)
14.10.1273417700659086943252185088.2	x^14 - 4x^13 - 16x^12 + 64x^11 + 123x^10 - 384x^9 - 618x^8 + 968x^7 + 1799x^6 - 700x^5 - 2296x^4 - 512x^3 + 800x^2 + 448x + 64	\( 2^{16}\cdot 13^{7}\cdot 17597207^{2} \)	14T52	Trivial (GRH)
14.10.203605885683812079006330175488.1	x^14 - 4x^13 - 36x^12 + 108x^11 + 504x^10 - 976x^9 - 2989x^8 + 4614x^7 + 8207x^6 - 12968x^5 - 8323x^4 + 20384x^3 - 8652x^2 - 210x + 313	\( 2^{14}\cdot 3^{7}\cdot 13^{4}\cdot 446040299^{2} \)	14T58	Trivial (GRH)
14.10.21487555788040560033827139878912.1	x^14 - 4x^13 - 36x^12 + 132x^11 + 432x^10 - 1576x^9 - 1404x^8 + 8476x^7 - 4934x^6 - 14484x^5 + 28590x^4 - 16792x^3 - 8061x^2 + 14280x - 4574	\( 2^{31}\cdot 23^{2}\cdot 73^{2}\cdot 59576897^{2} \)	14T58	Trivial (GRH)