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 1065)

Label	Polynomial	Discriminant	Galois group	Class group
18.10.6848747881843490473177.1	x^18 - 4x^17 - x^16 + 12x^15 + 15x^14 - 21x^13 - 62x^12 - 3x^11 + 117x^10 + 86x^9 - 121x^8 - 128x^7 + 57x^6 + 70x^5 - 6x^4 - 9x^3 - x^2 - 2x + 1	\( 73\cdot 9685993193^{2} \)	18T968	Trivial
18.10.8349843308000967837161.1	x^18 - 9x^17 + 34x^16 - 68x^15 + 60x^14 + 56x^13 - 254x^12 + 354x^11 - 193x^10 - 135x^9 + 327x^8 - 218x^7 - 12x^6 + 114x^5 - 63x^4 - 6x^3 + 14x^2 - 2x - 1	\( 89\cdot 9685993193^{2} \)	18T968	Trivial
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
18.10.11352034160315922565129.1	x^18 - 5x^17 + 7x^16 + 12x^15 - 49x^14 + 22x^13 + 97x^12 - 132x^11 - 48x^10 + 256x^9 - 151x^8 - 165x^7 + 222x^6 - 41x^5 - 73x^4 + 59x^3 - 7x^2 - 5x + 1	\( 11^{2}\cdot 9685993193^{2} \)	18T964	Trivial
18.10.11933079900270646767029.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 93x^14 + 147x^13 + 82x^12 - 297x^11 + 15x^10 + 288x^9 - 36x^8 - 171x^7 - 17x^6 + 66x^5 + 34x^4 - 14x^3 - 13x^2 + 2x + 1	\( 109^{2}\cdot 541^{2}\cdot 12041^{2}\cdot 23669 \)	18T968	Trivial
18.10.15855320438788354657081.1	x^18 - 5x^17 + 37x^15 - 50x^14 - 54x^13 + 130x^12 - 18x^11 - 35x^10 - 49x^9 - 4x^8 + 97x^7 - 76x^6 + 43x^5 - 15x^4 + 2x^3 + 2x^2 - 4x - 1	\( 13^{2}\cdot 9685993193^{2} \)	18T964	Trivial
18.10.17298154203755513310784.1	x^18 + 2x^16 - 16x^14 - 26x^12 + 73x^10 + 57x^8 - 132x^6 + 33x^4 + 8x^2 - 1	\( 2^{6}\cdot 37^{4}\cdot 229^{6} \)	18T711	Trivial (GRH)
18.10.19634130432842855035456.1	x^18 - 9x^16 - 8x^15 + 24x^14 + 41x^13 - 21x^12 - 91x^11 - 14x^10 + 151x^9 + 112x^8 - 119x^7 - 161x^6 + 5x^5 + 79x^4 + 27x^3 - 10x^2 - 7x - 1	\( 2^{6}\cdot 7^{12}\cdot 53^{6} \)	18T463	Trivial
18.10.29757978937277452163113.1	x^18 - 7x^17 + 16x^16 - 6x^15 - 41x^14 + 97x^13 - 93x^12 - 6x^11 + 141x^10 - 205x^9 + 141x^8 - 6x^7 - 93x^6 + 97x^5 - 41x^4 - 6x^3 + 16x^2 - 7x + 1	\( 7^{12}\cdot 53^{6}\cdot 97 \)	18T544	Trivial
18.10.43488796471211940304129.1	x^18 - 3x^17 - 3x^16 + 14x^15 - 11x^14 + 25x^13 - 28x^12 - 75x^11 + 161x^10 - 138x^9 + 34x^8 + 178x^7 - 246x^6 + 16x^5 + 216x^4 - 196x^3 + 51x^2 + 6x - 1	\( 23^{2}\cdot 5569^{3}\cdot 21817^{2} \)	18T968	Trivial
18.10.53977668015744910360576.1	x^18 + 3x^16 - 4x^14 - 11x^12 + 4x^10 - 4x^8 + 33x^6 - 32x^4 + 10x^2 - 1	\( 2^{18}\cdot 453771377^{2} \)	18T964	Trivial (GRH)
18.10.54463704731702620585984.1	x^18 - 8x^16 + 22x^14 - 26x^12 + 20x^10 - 20x^8 + 6x^6 + 2x^4 + 5x^2 - 1	\( 2^{18}\cdot 109^{2}\cdot 4181741^{2} \)	18T964	Trivial (GRH)
18.10.55412477560287811237001.1	x^18 - 6x^17 + 13x^16 - 12x^15 - 8x^14 + 56x^13 - 92x^12 + 64x^11 - 25x^10 + 24x^9 + 81x^8 - 221x^7 + 116x^6 - 31x^5 + 102x^4 - 54x^3 - 14x^2 + 6x + 1	\( 7^{12}\cdot 13^{4}\cdot 41\cdot 43^{4} \)	18T696	Trivial (GRH)
18.10.57388858189268996325376.1	x^18 - 8x^16 + 19x^14 - 4x^12 - 27x^10 + x^8 + 27x^6 - 9x^4 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T703	Trivial (GRH)
18.10.57388858189268996325376.2	x^18 - 7x^16 + 21x^14 - 41x^12 + 49x^10 - 28x^8 + 12x^6 - 14x^4 + 7x^2 - 1	\( 2^{18}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T703	Trivial (GRH)
18.10.63846808256261401083904.1	x^18 - 6x^17 + 9x^16 + 10x^15 - 44x^14 + 60x^13 - 44x^12 - 10x^11 + 78x^10 - 116x^9 + 78x^8 - 10x^7 - 44x^6 + 60x^5 - 44x^4 + 10x^3 + 9x^2 - 6x + 1	\( 2^{18}\cdot 101^{6}\cdot 479^{2} \)	18T883	Trivial
18.10.66983486784702356675569.1	x^18 - 4x^17 + 8x^15 - 3x^14 + 6x^13 + 14x^12 - 18x^11 - 59x^10 - 26x^9 + 69x^8 + 92x^7 + 23x^6 - 67x^5 - 69x^4 - x^3 + 23x^2 + 9x + 1	\( 7^{12}\cdot 97^{2}\cdot 22679^{2} \)	18T703	Trivial (GRH)
18.10.66983486784702356675569.2	x^18 - 6x^16 - 4x^15 - 12x^14 - 10x^13 + 111x^12 + 194x^11 - 28x^10 - 377x^9 - 412x^8 - 17x^7 + 333x^6 + 281x^5 + 54x^4 - 53x^3 - 28x^2 + x + 1	\( 7^{12}\cdot 97^{2}\cdot 22679^{2} \)	18T838	Trivial (GRH)
18.10.66983486784702356675569.3	x^18 - 3x^17 + 3x^16 - 18x^14 + 37x^13 - 27x^12 - 12x^11 + 107x^10 - 158x^9 - 7x^8 + 207x^7 - 134x^6 - 64x^5 + 90x^4 - 10x^3 - 16x^2 + 2x + 1	\( 7^{12}\cdot 97^{2}\cdot 22679^{2} \)	18T838	Trivial (GRH)
18.10.85598116744348371668992.1	x^18 - 4x^17 + 3x^16 + 14x^15 - 46x^14 + 41x^13 + 72x^12 - 216x^11 + 76x^10 + 273x^9 - 151x^8 - 170x^7 + 53x^6 + 93x^5 - 79x^4 + 45x^3 - 7x + 1	\( 2^{12}\cdot 37^{9}\cdot 401^{2} \)	18T319	Trivial
18.10.94665015950974046979001.1	x^18 - 3x^17 - 4x^16 + 32x^15 - 38x^14 - 92x^13 + 269x^12 - 37x^11 - 577x^10 + 459x^9 + 400x^8 - 596x^7 + 54x^6 + 295x^5 - 75x^4 - 92x^3 - 6x^2 + 10x + 1	\( 83\cdot 1523\cdot 865377817^{2} \)	18T968	Trivial (GRH)
18.10.100758244279412523585536.1	x^18 - 8x^16 - 3x^15 + 6x^14 - 14x^13 + 28x^12 + 68x^11 - 70x^10 - 101x^9 + 62x^8 + 66x^7 - 8x^6 - 2x^5 - 10x^4 - 19x^3 - 2x^2 + 4x + 1	\( 2^{12}\cdot 101^{7}\cdot 479^{2} \)	18T773	Trivial (GRH)
18.10.140215359130103174768525.1	x^18 - x^17 - 9x^16 + 15x^15 + 17x^14 - 71x^13 + 30x^12 + 89x^11 - 142x^10 + 61x^9 + 128x^8 - 265x^7 + 227x^6 - 66x^5 - 73x^4 + 95x^3 - 47x^2 + 11x - 1	\( 5^{2}\cdot 257^{6}\cdot 269^{3} \)	18T556	Trivial (GRH)
18.10.148166223769011413199501.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 93x^14 + 147x^13 + 83x^12 - 303x^11 + 24x^10 + 298x^9 - 69x^8 - 165x^7 + 18x^6 + 48x^5 + 21x^4 - 4x^3 - 12x^2 + 1	\( 3^{24}\cdot 19\cdot 2053^{2}\cdot 6551 \)	18T879	Trivial (GRH)
18.10.173460040503181804605289.1	x^18 - 4x^17 + x^16 + x^15 + 23x^14 + 6x^13 - 75x^12 - 10x^11 + 39x^10 + 124x^9 - 36x^8 - 145x^7 + 75x^6 + 12x^5 - 43x^4 + 15x^3 + 12x^2 - 2x - 1	\( 7^{12}\cdot 3540067^{2} \)	18T703	Trivial (GRH)
18.10.180040394398004750319616.1	x^18 + x^16 - 15x^14 + 56x^10 - 23x^8 - 57x^6 + 45x^4 - 6x^2 - 1	\( 2^{18}\cdot 37^{6}\cdot 16361^{2} \)	18T883	Trivial
18.10.180040394398004750319616.2	x^18 - 6x^17 + 10x^16 + 16x^15 - 91x^14 + 116x^13 + 83x^12 - 398x^11 + 415x^10 + 52x^9 - 624x^8 + 604x^7 - 28x^6 - 292x^5 + 151x^4 + 14x^3 - 33x^2 + 10x - 1	\( 2^{18}\cdot 37^{6}\cdot 16361^{2} \)	18T883	Trivial
18.10.180040394398004750319616.3	x^18 + 6x^16 - 13x^14 - 51x^12 + 47x^10 + 104x^8 - 64x^6 - 49x^4 + 19x^2 - 1	\( 2^{18}\cdot 37^{6}\cdot 16361^{2} \)	18T776	Trivial (GRH)
18.10.237179920636111459752529.1	x^18 - 2x^17 - 11x^16 + 9x^15 + 47x^14 + 14x^13 - 85x^12 - 98x^11 + 48x^10 + 147x^9 + 48x^8 - 98x^7 - 85x^6 + 14x^5 + 47x^4 + 9x^3 - 11x^2 - 2x + 1	\( 7^{14}\cdot 769^{4} \)	18T473	Trivial
18.10.250368673459725355913216.1	x^18 - 8x^17 + 23x^16 - 36x^15 + 57x^14 - 80x^13 + 30x^12 + 44x^11 - 70x^10 + 136x^9 - 139x^8 + 18x^7 + 83x^6 - 106x^5 + 35x^4 + 24x^3 - 12x^2 - 2x + 1	\( 2^{12}\cdot 37^{6}\cdot 89\cdot 16361^{2} \)	18T912	Trivial
18.10.256106564050292863664128.1	x^18 - 17x^14 - 15x^12 + 71x^10 + 62x^8 - 120x^6 - 79x^4 + 135x^2 - 37	\( 2^{24}\cdot 37^{7}\cdot 401^{2} \)	18T773	Trivial (GRH)
18.10.266250197057968263748517.1	x^18 - 3x^17 - 2x^16 + 9x^15 - 10x^14 - 14x^13 + 20x^12 + 46x^11 + 21x^10 - 78x^9 - 32x^8 + 42x^7 - 33x^6 + 4x^5 + 53x^4 - 3x^3 - 19x^2 - 2x + 1	\( 7^{12}\cdot 13^{4}\cdot 43^{4}\cdot 197 \)	18T696	Trivial (GRH)
18.10.269301993612775913230336.1	x^18 - 7x^17 + 26x^16 - 66x^15 + 111x^14 - 111x^13 + 19x^12 + 138x^11 - 198x^10 + 159x^9 - 188x^8 + 15x^7 + 326x^6 - 200x^5 - 118x^4 + 78x^3 + 22x^2 - 5x - 1	\( 2^{12}\cdot 7^{12}\cdot 41^{6} \)	18T646	Trivial (GRH)
18.10.272873722759475949703168.1	x^18 - 3x^17 - 2x^16 + 10x^15 + 3x^14 - 35x^13 + 24x^12 + 147x^11 - 120x^10 - 425x^9 + 194x^8 + 737x^7 - 254x^6 - 625x^5 + 287x^4 + 154x^3 - 114x^2 + 21x - 1	\( 2^{12}\cdot 37^{6}\cdot 97\cdot 16361^{2} \)	18T912	Trivial
18.10.289123420349393529839217.1	x^18 - 3x^17 + 12x^15 - 15x^14 - 15x^13 + 21x^12 + 33x^11 - 18x^10 - 114x^9 + 90x^8 + 171x^7 - 109x^6 - 105x^5 + 15x^4 + 24x^3 + 15x^2 - 3x - 1	\( 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.10.289123420349393529839217.2	x^18 - 6x^16 - 3x^15 + 9x^14 + 21x^13 - x^12 - 21x^11 + 27x^10 - 60x^9 - 162x^8 - 3x^7 + 183x^6 + 162x^5 - 48x^4 - 92x^3 + 12x^2 + 9x - 1	\( 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.10.289123420349393529839217.3	x^18 - 3x^17 - 9x^16 + 26x^15 + 18x^14 - 57x^13 + 9x^12 - 75x^10 + 123x^9 + 105x^8 - 129x^7 - 34x^6 + 51x^5 - 33x^4 - 20x^3 + 18x^2 + 9x + 1	\( 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.10.289123420349393529839217.4	x^18 - 3x^17 + 20x^15 - 30x^14 - 66x^13 + 79x^12 + 147x^11 + 3x^10 - 107x^9 - 180x^8 - 210x^7 + 12x^6 + 273x^5 + 231x^4 + 48x^3 - 24x^2 - 12x - 1	\( 3^{24}\cdot 73^{2}\cdot 577^{3} \)	18T879	Trivial
18.10.306631296709101840388096.1	x^18 - 2x^17 - 7x^16 + 23x^15 - 19x^14 - 17x^13 + 101x^12 - 207x^11 + 139x^10 + 202x^9 - 406x^8 + 149x^7 + 137x^6 - 109x^5 - 9x^4 + 32x^3 - 7x^2 - 3x + 1	\( 2^{12}\cdot 37^{6}\cdot 109\cdot 16361^{2} \)	18T912	Trivial
18.10.334750966203983365623808.1	x^18 - 13x^16 - 10x^15 + 58x^14 + 89x^13 - 98x^12 - 286x^11 - 20x^10 + 429x^9 + 229x^8 - 282x^7 - 227x^6 + 53x^5 + 71x^4 + 5x^3 - 2x^2 + 3x + 1	\( 2^{12}\cdot 13^{2}\cdot 37^{9}\cdot 61^{2} \)	18T319	Trivial (GRH)
18.10.385398969258228918652928.1	x^18 - x^17 - 13x^16 + 4x^15 + 70x^14 + 21x^13 - 184x^12 - 139x^11 + 233x^10 + 255x^9 - 148x^8 - 188x^7 + 84x^6 + 61x^5 - 48x^4 - 5x^3 + 4x^2 + 1	\( 2^{12}\cdot 37^{6}\cdot 137\cdot 16361^{2} \)	18T912	Trivial
18.10.394876295174073378555289.1	x^18 - 7x^17 + 13x^16 + 14x^15 - 64x^14 + 25x^13 + 62x^12 - 6x^11 - 16x^10 - 110x^9 + 40x^8 + 67x^7 + 43x^6 - 53x^5 - 20x^4 + 14x^3 - 4x^2 - x + 1	\( 19^{16}\cdot 37^{2} \)	18T368	Trivial
18.10.394876295174073378555289.2	x^18 - 8x^17 + 21x^16 + 7x^15 - 171x^14 + 414x^13 - 353x^12 - 237x^11 + 757x^10 - 490x^9 - 127x^8 + 306x^7 - 159x^6 + 12x^5 + 57x^4 - 27x^3 - 9x^2 + 4x + 1	\( 19^{16}\cdot 37^{2} \)	18T368	Trivial
18.10.402164965985304939453125.1	x^18 - x^17 - 10x^16 + 9x^15 + 32x^14 - 12x^13 - 34x^12 - 81x^11 - 41x^10 + 173x^9 + 109x^8 - 111x^7 - 63x^6 + 22x^5 - 2x^4 + 9x^2 - 1	\( 5^{9}\cdot 453771377^{2} \)	18T913	Trivial (GRH)
18.10.425858628960508313600000.1	x^18 - 2x^17 - 7x^16 + 10x^15 + 18x^14 - 12x^13 - 10x^12 + 14x^11 - 52x^10 - 28x^9 + 52x^8 + 14x^7 + 10x^6 - 12x^5 - 18x^4 + 10x^3 + 7x^2 - 2x - 1	\( 2^{20}\cdot 5^{5}\cdot 37^{9} \)	18T485	Trivial
18.10.427580313304580720703125.1	x^18 - 2x^17 - x^16 + 10x^15 - 22x^14 - 16x^13 + 27x^12 - 47x^11 - 41x^10 + 83x^9 + 135x^8 + 65x^7 - 52x^6 - 66x^5 - 20x^4 + 7x^3 + 10x^2 + x - 1	\( 5^{9}\cdot 7^{12}\cdot 41^{2}\cdot 97^{2} \)	18T286	Trivial (GRH)
18.10.442995137816722791202816.1	x^18 - 9x^16 + 29x^14 - 36x^12 + 33x^8 - 17x^6 - 5x^4 + 6x^2 - 1	\( 2^{30}\cdot 37^{6}\cdot 401^{2} \)	18T776	Trivial (GRH)
18.10.442995137816722791202816.2	x^18 - 3x^16 + 5x^14 - 18x^12 + 54x^10 - 97x^8 + 103x^6 - 57x^4 + 14x^2 - 1	\( 2^{30}\cdot 37^{6}\cdot 401^{2} \)	18T776	Trivial (GRH)
18.10.655088336820521017856000.1	x^18 - 7x^17 + 12x^16 + 13x^15 - 22x^14 - 136x^13 + 316x^12 - 145x^11 - 39x^10 - 229x^9 + 332x^8 + 77x^7 - 618x^6 + 931x^5 - 367x^4 - 349x^3 + 245x^2 - 15x - 1	\( 2^{12}\cdot 5^{3}\cdot 13^{3}\cdot 37^{6}\cdot 61^{3} \)	18T556	Trivial (GRH)
18.10.770110100710329092297157.1	x^18 - 3x^17 - 6x^16 + 29x^15 - 45x^14 + 21x^13 + 110x^12 - 246x^11 + 186x^10 + 44x^9 - 144x^8 + 27x^7 - 62x^6 + 123x^5 - 243x^4 + 214x^3 - 84x^2 + 15x - 1	\( 3^{24}\cdot 7^{12}\cdot 197 \)	18T459	Trivial