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 60)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.1678237502892756571.1	x^18 - 2x^17 + x^16 + 5x^15 - 10x^14 + 5x^13 + 13x^12 - 29x^11 + 24x^10 + 9x^9 - 48x^8 + 56x^7 - 16x^6 - 44x^5 + 74x^4 - 60x^3 + 29x^2 - 8x + 1	\( -\,139\cdot 367^{2}\cdot 299401^{2} \)	18T968	Trivial
18.0.6646436567333419399.1	x^18 - 9x^17 + 42x^16 - 132x^15 + 310x^14 - 574x^13 + 865x^12 - 1082x^11 + 1139x^10 - 1020x^9 + 787x^8 - 532x^7 + 321x^6 - 174x^5 + 85x^4 - 37x^3 + 14x^2 - 4x + 1	\( -\,17^{2}\cdot 43^{2}\cdot 2311\cdot 73363^{2} \)	18T968	Trivial
18.2.8678645063271073481.1	x^18 - x^17 + 2x^16 - 5x^15 + x^14 - 6x^13 + 2x^12 + 4x^10 + 3x^9 + 4x^8 + 2x^6 - 6x^5 + x^4 - 5x^3 + 2x^2 - x + 1	\( 41^{3}\cdot 11221481^{2} \)	18T968	Trivial
18.2.10910724785335819009.1	x^18 - 2x^17 + 4x^15 - 7x^14 + x^13 + 7x^12 + 2x^11 - 10x^10 + x^9 + 20x^8 - 22x^7 - 2x^6 + 7x^5 + 2x^4 - 10x^3 + 11x^2 - 5x + 1	\( 43^{2}\cdot 83\cdot 107\cdot 311^{2}\cdot 2621^{2} \)	18T968	Trivial
18.2.10913148516977234837.1	x^18 - x^17 + 3x^16 - 5x^15 + 4x^14 - 6x^13 - 5x^12 - 2x^11 - 16x^10 + x^9 - 16x^8 - 2x^7 - 5x^6 - 6x^5 + 4x^4 - 5x^3 + 3x^2 - x + 1	\( 53\cdot 453771377^{2} \)	18T968	Trivial
18.2.11675081596366988689.1	x^18 - 4x^17 + 4x^16 + 9x^15 - 27x^14 + 17x^13 + 26x^12 - 46x^11 + 12x^10 + 20x^9 - 12x^8 + 15x^7 - 48x^6 + 48x^5 - x^4 - 29x^3 + 20x^2 - 5x + 1	\( 5881\cdot 44555813^{2} \)	18T968	Trivial
18.4.34386713251607513543.1	x^18 - 2x^17 - 3x^15 + 6x^14 + 11x^13 - 22x^12 + 12x^11 - 27x^10 + 47x^9 - 27x^8 + 12x^7 - 22x^6 + 11x^5 + 6x^4 - 3x^3 - 2x + 1	\( -\,167\cdot 453771377^{2} \)	18T968	Trivial
18.4.60240587730612391171.1	x^18 - 5x^17 + 8x^16 - 2x^15 - 2x^14 - 10x^13 + 12x^12 + 16x^11 - 39x^10 + 26x^9 + 6x^8 - 28x^7 + 27x^6 - 6x^5 - 12x^4 + 11x^3 - x^2 - 2x + 1	\( -\,3331\cdot 134479871^{2} \)	18T968	Trivial
18.4.60346129003922492771.1	x^18 - 3x^17 + 2x^16 + 7x^15 - 16x^14 + 13x^13 + 8x^12 - 38x^11 + 62x^10 - 47x^9 - 28x^8 + 114x^7 - 123x^6 + 42x^5 + 42x^4 - 60x^3 + 33x^2 - 9x + 1	\( -\,131\cdot 678717521^{2} \)	18T968	Trivial
18.2.64577632169935983809.1	x^18 - x^17 + x^16 - x^15 + 9x^13 - 17x^12 + 12x^11 - x^10 - 15x^9 + 47x^8 - 76x^7 + 56x^6 + 14x^5 - 70x^4 + 68x^3 - 34x^2 + 9x - 1	\( 19\cdot 31^{2}\cdot 59\cdot 7742417^{2} \)	18T968	Trivial
18.4.122478876518131667543.1	x^18 - 5x^17 + 11x^16 - 13x^15 + x^14 + 20x^13 - 28x^12 + 10x^11 + 21x^10 - 35x^9 + 21x^8 + 10x^7 - 28x^6 + 20x^5 + x^4 - 13x^3 + 11x^2 - 5x + 1	\( -\,23\cdot 2307632671^{2} \)	18T968	Trivial
18.0.129568196354899759211.1	x^18 - 2x^17 + x^16 + 5x^15 - 10x^14 + 6x^13 + 13x^12 - 34x^11 + 30x^10 + 14x^9 - 71x^8 + 84x^7 - 27x^6 - 56x^5 + 96x^4 - 76x^3 + 35x^2 - 9x + 1	\( -\,53\cdot 2383\cdot 32029433^{2} \)	18T968	Trivial
18.4.378086966642928191111.1	x^18 + 2x^16 - 2x^15 - 5x^13 - 7x^12 - 7x^11 - 14x^10 - 7x^9 - 14x^8 - 7x^7 - 7x^6 - 5x^5 - 2x^3 + 2x^2 + 1	\( -\,71\cdot 2307632671^{2} \)	18T968	Trivial
18.6.424493288077110573961.1	x^18 - 9x^17 + 34x^16 - 68x^15 + 69x^14 - 7x^13 - 75x^12 + 99x^11 - 53x^10 + x^9 + 17x^8 - 25x^7 + 29x^6 - 11x^5 - 6x^4 + 4x^3 - x^2 + x - 1	\( 601\cdot 2293^{2}\cdot 366517^{2} \)	18T968	Trivial
18.6.473940000439726887449.1	x^18 - 3x^17 - 2x^16 + 18x^15 - 7x^14 - 48x^13 + 40x^12 + 87x^11 - 88x^10 - 109x^9 + 121x^8 + 111x^7 - 96x^6 - 83x^5 + 31x^4 + 24x^3 - 11x^2 - 8x - 1	\( 89\cdot 2307632671^{2} \)	18T968	Trivial
18.6.580443371325058772269.1	x^18 - 5x^17 + 8x^16 - 2x^15 - 7x^14 + 16x^13 - 42x^12 + 55x^11 - 6x^10 - 38x^9 + 21x^8 - 16x^7 + 17x^6 + 12x^5 + 7x^4 - 53x^3 + 44x^2 - 10x - 1	\( 109\cdot 2307632671^{2} \)	18T968	Trivial
18.2.836051461449855295837.1	x^18 - 6x^17 + 14x^16 - 16x^15 + 10x^14 - 7x^13 + 12x^12 - 13x^11 + 2x^10 + 5x^9 + 2x^8 - 13x^7 + 12x^6 - 7x^5 + 10x^4 - 16x^3 + 14x^2 - 6x + 1	\( 157\cdot 2307632671^{2} \)	18T968	Trivial
18.2.1049058203220519065477.1	x^18 - x^17 + 2x^16 - 5x^15 + 9x^14 - 12x^13 + 15x^12 - 20x^11 + 22x^10 - 23x^9 + 22x^8 - 20x^7 + 15x^6 - 12x^5 + 9x^4 - 5x^3 + 2x^2 - x + 1	\( 197\cdot 2307632671^{2} \)	18T968	Trivial
18.8.2533098531640743051723.1	x^18 - 9x^16 - 4x^15 + 24x^14 + 21x^13 - 18x^12 - 27x^11 + 9x^10 + 33x^9 + 9x^8 - 27x^7 - 18x^6 + 21x^5 + 24x^4 - 4x^3 - 9x^2 + 1	\( -\,3^{3}\cdot 9685993193^{2} \)	18T968	Trivial
18.8.2908372388180112392719.1	x^18 - 9x^17 + 31x^16 - 41x^15 - 36x^14 + 217x^13 - 323x^12 + 108x^11 + 361x^10 - 641x^9 + 423x^8 + 68x^7 - 358x^6 + 294x^5 - 94x^4 - 20x^3 + 28x^2 - 9x + 1	\( -\,31\cdot 9685993193^{2} \)	18T968	Trivial
18.4.3165035193944739414016.1	x^18 + 2x^12 - 6x^10 + 9x^8 - 16x^6 + 11x^4 - 3x^2 + 1	\( -\,2^{18}\cdot 367^{2}\cdot 299401^{2} \)	18T968	Trivial
18.0.3165035193944739414016.2	x^18 - 5x^14 - 4x^12 + 3x^10 + 11x^8 + 13x^6 + 7x^4 + 4x^2 + 1	\( -\,2^{18}\cdot 367^{2}\cdot 299401^{2} \)	18T968	Trivial
18.2.3614863212975497914489.1	x^18 - 2x^17 + x^16 + 6x^15 - 9x^14 + 24x^13 + 18x^12 + 14x^11 + 48x^10 + 22x^9 + 27x^8 + 58x^7 - 14x^6 + 61x^5 - 15x^4 + 26x^3 - 2x^2 + 4x + 1	\( 367^{2}\cdot 299401^{3} \)	18T968	Trivial
18.2.3846557029528535745209.1	x^18 - 2x^17 + 2x^16 - 2x^15 + 2x^14 - 2x^13 + 2x^12 - 3x^11 + 3x^10 - 3x^9 + 3x^8 - 3x^7 + 2x^6 - 2x^5 + 2x^4 - 2x^3 + 2x^2 - 2x + 1	\( 41\cdot 9685993193^{2} \)	18T968	Trivial
18.4.4034193957798220415707.1	x^18 - 3x^14 - 2x^13 - 5x^12 - 5x^11 - 4x^10 - 7x^9 - 4x^8 - 5x^7 - 5x^6 - 2x^5 - 3x^4 + 1	\( -\,43\cdot 9685993193^{2} \)	18T968	Trivial
18.8.4714971270006434875019.1	x^18 - x^17 - 8x^16 + 5x^15 + 28x^14 - 18x^13 - 64x^12 + 44x^11 + 86x^10 - 56x^9 - 56x^8 + 38x^7 + 23x^6 - 16x^5 - 17x^4 + 6x^3 + 8x^2 - x - 1	\( -\,19\cdot 37^{2}\cdot 89\cdot 757^{2}\cdot 59617^{2} \)	18T968	Trivial
18.6.4854672125686801686113.1	x^18 - x^16 - 3x^15 - 5x^14 - 2x^13 + 5x^11 + 9x^10 + 9x^9 + 9x^8 + 5x^7 - 2x^5 - 5x^4 - 3x^3 - x^2 + 1	\( 17^{3}\cdot 994046201^{2} \)	18T968	Trivial
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
18.6.6848747881843490473177.1	x^18 - 7x^17 + 21x^16 - 39x^15 + 51x^14 - 42x^13 + 6x^12 + 48x^11 - 97x^10 + 117x^9 - 97x^8 + 48x^7 + 6x^6 - 42x^5 + 51x^4 - 39x^3 + 21x^2 - 7x + 1	\( 73\cdot 9685993193^{2} \)	18T968	Trivial
18.6.7038753626787421437161.1	x^18 - 4x^17 + 12x^16 - 23x^15 + 23x^14 - 6x^13 - 48x^12 + 98x^11 - 67x^10 + 110x^8 - 114x^7 - 130x^6 + 74x^5 + 121x^4 + 25x^3 - 23x^2 - 11x - 1	\( 167^{2}\cdot 498761\cdot 711353^{2} \)	18T968	Trivial
18.4.7411658666652544484671.1	x^18 - 2x^17 + x^16 - 3x^15 + 5x^14 - 4x^13 + 6x^12 - 7x^11 + 7x^10 - 7x^9 + 7x^8 - 7x^7 + 6x^6 - 4x^5 + 5x^4 - 3x^3 + x^2 - 2x + 1	\( -\,79\cdot 9685993193^{2} \)	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
18.10.11933079900270646767029.1	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
18.8.19394593215706131190039.1	x^18 - 5x^17 - x^16 + 38x^15 - 29x^14 - 110x^13 + 108x^12 + 172x^11 - 126x^10 - 215x^9 + 30x^8 + 215x^7 + 49x^6 - 105x^5 - 81x^4 + 44x^3 + 23x^2 - 8x - 1	\( -\,2791^{3}\cdot 944497^{2} \)	18T968	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
18.8.53977668015744910360576.1	x^18 - 4x^16 + 5x^14 - 6x^12 + 12x^10 - x^8 - 23x^6 + 22x^4 - 8x^2 + 1	\( -\,2^{18}\cdot 453771377^{2} \)	18T968	Trivial
18.0.53977668015744910360576.2	x^18 - 3x^16 - 4x^14 + 11x^12 + 4x^10 + 4x^8 + 33x^6 + 32x^4 + 10x^2 + 1	\( -\,2^{18}\cdot 453771377^{2} \)	18T968	Trivial
18.0.54463704731702620585984.2	x^18 + 8x^16 + 22x^14 + 26x^12 + 20x^10 + 20x^8 + 6x^6 - 2x^4 + 5x^2 + 1	\( -\,2^{18}\cdot 109^{2}\cdot 4181741^{2} \)	18T968	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)
18.12.153849444412406174216731.1	x^18 - 9x^17 + 27x^16 - 12x^15 - 94x^14 + 154x^13 + 70x^12 - 316x^11 + 80x^10 + 304x^9 - 188x^8 - 154x^7 + 168x^6 + 28x^5 - 78x^4 + 5x^3 + 15x^2 - x - 1	\( -\,167\cdot 173\cdot 2307632671^{2} \)	18T968	Trivial (GRH)
18.12.1000242318837874626994967.1	x^18 - 4x^17 - 12x^16 + 54x^15 + 63x^14 - 307x^13 - 186x^12 + 961x^11 + 307x^10 - 1779x^9 - 187x^8 + 1893x^7 - 151x^6 - 988x^5 + 200x^4 + 161x^3 - 13x^2 - 11x - 1	\( -\,23^{3}\cdot 5569^{3}\cdot 21817^{2} \)	18T968	Trivial (GRH)
18.6.1161567916177719364943872.1	x^18 - 10x^16 + 37x^14 - 61x^12 + 51x^10 - 164x^8 + 686x^6 - 1283x^4 + 1109x^2 - 367	\( 2^{18}\cdot 367^{3}\cdot 299401^{2} \)	18T968	Trivial (GRH)
18.8.1821632477226108224536576.1	x^18 + 4x^16 - 2x^14 - 21x^12 - 6x^10 + 31x^8 + 7x^6 - 14x^4 + 1	\( -\,2^{18}\cdot 2791^{2}\cdot 944497^{2} \)	18T968	Trivial (GRH)
18.0.1821632477226108224536576.2	x^18 + 11x^16 + 40x^14 + 50x^12 - x^10 - 25x^8 + 23x^6 + 38x^4 + 13x^2 + 1	\( -\,2^{18}\cdot 2791^{2}\cdot 944497^{2} \)	18T968	Trivial
18.0.2047104877383620556488704.2	x^18 + 9x^16 + 32x^14 + 74x^12 + 152x^10 + 221x^8 + 180x^6 + 76x^4 + 15x^2 + 1	\( -\,2^{18}\cdot 23^{2}\cdot 5569^{2}\cdot 21817^{2} \)	18T968	Trivial
18.6.2275054731466132286603264.1	x^18 - 6x^16 + x^14 - 6x^12 - 22x^10 - 4x^8 - 106x^6 - 7x^4 + 123x^2 - 41	\( 2^{18}\cdot 41^{3}\cdot 11221481^{2} \)	18T968	Trivial (GRH)
18.14.3079475991408027794037529.1	x^18 - 9x^17 + 24x^16 + 12x^15 - 151x^14 + 133x^13 + 328x^12 - 499x^11 - 350x^10 + 771x^9 + 235x^8 - 655x^7 - 141x^6 + 322x^5 + 67x^4 - 81x^3 - 14x^2 + 7x + 1	\( 41\cdot 641^{2}\cdot 1721\cdot 10306187^{2} \)	18T968	Trivial (GRH)
18.16.13281973786033764243536179.1	x^18 - 9x^17 + 25x^16 + 4x^15 - 137x^14 + 175x^13 + 179x^12 - 515x^11 + 116x^10 + 542x^9 - 442x^8 - 181x^7 + 375x^6 - 49x^5 - 136x^4 + 35x^3 + 20x^2 - 3x - 1	\( -\,67\cdot 2113\cdot 9685993193^{2} \)	18T968	Trivial (GRH)
18.12.36374607805480156224815104.1	x^18 + 2x^16 - 19x^14 - 6x^12 + 104x^10 - 78x^8 - 88x^6 + 105x^4 - 21x^2 + 1	\( -\,2^{18}\cdot 11779563529^{2} \)	18T968	Trivial (GRH)
18.16.36374607805480156224815104.1	x^18 - 11x^16 + 39x^14 - 29x^12 - 110x^10 + 246x^8 - 204x^6 + 81x^4 - 15x^2 + 1	\( -\,2^{18}\cdot 11779563529^{2} \)	18T968	Trivial (GRH)