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 all 28 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.398525415137778548683.1	x^18 + 6x^16 - 5x^15 + 15x^14 - 25x^13 + 31x^12 - 50x^11 + 59x^10 - 63x^9 + 72x^8 - 64x^7 + 54x^6 - 44x^5 + 29x^4 - 16x^3 + 9x^2 - 3x + 1	\( -\,7^{16}\cdot 43\cdot 278881 \)	18T857	Trivial
18.6.9020122667090838004928525.1	x^18 + x^16 - 6x^15 - 5x^14 - 5x^13 + 11x^12 + 20x^11 + 16x^10 - 8x^9 - 27x^8 - 22x^7 + 2x^6 + 17x^5 + 11x^4 - 2x^3 - 5x^2 - x + 1	\( 5^{2}\cdot 13^{15}\cdot 7048913 \)	18T857	Trivial (GRH)
18.8.9480778877639637107421875.1	x^18 + x^16 - 6x^15 - 7x^14 - 5x^13 + 13x^12 + 28x^11 + 17x^10 - 14x^9 - 40x^8 - 24x^7 + 8x^6 + 26x^5 + 12x^4 - 4x^3 - 7x^2 - x + 1	\( -\,5^{9}\cdot 7^{12}\cdot 350701399 \)	18T857	Trivial (GRH)
18.10.15484366983534577619251501.1	x^18 - 5x^16 - 6x^15 + 5x^14 + 25x^13 + 21x^12 - 20x^11 - 57x^10 - 38x^9 + 28x^8 + 64x^7 + 34x^6 - 18x^5 - 32x^4 - 12x^3 + 5x^2 + 5x + 1	\( 13^{15}\cdot 53\cdot 5707781 \)	18T857	Trivial (GRH)
18.12.129673881181261864685546875.1	x^18 - 11x^16 - 6x^15 + 43x^14 + 55x^13 - 51x^12 - 172x^11 - 99x^10 + 178x^9 + 320x^8 + 88x^7 - 224x^6 - 234x^5 - 44x^4 + 60x^3 + 43x^2 + 11x + 1	\( -\,5^{9}\cdot 7^{12}\cdot 71\cdot 67559689 \)	18T857	Trivial (GRH)
18.16.3520799260895172463279296875.1	x^18 - 17x^16 - 6x^15 + 113x^14 + 85x^13 - 353x^12 - 452x^11 + 422x^10 + 1084x^9 + 287x^8 - 1014x^7 - 1060x^6 - 61x^5 + 507x^4 + 362x^3 + 113x^2 + 17x + 1	\( -\,5^{9}\cdot 7^{12}\cdot 41\cdot 419\cdot 1399\cdot 5419 \)	18T857	Trivial (GRH)
18.14.3671787551620818172076520389.1	x^18 - 17x^16 - 6x^15 + 115x^14 + 85x^13 - 379x^12 - 460x^11 + 547x^10 + 1162x^9 + 36x^8 - 1264x^7 - 934x^6 + 194x^5 + 632x^4 + 388x^3 + 115x^2 + 17x + 1	\( 13^{15}\cdot 701\cdot 6421\cdot 15937 \)	18T857	Trivial (GRH)
18.8.24704970275997896785381087551.1	x^18 - 5x^17 + 14x^16 - 25x^15 + 21x^14 + 9x^13 - 75x^12 + 169x^11 - 222x^10 + 218x^9 - 79x^8 - 126x^7 + 75x^6 - 103x^5 + 65x^4 + 597x^3 - 640x^2 - 104x + 211	\( -\,3^{9}\cdot 7^{15}\cdot 43^{2}\cdot 337^{2}\cdot 1259 \)	18T857	Trivial (GRH)
18.14.136526245789422674995678150633.1	x^18 - 7x^17 + x^16 + 59x^15 - 27x^14 - 132x^13 + 82x^12 - 244x^11 - 620x^10 + 394x^9 + 359x^8 - 524x^7 + 893x^6 + 1342x^5 - 469x^4 - 802x^3 - 130x^2 + 4x + 1	\( 13^{15}\cdot 181\cdot 233^{2}\cdot 521^{2} \)	18T857	Trivial (GRH)
18.18.176690170887148094026784640733.1	x^18 - 23x^16 - 6x^15 + 215x^14 + 115x^13 - 1029x^12 - 860x^11 + 2544x^10 + 3112x^9 - 2531x^8 - 5318x^7 - 986x^6 + 2961x^5 + 2659x^4 + 1038x^3 + 215x^2 + 23x + 1	\( 13^{15}\cdot 3451931000569 \)	18T857	Trivial (GRH)
18.10.10557375333191113763691266310144.1	x^18 - 18x^16 - 12x^15 + 135x^14 + 180x^13 - 612x^12 - 1080x^11 + 2079x^10 + 3704x^9 - 5346x^8 - 9036x^7 + 8169x^6 + 15444x^5 - 3816x^4 - 13104x^3 - 3024x^2 + 1728x + 64	\( 2^{24}\cdot 3^{46}\cdot 71 \)	18T857	Trivial (GRH)
18.6.10557375333191113763691266310144.1	x^18 + 18x^16 + 81x^14 - 72x^13 - 102x^12 - 756x^11 - 1062x^10 - 1004x^9 - 972x^8 + 2088x^7 + 225x^6 + 2916x^5 - 792x^4 - 2832x^3 + 432x^2 + 576x + 64	\( 2^{24}\cdot 3^{46}\cdot 71 \)	18T857	Trivial (GRH)
18.0.11759452462469462530524552364032.1	x^18 + 60x^16 - 40x^15 + 1458x^14 - 1944x^13 + 19430x^12 - 36612x^11 + 165189x^10 - 348920x^9 + 964062x^8 - 1863372x^7 + 3719465x^6 - 5763924x^5 + 8297016x^4 - 9426624x^3 + 8598384x^2 - 5005632x + 1560896	\( -\,2^{18}\cdot 3^{18}\cdot 7^{15}\cdot 29^{3} \)	18T857	Trivial (GRH)
18.10.1011167298805722181508656609099776.1	x^18 - 18x^16 - 8x^15 + 45x^14 + 96x^13 + 468x^12 - 288x^11 - 1605x^10 + 512x^9 - 2394x^8 - 4536x^7 + 11599x^6 + 8064x^5 - 16296x^4 - 3584x^3 + 12096x^2 - 3584	\( 2^{39}\cdot 3^{18}\cdot 7^{15} \)	18T857	Trivial (GRH)
18.12.51096294546839412676148707927734375.1	x^18 - 18x^16 - 135x^15 - 855x^14 + 2664x^13 + 16536x^12 + 35649x^11 + 86868x^10 - 662256x^9 - 1868265x^8 + 954900x^7 + 9189660x^6 + 3497886x^5 - 13877136x^4 - 8094474x^3 + 5595606x^2 + 4107591x + 603649	\( -\,3^{36}\cdot 5^{9}\cdot 19^{3}\cdot 71^{4} \)	18T857	Trivial (GRH)
18.12.295535253012026694638815126273130496.1	x^18 - 18x^16 - 24x^15 - 27x^14 + 288x^13 + 1524x^12 - 3141x^10 - 4416x^9 - 9882x^8 + 14328x^7 + 14583x^6 - 17280x^5 + 18072x^4 + 7680x^3 - 29376x^2 + 8704	\( -\,2^{39}\cdot 3^{42}\cdot 17^{3} \)	18T857	Trivial (GRH)
18.12.48801053907192911222729739691193359375.1	x^18 - 6x^17 - 132x^16 + 548x^15 + 8312x^14 - 15681x^13 - 302453x^12 - 72891x^11 + 6132831x^10 + 13144625x^9 - 52777043x^8 - 252477790x^7 - 152131512x^6 + 1244201712x^5 + 3892288402x^4 + 5616772596x^3 + 4623947060x^2 + 2061278913x + 329341949	\( -\,5^{9}\cdot 7^{12}\cdot 41^{2}\cdot 251\cdot 65409469^{2} \)	18T857	$[3]$ (GRH)
18.10.315354497788882418993233673419533203125.1	x^18 - 7x^17 - 91x^16 + 823x^15 + 2288x^14 - 37506x^13 + 27317x^12 + 802216x^11 - 2365365x^10 - 6737760x^9 + 43676548x^8 - 26267862x^7 - 298465159x^6 + 784800422x^5 - 39173568x^4 - 3079626438x^3 + 6140547357x^2 - 5276020218x + 1789324621	\( 5^{9}\cdot 7^{12}\cdot 41\cdot 139^{2}\cdot 121349929^{2} \)	18T857	$[3]$ (GRH)
18.14.1484875323272941639219759100572157607936.1	x^18 - 6x^17 - 174x^16 + 1418x^15 + 9183x^14 - 114246x^13 - 45249x^12 + 3906366x^11 - 9250809x^10 - 55245248x^9 + 276982620x^8 + 64877160x^7 - 2854359357x^6 + 5466517950x^5 + 5498508363x^4 - 34368736612x^3 + 50028443868x^2 - 29023484352x + 4128916321	\( 2^{18}\cdot 3^{27}\cdot 73\cdot 3189897037^{2} \)	18T857	Trivial (GRH)
18.12.2781519119947489262355092486938201171875.1	x^18 - 3x^17 - 216x^16 + 39x^15 + 19896x^14 + 46632x^13 - 900210x^12 - 4347954x^11 + 16346880x^10 + 156699733x^9 + 118087020x^8 - 2202823131x^7 - 7870564363x^6 - 203134881x^5 + 61730463267x^4 + 178677196446x^3 + 243718173702x^2 + 168126981534x + 46470800799	\( -\,3^{24}\cdot 5^{9}\cdot 19^{2}\cdot 199\cdot 264935899^{2} \)	18T857	Trivial (GRH)
18.10.6867244576973684096872169267219884765625.1	x^18 - 4x^17 - 118x^16 + 618x^15 + 5114x^14 - 36841x^13 - 79332x^12 + 1072913x^11 - 752532x^10 - 15079175x^9 + 41375910x^8 + 64149377x^7 - 470393141x^6 + 585728929x^5 + 1137717969x^4 - 4711668497x^3 + 6735093618x^2 - 4710371951x + 1353125341	\( 5^{9}\cdot 7^{12}\cdot 181\cdot 37462668601^{2} \)	18T857	$[3]$ (GRH)
18.14.14503293777515810243222263717959408085625.1	x^18 - 7x^17 - 103x^16 + 937x^15 + 2933x^14 - 47143x^13 + 31349x^12 + 1093608x^11 - 3268795x^10 - 9845841x^9 + 65031017x^8 - 40903477x^7 - 469853154x^6 + 1288958095x^5 - 114785660x^4 - 5285633443x^3 + 11033016132x^2 - 9866585215x + 3469475203	\( 5^{4}\cdot 13^{15}\cdot 181^{2}\cdot 389\cdot 5964373^{2} \)	18T857	$[3]$ (GRH)
18.12.35767587485187533896383746613170763671875.1	x^18 - 4x^17 - 146x^16 + 313x^15 + 9545x^14 - 2065x^13 - 340175x^12 - 538830x^11 + 6336306x^10 + 22114246x^9 - 39707430x^8 - 329930479x^7 - 419052482x^6 + 1232709748x^5 + 5212337547x^4 + 8370279909x^3 + 7123141625x^2 + 3174608191x + 591169879	\( -\,5^{9}\cdot 7^{12}\cdot 71\cdot 47221^{2}\cdot 2890861^{2} \)	18T857	$[3]$ (GRH)
18.14.50504892913025399729453656274066127435625.1	x^18 - x^17 - 135x^16 + 299x^15 + 7337x^14 - 26371x^13 - 189044x^12 + 1065482x^11 + 1618181x^10 - 21266729x^9 + 26331093x^8 + 173217555x^7 - 646229978x^6 + 300860113x^5 + 2997941500x^4 - 8745926570x^3 + 11572272509x^2 - 7912659482x + 2273671009	\( 5^{4}\cdot 13^{15}\cdot 181\cdot 2953332121^{2} \)	18T857	$[3]$ (GRH)
18.10.167934190485676783463200582052921330078125.1	x^18 - 6x^17 - 184x^16 + 521x^15 + 15408x^14 + 3231x^13 - 672908x^12 - 1879383x^11 + 13386840x^10 + 79559527x^9 - 11020952x^8 - 1189453818x^7 - 3366477940x^6 + 1266037761x^5 + 28793196055x^4 + 77749789756x^3 + 105636350706x^2 + 76119957655x + 23276366329	\( 5^{9}\cdot 7^{12}\cdot 41\cdot 389246193841^{2} \)	18T857	$[3]$ (GRH)
18.16.180083807836107946968856890731528000000000.1	x^18 - x^17 - 128x^16 + 3x^15 + 6745x^14 + 7297x^13 - 182721x^12 - 427804x^11 + 2428094x^10 + 10108718x^9 - 6884230x^8 - 101964173x^7 - 171939012x^6 + 187792795x^5 + 1219578806x^4 + 2274145760x^3 + 2281855540x^2 + 1249636670x + 295064741	\( -\,2^{12}\cdot 5^{9}\cdot 7^{12}\cdot 379^{2}\cdot 106405699^{2} \)	18T857	$[3]$ (GRH)
18.14.621490009368905226882279513578805666015625.1	x^18 - 5x^17 - 157x^16 + 486x^15 + 10751x^14 - 9911x^13 - 403555x^12 - 460550x^11 + 7949527x^10 + 25467429x^9 - 52542708x^8 - 416975522x^7 - 585458473x^6 + 1502886480x^5 + 7472596864x^4 + 13917309913x^3 + 14049712931x^2 + 7530492799x + 1656514609	\( 5^{9}\cdot 7^{12}\cdot 701\cdot 2689^{2}\cdot 67346341^{2} \)	18T857	$[3]$ (GRH)
18.18.17363537439858654395185498512903406173828125.1	x^18 - 168x^16 - 245x^15 + 11507x^14 + 32286x^13 - 392323x^12 - 1673273x^11 + 6192513x^10 + 42146147x^9 - 12517755x^8 - 498874326x^7 - 807007244x^6 + 1787229816x^5 + 7089009467x^4 + 6983075268x^3 - 1206137365x^2 - 5694641308x - 2451406229	\( 5^{9}\cdot 7^{12}\cdot 41\cdot 281\cdot 236113465771^{2} \)	18T857	$[3]$ (GRH)