Number field search results

Results (1-50 of 81 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
29.1.186...489.1	x^29 - x^28 + 7x^27 + 7x^26 + 29x^25 + 70x^24 + 115x^23 + 217x^22 + 336x^21 + 447x^20 + 628x^19 + 758x^18 + 820x^17 + 951x^16 + 953x^15 + 866x^14 + 839x^13 + 574x^12 + 405x^11 + 413x^10 + 349x^9 + 268x^8 + 247x^7 - 13x^6 - 6x^5 + 265x^4 + 95x^3 - 98x^2 + 32x + 1	$29$	[1,14]	$887^{14}$	$1$	$26.493268480367817$				$D_{29}$ (as 29T2)	trivial	$2$	$14$	$961536136.7336683$
29.1.253...733.1	x^29 - x - 1	$29$	[1,14]	$41393681953973\cdot 61230132484136034758796880121$	$2$	$28.9870101558$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$3449310408.0836196$
29.1.756...121.1	x^29 - 9x^28 + 56x^27 - 308x^26 + 1574x^25 - 7243x^24 + 28966x^23 - 99448x^22 + 293090x^21 - 744900x^20 + 1641343x^19 - 3148829x^18 + 5274672x^17 - 7725970x^16 + 9897023x^15 - 11084677x^14 + 10859104x^13 - 9337717x^12 + 7122047x^11 - 4916951x^10 + 3150459x^9 - 1890622x^8 + 1028653x^7 - 470622x^6 + 165361x^5 - 41848x^4 + 8324x^3 - 1810x^2 + 323x - 1	$29$	[1,14]	$23^{14}\cdot 97^{14}$	$2$	$41.35395339075522$			not computed	$D_{29}$ (as 29T2)	trivial	$2$	$14$	$737823739010.7355$
29.1.107...689.1	x^29 - 12x^28 + 55x^27 - 97x^26 + 34x^25 + 11x^24 + 138x^23 - 214x^22 + 43x^21 + 224x^20 - 104x^19 - 50x^18 + 748x^17 - 1490x^16 + 1965x^15 - 460x^14 - 575x^13 + 2189x^12 - 1286x^11 - 53x^10 + 3178x^9 - 2804x^8 + 3117x^7 - 748x^6 + 585x^5 + 965x^4 + 480x^3 + 353x^2 + 369x - 1	$29$	[1,14]	$2287^{14}$	$1$	$41.85185385923885$				$D_{29}$ (as 29T2)	trivial	$2$	$14$	$4657227595142.479$
29.1.123...441.1	x^29 - 8x^28 + 6x^27 + 45x^26 + 49x^25 - 158x^24 - 252x^23 - 117x^22 + 459x^21 + 1008x^20 + 2232x^19 + 2691x^18 + 1728x^17 - 2718x^16 - 7677x^15 - 13104x^14 - 15537x^13 - 15042x^12 - 6534x^11 + 6768x^10 + 22065x^9 + 32523x^8 + 38385x^7 + 37197x^6 + 29657x^5 + 17606x^4 + 7536x^3 + 1998x^2 + 377x - 1	$29$	[1,14]	$2311^{14}$	$1$	$42.06330779500418$				$D_{29}$ (as 29T2)	trivial	$2$	$14$	$4095120529090.4673$
29.1.190...729.1	x^29 - 8x^28 + 42x^27 - 91x^26 + 71x^25 - 172x^24 + 980x^23 - 2477x^22 + 4032x^21 - 5998x^20 + 8995x^19 - 12396x^18 + 15464x^17 - 17477x^16 + 17661x^15 - 16777x^14 + 14899x^13 - 10749x^12 + 6197x^11 - 2594x^10 - 1233x^9 + 2318x^8 - 113x^7 - 855x^6 + 1459x^5 - 2625x^4 + 2079x^3 - 978x^2 + 419x + 1	$29$	[1,14]	$2383^{14}$	$1$	$42.69094266015672$				$D_{29}$ (as 29T2)	trivial	$2$	$14$	$6346995452652.517$
29.1.358...441.1	x^29 - x^28 - 7x^27 - 50x^26 + 119x^25 + 495x^24 + 59x^23 - 530x^22 + 637x^21 + 2591x^20 + 2977x^19 + 1178x^18 + 2213x^17 + 5385x^16 + 5965x^15 + 6650x^14 + 10883x^13 + 16281x^12 + 23955x^11 + 21146x^10 - 8059x^9 - 7103x^8 + 28957x^7 + 37734x^6 + 35524x^5 + 2552x^4 - 22800x^3 - 19616x^2 - 17024x - 11776	$29$	[1,14]	$2939^{14}$	$1$	$47.239277691781375$				$D_{29}$ (as 29T2)	trivial	$2$	$14$	$191758984500558.16$
29.1.894...288.1	x^29 + 4x - 4	$29$	[1,14]	$2^{28}\cdot 27325532669\cdot 12\!\cdots\!17$	$3$	$48.7519268384$			not computed	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$20818517115126.277$
29.1.177...701.1	x^29 + 2x - 1	$29$	[1,14]	$461801\cdot 20212226753\cdot 3536300443131271\cdot 539109057311673427$	$4$	$49.9213163004$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$19372925588185.117$
29.1.261...256.1	x^29 - 4x - 4	$29$	[1,14]	$2^{28}\cdot 53\cdot 179\cdot 10\!\cdots\!23$	$4$	$50.5881590927$			not computed	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$28349352931361.156$
29.29.383...121.1	x^29 - x^28 - 28x^27 + 27x^26 + 351x^25 - 325x^24 - 2600x^23 + 2300x^22 + 12650x^21 - 10626x^20 - 42504x^19 + 33649x^18 + 100947x^17 - 74613x^16 - 170544x^15 + 116280x^14 + 203490x^13 - 125970x^12 - 167960x^11 + 92378x^10 + 92378x^9 - 43758x^8 - 31824x^7 + 12376x^6 + 6188x^5 - 1820x^4 - 560x^3 + 105x^2 + 15x - 1	$29$	[29,0]	$59^{28}$	$1$	$51.2611268879$		✓	✓	$C_{29}$ (as 29T1)	trivial	$2$	$28$	$2275980944744796.5$
29.1.506...201.1	x^29 - 11x^28 + 45x^27 - 70x^26 + 66x^25 - 800x^24 + 4130x^23 - 11632x^22 + 26627x^21 - 43970x^20 + 56823x^19 - 114622x^18 + 216543x^17 - 400317x^16 + 743290x^15 - 1619073x^14 + 3038554x^13 - 4110770x^12 + 3834768x^11 - 1791942x^10 - 198548x^9 + 1096532x^8 - 913725x^7 + 101442x^6 + 212195x^5 - 352802x^4 + 186129x^3 - 93243x^2 + 23048x - 4757	$29$	[1,14]	$53^{14}\cdot 67^{14}$	$2$	$51.75620132238975$			not computed	$D_{29}$ (as 29T2)	trivial	$2$	$14$	$21909985755609.77$
29.1.574...129.1	x^29 - x^28 + 18x^27 + 12x^26 + 179x^25 + 123x^24 + 1662x^23 - 196x^22 + 11119x^21 - 9104x^20 + 47466x^19 - 44547x^18 + 83114x^17 - 23886x^16 - 121329x^15 + 248495x^14 - 275546x^13 - 188738x^12 + 573921x^11 - 476142x^10 + 379865x^9 - 32019x^8 + 20658x^7 - 6163x^6 - 27930x^5 + 2012x^4 - 1404x^3 + 2898x^2 - 594x + 81	$29$	[1,14]	$3583^{14}$	$1$	$51.98083920609783$				$D_{29}$ (as 29T2)	trivial	$2$	$14$	$133207857013622.31$
29.1.771...361.1	x^29 - 7x^28 + 47x^27 - 186x^26 + 710x^25 - 970x^24 + 1144x^23 + 2298x^22 - 8465x^21 + 16505x^20 - 20589x^19 + 3590x^18 + 30661x^17 - 81803x^16 + 117497x^15 - 94780x^14 + 10260x^13 + 127678x^12 - 249606x^11 + 245472x^10 - 99463x^9 - 191187x^8 + 582067x^7 - 785770x^6 + 915704x^5 - 793384x^4 + 541792x^3 - 324448x^2 + 144320x - 23552	$29$	[1,14]	$3659^{14}$	$1$	$52.51023015441575$				$D_{29}$ (as 29T2)	trivial	$2$	$14$	$1075559501191057.0$
29.1.142...409.1	x^29 - x^28 + 33x^27 - 64x^26 + 535x^25 - 1144x^24 + 5145x^23 - 10327x^22 + 31220x^21 - 55583x^20 + 124455x^19 - 188951x^18 + 323227x^17 - 411652x^16 + 521736x^15 - 591430x^14 + 489137x^13 - 738131x^12 + 175881x^11 - 1211717x^10 + 917449x^9 - 3034006x^8 + 2818536x^7 - 6798367x^6 + 6818314x^5 - 8408506x^4 + 7552950x^3 - 8000650x^2 + 5448750x - 1749375	$29$	[1,14]	$3823^{14}$	$1$	$53.633551708687826$				$D_{29}$ (as 29T2)	trivial	$2$	$14$	$254102374099303.56$
29.1.671...632.1	x^29 - 2x - 2	$29$	[1,14]	$2^{28}\cdot 3\cdot 11\cdot 563\cdot 13\!\cdots\!43$	$5$	$56.5790872551$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$167099208611677.7$
29.1.689...128.1	x^29 - x - 2	$29$	[1,14]	$2^{28}\cdot 23\cdot 2505541501481\cdot 44556647066894154934970530051$	$4$	$56.6301417736$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$261495167861816.16$
29.1.689...608.1	x^29 - x - 4	$29$	[1,14]	$2^{30}\cdot 13\cdot 3373\cdot 84163\cdot 17\!\cdots\!41$	$5$	$56.6301417737$			not computed	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$216030725427151.9$
29.1.689...864.1	x^29 - 2	$29$	[1,14]	$2^{28}\cdot 29^{29}$	$2$	$56.6301417737$			✓	$F_{29}$ (as 29T6)	trivial	$2$	$14$	$170509022606467.78$
29.1.707...096.1	x^29 + 2x - 2	$29$	[1,14]	$2^{28}\cdot 499\cdot 541\cdot 695389\cdot 2739817\cdot 5913513689\cdot 866002650952007$	$7$	$56.6799391738$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$88931326459060.03$
29.3.227...419.1	x^29 - 3x - 1	$29$	[3,13]	$-\,19\cdot 157273\cdot 116400694409\cdot 65\!\cdots\!93$	$4$	$74.8819740781$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$15$	$6315065032809016.0$
29.1.227...357.1	x^29 + 3x - 1	$29$	[1,14]	$17\cdot 41\cdot 74959\cdot 160217\cdot 2662789\cdot 25396823\cdot 76318073627\cdot 52654144463043283$	$8$	$74.8819740781$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$6546753152959768.0$
29.1.227...752.1	x^29 + 3x - 2	$29$	[1,14]	$2^{28}\cdot 8447\cdot 10\!\cdots\!11$	$3$	$74.8827563475$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$23857799922719012$
29.1.564...821.1	x^29 - 3x - 3	$29$	[1,14]	$3^{28}\cdot 13\cdot 41\cdot 389\cdot 1619\cdot 4483\cdot 202067\cdot 1052207903\cdot 7714356793195489$	$9$	$83.6518051917$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$29272458686891230$
29.1.565...237.1	x^29 + 4x - 1	$29$	[1,14]	$3\cdot 258439534144219859900797151\cdot 72911782755634284235524422729$	$3$	$83.6550844791$			not computed	$S_{29}$ (as 29T8)	$[2]$	$2$	$14$	$20099249152408180$
29.1.587...477.1	x^29 - 2x - 3	$29$	[1,14]	$43\cdot 907\cdot 40322333\cdot 5439157486181\cdot 68\!\cdots\!49$	$5$	$83.7658097346$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$47730899898626100$
29.1.587...973.1	x^29 - x - 3	$29$	[1,14]	$179\cdot 373\cdot 277813\cdot 42259019123\cdot 2243721410717\cdot 33399064272490942843393$	$6$	$83.7658106097$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$46185846405204810$
29.1.587...709.1	x^29 - 3	$29$	[1,14]	$3^{28}\cdot 29^{29}$	$2$	$83.7658106097$			✓	$F_{29}$ (as 29T6)	trivial	$2$	$14$	$49661461097293670$
29.1.587...445.1	x^29 + x - 3	$29$	[1,14]	$5\cdot 11\cdot 16381\cdot 127865750920013\cdot 1994744457920647\cdot 255618611114956521989$	$6$	$83.7658106097$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$42821205896121990$
29.1.610...597.1	x^29 + 3x - 3	$29$	[1,14]	$3^{28}\cdot 119533\cdot 419161\cdot 53\!\cdots\!29$	$4$	$83.8756304656$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$34353828610448830$
29.3.955...720.1	x^29 - 4x - 2	$29$	[3,13]	$-\,2^{28}\cdot 5\cdot 71\!\cdots\!99$	$3$	$99.8426318557$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$15$	$819283530647138000$
29.3.955...115.1	x^29 - 4x - 1	$29$	[3,13]	$-\,5\cdot 71\cdot 1070754779627347\cdot 25\!\cdots\!79$	$4$	$99.8426321041$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$15$	$440767023565659140$
29.1.955...448.1	x^29 + 4x - 2	$29$	[1,14]	$2^{28}\cdot 3\cdot 3783589506654278873\cdot 31\!\cdots\!07$	$4$	$99.8426323525$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$489687221548003600$
29.1.961...293.1	x^29 + 4x - 3	$29$	[1,14]	$3744524429\cdot 8675517281441\cdot 29\!\cdots\!37$	$3$	$99.863738041$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$632109057751709300$
29.1.462...688.1	x^29 - 2x - 4	$29$	[1,14]	$2^{54}\cdot 3\cdot 151\cdot 1208109059\cdot 46\!\cdots\!91$	$5$	$105.423300964$			not computed	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$2408495413358637000$
29.1.462...304.1	x^29 + 2x - 4	$29$	[1,14]	$2^{54}\cdot 853\cdot 133051\cdot 22\!\cdots\!27$	$4$	$105.423300965$			not computed	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$2017302844328075800$
29.1.185...096.1	x^29 - 3x - 4	$29$	[1,14]	$2^{57}\cdot 71\cdot 14785399\cdot 5818658096101217\cdot 210180474110289901$	$5$	$110.585227506$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$6702753215427773000$
29.1.185...720.1	x^29 + x - 4	$29$	[1,14]	$2^{57}\cdot 3\cdot 5\cdot 5205763\cdot 56893477\cdot 288984011824906401353807959$	$6$	$110.58527439$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$7158511448931481000$
29.1.154...216.1	x^29 + 5x - 2	$29$	[1,14]	$2^{26}\cdot 337\cdot 709\cdot 224066062071001\cdot 7834502381769247\cdot 54834197285853919$	$6$	$118.977638654$				$S_{29}$ (as 29T8)	trivial	$2$	$14$	$22143705810942657000$
29.3.617...291.1	x^29 - 5x - 3	$29$	[3,13]	$-\,17\cdot 640949\cdot 12442531\cdot 15716663\cdot 28\!\cdots\!59$	$5$	$124.803249184$			✓	$S_{29}$ (as 29T8)	not computed	$2$	$15$	$$
29.3.617...136.1	x^29 - 5x - 2	$29$	[3,13]	$-\,2^{28}\cdot 3\cdot 47\cdot 19231\cdot 1239599\cdot 17156593\cdot 53138329\cdot 7505402452445630661805687$	$8$	$124.80329013$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$15$	$48016386518967206000$
29.3.617...531.1	x^29 - 5x - 1	$29$	[3,13]	$-\,3\cdot 9533\cdot 2608914479\cdot 82\!\cdots\!11$	$4$	$124.80329013$			✓	$S_{29}$ (as 29T8)	not computed	$2$	$15$	$$
29.1.617...709.1	x^29 + 5x - 3	$29$	[1,14]	$23\cdot 79\cdot 107\cdot 931421\cdot 23882194037539\cdot 14\!\cdots\!69$	$6$	$124.803331076$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$21861542052281573000$
29.1.635...984.1	x^29 + 5x - 4	$29$	[1,14]	$2^{57}\cdot 37\cdot 1397743\cdot 85\!\cdots\!67$	$4$	$124.930431849$			✓	$S_{29}$ (as 29T8)	not computed	$2$	$14$	$$
29.1.994...125.1	x^29 - 5x - 5	$29$	[1,14]	$5^{28}\cdot 17\cdot 401\cdot 578483771\cdot 67676598636720696780695919103$	$5$	$126.870744047$			not computed	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$13281089874686380000$
29.1.956...541.1	x^29 - 4x - 5	$29$	[1,14]	$167\cdot 239\cdot 23\!\cdots\!57$	$3$	$137.171564666$			✓	$S_{29}$ (as 29T8)	not computed	$2$	$14$	$$
29.1.956...237.1	x^29 - 3x - 5	$29$	[1,14]	$42691141\cdot 481626857\cdot 2939004407579\cdot 35136939022453\cdot 45049443348110236823$	$5$	$137.172036998$			✓	$S_{29}$ (as 29T8)	trivial	$2$	$14$	$46446705639915990000$
29.1.956...893.1	x^29 - 2x - 5	$29$	[1,14]	$3\cdot 43\cdot 57617873845633\cdot 10667339907787007\cdot 12\!\cdots\!07$	$5$	$137.17203711$			✓	$S_{29}$ (as 29T8)	not computed	$2$	$14$	$$
29.1.956...389.1	x^29 - x - 5	$29$	[1,14]	$7976611\cdot 37252257474505795723\cdot 32\!\cdots\!13$	$3$	$137.17203711$			✓	$S_{29}$ (as 29T8)	not computed	$2$	$14$	$$
29.1.956...125.1	x^29 - 5	$29$	[1,14]	$5^{28}\cdot 29^{29}$	$2$	$137.17203711$			✓	$F_{29}$ (as 29T6)	trivial	$2$	$14$	$64731836915276810000$