Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (50 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
11.3.124...376.1	$x^{11} - 11 x^{3} - 8$	$11$	[3,4]	$2^{25}\cdot 11^{11}\cdot 13$	$3$	$67.1149612375$	$692.8724020542852$			?	$S_{11}$ (as 11T8)	trivial	$2$	$6$	$2787639.21648$
11.1.116...287.1	$x^{11} - 99 x^{2} - 81$	$11$	[1,5]	$-\,3^{22}\cdot 11^{11}\cdot 13$	$3$	$124.997915911$	$849.9352215885555$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$26829947.3636$
11.1.942...247.1	$x^{11} + 11 x^{9} - 59049$	$11$	[1,5]	$-\,3^{26}\cdot 11^{11}\cdot 13$	$3$	$186.380902415$	$1384.9679325797322$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$244970704.802$
11.1.942...247.2	$x^{11} - 363 x^{2} - 594 x - 243$	$11$	[1,5]	$-\,3^{26}\cdot 11^{11}\cdot 13$	$3$	$186.380902415$	$1442.483570918464$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$260606056.721$
11.1.208...752.1	$x^{11} - 44 x^{9} + 726 x^{7} - 5324 x^{5} + 14641 x^{3} - 22528$	$11$	[1,5]	$-\,2^{18}\cdot 11^{19}\cdot 13$	$3$	$246.962662885$	$1391.0701736658914$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1944016552.46$
11.1.380...727.1	$x^{11} - 11 x^{9} - 216513$	$11$	[1,5]	$-\,3^{14}\cdot 11^{19}\cdot 13$	$3$	$321.574789642$	$3013.881853424313$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$4462118626.0$
11.1.380...727.2	$x^{11} - 33 x^{9} - 17537553$	$11$	[1,5]	$-\,3^{14}\cdot 11^{19}\cdot 13$	$3$	$321.574789642$	$1830.8574991422927$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$6934535437.05$
11.1.751...896.1	$x^{11} - 484 x^{7} + 58564 x^{3} - 1362944$	$11$	[1,5]	$-\,2^{33}\cdot 11^{20}\cdot 13$	$3$	$790.312425739$	$4645.9637941866895$			?	$S_{11}$ (as 11T8)	trivial	$2$	$5$	$1430081294600$
15.1.3703260525677583.1	$x^{15} - 2 x^{14} + x^{13} - x^{12} - 5 x^{11} + 4 x^{10} - 3 x^{9} + 2 x^{8} + 6 x^{7} - 3 x^{6} + 3 x^{5} - 4 x^{4} - 5 x^{3} - 3 x^{2} - 3 x - 1$	$15$	[1,7]	$-\,3\cdot 13^{3}\cdot 561866260913$	$3$	$10.912031669$	$8888625.705547903$			?	$S_{15}$ (as 15T104)	trivial	$2$	$7$	$39.9823344692$
15.3.11354350039657729.1	$x^{15} - 4 x^{14} + 5 x^{13} + x^{12} - 7 x^{11} + x^{10} + 7 x^{9} - 2 x^{8} - 8 x^{7} + 22 x^{6} - 37 x^{5} + 35 x^{4} - 20 x^{3} + 11 x^{2} - 7 x + 1$	$15$	[3,6]	$13^{2}\cdot 127^{2}\cdot 1609^{3}$	$3$	$11.7582895867$	$5603.285322545042$			?	$C_3\wr S_5$ (as 15T78)	trivial	$2$	$8$	$79.4890458165$
16.12.134...584.1	$x^{16} - 6 x^{15} - 2 x^{14} + 176 x^{13} - 989 x^{12} - 412 x^{11} + 14946 x^{10} - 19310 x^{9} - 58059 x^{8} + 112806 x^{7} + 17708 x^{6} + 13772 x^{5} - 313401 x^{4} + 252950 x^{3} + 32720 x^{2} - 44094 x - 7545$	$16$	[12,2]	$2^{24}\cdot 3^{4}\cdot 13^{2}\cdot 157^{2}\cdot 1327^{4}\cdot 7649$	$6$	$101.858835028$				?	$C_2^8.S_3\wr S_4$ (as 16T1947)	trivial	$2$	$13$	$59053365005.7$
18.0.828...936.1	$x^{18} + 4 x^{12} - 4 x^{9} + 13 x^{6} - 26 x^{3} + 13$	$18$	[0,9]	$-\,2^{18}\cdot 3^{18}\cdot 13^{8}$	$3$	$18.7601879359$				?	$\He_3^2:S_3^2$ (as 18T650)	trivial	$4$	$8$	$18508.8363905$
18.0.828...936.2	$x^{18} - 6 x^{12} - 6 x^{9} + 13 x^{6} + 26 x^{3} + 13$	$18$	[0,9]	$-\,2^{18}\cdot 3^{18}\cdot 13^{8}$	$3$	$18.7601879359$				?	$\He_3^2:S_3^2$ (as 18T650)	trivial	$4$	$8$	$20735.3162984$
18.0.272...627.1	$x^{18} - 5 x^{15} + x^{12} - 58 x^{9} + 1639 x^{6} - 7062 x^{3} + 11323$	$18$	[0,9]	$-\,3^{27}\cdot 13^{2}\cdot 19^{6}\cdot 67^{2}$	$4$	$29.4172293379$				?	$C_3\wr (C_3\times S_3)$ (as 18T584)	trivial	$6$	$8$	$1639391.44819$
18.0.122...168.1	$x^{18} - 2 x^{17} + 5 x^{16} - 4 x^{15} + 4 x^{14} - 4 x^{11} + x^{10} - 6 x^{9} - 5 x^{8} - 2 x^{7} + 16 x^{4} + 24 x^{3} + 17 x^{2} + 6 x + 1$	$18$	[0,9]	$-\,2^{16}\cdot 3^{9}\cdot 7^{16}\cdot 13^{4}$	$4$	$31.9804131992$					$\SL(2,8)^2:C_6$ (as 18T937)	trivial	$6$	$8$	$8118260.80498$
18.0.193...747.1	$x^{18} - x^{15} - 3 x^{12} - 6 x^{9} + 11 x^{6} + 22 x^{3} + 13$	$18$	[0,9]	$-\,3^{27}\cdot 13^{2}\cdot 107^{6}$	$3$	$32.8030801352$				?	$C_3\wr S_3^2$ (as 18T653)	trivial	$6$	$8$	$5910758.58006$
18.0.369...987.1	$x^{18} - 8 x^{15} - 37 x^{12} + 258 x^{9} + 2229 x^{6} - 5395 x^{3} + 41743$	$18$	[0,9]	$-\,3^{27}\cdot 13^{4}\cdot 19^{8}$	$3$	$34.0063314161$				?	$C_3^5.(C_3\times S_3)$ (as 18T454)	$[3]$	$6$	$8$	$1611178.39201$
18.0.369...987.2	$x^{18} - 2 x^{15} - 37 x^{12} - 132 x^{9} + 4503 x^{6} - 19825 x^{3} + 41743$	$18$	[0,9]	$-\,3^{27}\cdot 13^{4}\cdot 19^{8}$	$3$	$34.0063314161$				?	$C_3^5.(C_3\times S_3)$ (as 18T454)	$[3]$	$6$	$8$	$1452209.16804$
18.0.369...987.3	$x^{18} - 10 x^{15} + 158 x^{12} - 1038 x^{9} + 5943 x^{6} - 25220 x^{3} + 41743$	$18$	[0,9]	$-\,3^{27}\cdot 13^{4}\cdot 19^{8}$	$3$	$34.006331416120965$				?	$C_3^5.(C_3\times S_3)$ (as 18T454)	$[3]$	$6$	$8$	$2017841.569027805$
18.0.129...712.1	$x^{18} - 6 x^{17} + 17 x^{16} - 24 x^{15} + 16 x^{14} + 14 x^{11} - 35 x^{10} + 42 x^{9} + 7 x^{8} + 28 x^{7} + 52 x^{4} + 52 x^{3} + 65 x^{2} + 26 x + 13$	$18$	[0,9]	$-\,2^{12}\cdot 3^{9}\cdot 7^{16}\cdot 13^{6}$	$4$	$36.4552431875$	$257.34404899073485$				$\SL(2,8)^2:C_6$ (as 18T937)	trivial	$6$	$8$	$41447682.1458$
18.0.291...000.1	$x^{18} - 22 x^{15} + 250 x^{12} - 1634 x^{9} + 9425 x^{6} - 27040 x^{3} + 54080$	$18$	[0,9]	$-\,2^{18}\cdot 3^{20}\cdot 5^{8}\cdot 13^{8}$	$4$	$43.3415054956$	$424.80577976779654$				$C_3^4.S_3^2$ (as 18T413)	$[3]$	$4$	$8$	$139848639.045$
18.6.944...312.1	$x^{18} - 19 x^{16} - 14 x^{15} + 117 x^{14} + 104 x^{13} - 418 x^{12} - 444 x^{11} + 890 x^{10} + 1282 x^{9} - 793 x^{8} - 2154 x^{7} - 769 x^{6} + 932 x^{5} + 1107 x^{4} + 526 x^{3} + 134 x^{2} + 18 x + 1$	$18$	[6,6]	$2^{24}\cdot 3^{13}\cdot 13^{4}\cdot 17^{4}\cdot 23^{6}$	$5$	$52.5831065192$				?	$C_3^5:S_3^2$ (as 18T541)	$[3]$	$2$	$11$	$249959188.611$
18.0.206...907.2	$x^{18} - 42 x^{15} - 167 x^{12} + 13136 x^{9} - 110969 x^{6} + 5921929 x^{3} + 128210329$	$18$	[0,9]	$-\,3^{27}\cdot 13^{4}\cdot 19^{6}\cdot 67^{4}$	$4$	$62.4123377678$				?	$C_3\wr (C_3\times S_3)$ (as 18T584)	$[3]$	$6$	$8$	$495723249.783$
18.18.631...832.1	$x^{18} - 72 x^{16} + 2079 x^{14} - 31272 x^{12} + 266535 x^{10} - 4466 x^{9} - 1305720 x^{8} + 88686 x^{7} + 3537846 x^{6} - 560898 x^{5} - 4745520 x^{4} + 1142700 x^{3} + 2313441 x^{2} - 311922 x - 360386$	$18$	[18,0]	$2^{18}\cdot 3^{45}\cdot 13^{8}$	$3$	$97.4807959936$	$399.7723180357622$				$C_9^2:C_6$ (as 18T158)	trivial	$2$	$17$	$15747212661600$
18.14.197...648.1	$x^{18} - 47 x^{16} - 47 x^{15} + 899 x^{14} + 1798 x^{13} - 8043 x^{12} - 26826 x^{11} + 21861 x^{10} + 185806 x^{9} + 154879 x^{8} - 491467 x^{7} - 1167834 x^{6} - 436976 x^{5} + 1652420 x^{4} + 2980937 x^{3} + 2338635 x^{2} + 935454 x + 155909$	$18$	[14,2]	$2^{6}\cdot 13^{2}\cdot 17^{9}\cdot 67^{2}\cdot 101^{7}\cdot 179^{2}$	$6$	$118.035268408$	$604040.8065579127$			?	$C_3^6.A_4^2:D_4$ (as 18T921)	trivial	$2$	$15$	$5242948282790$
18.2.231...512.1	$x^{18} - 72 x^{15} + 36 x^{14} + 5712 x^{12} + 12024 x^{11} + 77958 x^{10} - 5152 x^{9} - 638496 x^{8} - 3394872 x^{7} - 7824204 x^{6} + 1372608 x^{5} + 40365648 x^{4} + 148451496 x^{3} + 254837349 x^{2} + 293877216 x + 300134656$	$18$	[2,8]	$2^{38}\cdot 3^{45}\cdot 13^{4}$	$3$	$119.084125734$				?	${}^2G(2,3)\wr C_2$ (as 18T952)	$[3]$	$2$	$9$	$353312749215$
18.6.122...152.1	$x^{18} + 72 x^{16} - 48 x^{15} + 1539 x^{14} - 2052 x^{13} + 12780 x^{12} - 24192 x^{11} + 42615 x^{10} - 74216 x^{9} + 18144 x^{8} + 143568 x^{7} - 358539 x^{6} + 677484 x^{5} - 921780 x^{4} + 780192 x^{3} - 386640 x^{2} + 103104 x - 11456$	$18$	[6,6]	$2^{28}\cdot 3^{45}\cdot 13^{6}\cdot 179^{2}$	$4$	$191.735916243$					$C_3^6.A_4^2:C_2^2$ (as 18T891)	trivial	$2$	$11$	$5694862726710000$
18.0.388...587.1	$x^{18} - 5 x^{17} - 388 x^{16} + 1895 x^{15} + 53742 x^{14} - 2501483 x^{13} - 5379364 x^{12} + 1291779016 x^{11} + 11535679898 x^{10} - 177256309790 x^{9} + 563135892127 x^{8} - 47099222096866 x^{7} - 1006994261594410 x^{6} - 9171517908797241 x^{5} + 182299081236148981 x^{4} + 2029933165042808933 x^{3} + 14137926945484811926 x^{2} + 24100348226462845274 x + 331301229942500093733$	$18$	[0,9]	$-\,3^{5}\cdot 13^{6}\cdot 61^{12}\cdot 7069^{6}$	$4$	$948.827688857$					$C_3^6:(C_2\times A_4)$ (as 18T611)	$[3, 3]$	$2$	$8$	$18856210183800000000$
18.0.388...587.2	$x^{18} - 6 x^{17} + 21 x^{16} + 5137 x^{15} - 51804 x^{14} - 1290722 x^{13} + 36154469 x^{12} - 521223572 x^{11} + 6038836206 x^{10} - 16578533427 x^{9} + 304983625322 x^{8} - 8454795436553 x^{7} + 33178851617452 x^{6} + 692158306635455 x^{5} - 2754562473379645 x^{4} - 43951803605317053 x^{3} + 188500024937395669 x^{2} + 212655440349014754 x + 286329779695199889$	$18$	[0,9]	$-\,3^{5}\cdot 13^{6}\cdot 61^{12}\cdot 7069^{6}$	$4$	$948.827688857$					$C_3^6:(C_2\times A_4)$ (as 18T611)	$[3, 3]$	$2$	$8$	$6614651445670000000$
18.0.349...283.1	$x^{18} - 1788 x^{15} + 1966668 x^{12} - 1619227253 x^{9} + 2349501559548 x^{6} - 2551860249998748 x^{3} + 1705037985527826781$	$18$	[0,9]	$-\,3^{7}\cdot 13^{6}\cdot 61^{12}\cdot 7069^{6}$	$4$	$1072.01490229$					$S_3\times C_3^3:A_4$ (as 18T347)	$[3, 3]$	$2$	$8$	$93871258993300000000$
18.0.314...547.1	$x^{18} - 3 x^{17} - 1741 x^{16} + 5750 x^{15} + 1345004 x^{14} - 4490355 x^{13} - 612411438 x^{12} + 1760207911 x^{11} + 185064723741 x^{10} - 322833949732 x^{9} - 39427315041634 x^{8} + 10809763495833 x^{7} + 5939165295762443 x^{6} + 3211879322637265 x^{5} - 571978159937264939 x^{4} + 122210076997098114 x^{3} + 23161926248083405077 x^{2} - 70066206954230444829 x + 728888560740521913681$	$18$	[0,9]	$-\,3^{9}\cdot 13^{6}\cdot 61^{12}\cdot 7069^{6}$	$4$	$1211.19563037$				?	$C_3^6:(C_2\times A_4)$ (as 18T609)	$[6, 6]$	$6$	$8$	$23101592188500000000$
18.18.973...400.1	$x^{18} - 120 x^{16} - 296 x^{15} + 3264 x^{14} + 9408 x^{13} - 38656 x^{12} - 109824 x^{11} + 251904 x^{10} + 614912 x^{9} - 1007616 x^{8} - 1757184 x^{7} + 2473984 x^{6} + 2408448 x^{5} - 3342336 x^{4} - 1212416 x^{3} + 1966080 x^{2} - 266240$	$18$	[18,0]	$2^{27}\cdot 3^{18}\cdot 5^{2}\cdot 13\cdot 43\cdot 781247\cdot 20541943834793\cdot 23806568934241927\cdot 35075122994025941$	$9$	$11347.8872176$				?	$S_{18}$ (as 18T983)	trivial	$2$	$17$	$50130297227300000000000000000000$
19.13.801...664.1	$x^{19} - 2 x^{18} - 18 x^{17} + 32 x^{16} + 132 x^{15} - 202 x^{14} - 502 x^{13} + 645 x^{12} + 1045 x^{11} - 1122 x^{10} - 1176 x^{9} + 1078 x^{8} + 700 x^{7} - 557 x^{6} - 220 x^{5} + 151 x^{4} + 34 x^{3} - 20 x^{2} - 2 x + 1$	$19$	[13,3]	$-\,2^{3}\cdot 13^{2}\cdot 17\cdot 3229\cdot 34365587\cdot 85132367\cdot 3692009831$	$7$	$53.9247520599$	$1.2041290670651694e+16$			✓	$S_{19}$ (as 19T8)	trivial	$2$	$15$	$23798894722.8$
20.4.438...216.1	$x^{20} - 6 x^{19} - 32 x^{18} + 310 x^{17} - 469 x^{16} - 3502 x^{15} + 23272 x^{14} - 25660 x^{13} - 272270 x^{12} + 560690 x^{11} + 3789962 x^{10} - 12395748 x^{9} - 17547575 x^{8} + 99212146 x^{7} - 13520212 x^{6} - 294729262 x^{5} + 16568237 x^{4} + 379284204 x^{3} + 703850006 x^{2} + 914384780 x + 329131259$	$20$	[4,8]	$2^{30}\cdot 13^{2}\cdot 127^{2}\cdot 1609^{4}\cdot 149563^{2}$	$5$	$85.5289866304$				?	$C_2^{10}.C_3\wr S_5$ (as 20T1048)	trivial	$2$	$11$	$334022260094$
20.8.253...000.1	$x^{20} - 1008 x^{18} - 8064 x^{17} + 308644 x^{16} + 5180224 x^{15} - 6775416 x^{14} - 816447168 x^{13} - 7805753008 x^{12} - 14705332352 x^{11} + 312302109824 x^{10} + 3437586736128 x^{9} + 18843275841536 x^{8} + 66362572400640 x^{7} + 160541265039360 x^{6} + 272705816576000 x^{5} + 325266292633600 x^{4} + 267064385536000 x^{3} + 143885746176000 x^{2} + 45833912320000 x + 6547701760000$	$20$	[8,6]	$2^{24}\cdot 3^{10}\cdot 5^{8}\cdot 7\cdot 13^{2}\cdot 61^{12}\cdot 97^{4}\cdot 103^{4}\cdot 509^{2}\cdot 28447^{2}$	$10$	$4170.89233566$	$35510085879.75981$				$A_5^4.C_2\wr A_4$ (as 20T1107)	trivial	$2$	$13$	$1347999509140000000000000000000$
20.16.345...000.1	$x^{20} - 4068 x^{18} - 32544 x^{17} + 4247054 x^{16} + 68929184 x^{15} - 1149507396 x^{14} - 36277810848 x^{13} - 188726719143 x^{12} + 3814685417568 x^{11} + 74673095388144 x^{10} + 637303513042368 x^{9} + 3319238672357216 x^{8} + 11545267037187840 x^{7} + 27847847642876160 x^{6} + 47276566606976000 x^{5} + 56384349017401600 x^{4} + 46295149129216000 x^{3} + 24942345133056000 x^{2} + 7945229393920000 x + 1135032770560000$	$20$	[16,2]	$2^{20}\cdot 3^{10}\cdot 5^{8}\cdot 13^{4}\cdot 61^{10}\cdot 12613^{4}\cdot 166539805319^{2}$	$7$	$7532.64841233$	$1455103668460.678$				$A_5\wr A_4.C_2$ (as 20T1077)	trivial	$2$	$17$	$2037564945480000000000000000000000$
21.3.396...527.1	$x^{21} - 5 x^{20} + 11 x^{19} - 20 x^{18} + 37 x^{17} - 68 x^{16} + 120 x^{15} - 168 x^{14} + 237 x^{13} - 331 x^{12} + 362 x^{11} - 431 x^{10} + 452 x^{9} - 381 x^{8} + 350 x^{7} - 238 x^{6} + 169 x^{5} - 90 x^{4} + 43 x^{3} + 6 x^{2} + 27$	$21$	[3,9]	$-\,13^{2}\cdot 1801^{2}\cdot 193327^{3}$	$3$	$14.8362250548$	$359846.7897340511$			?	$C_3^7.S_7$ (as 21T139)	trivial	$2$	$11$	$6158.71427835$
21.5.112...600.1	$x^{21} - x^{20} - 3 x^{19} + 10 x^{18} - 9 x^{17} - 5 x^{16} + 83 x^{15} - 139 x^{14} - 436 x^{13} - 411 x^{12} - 872 x^{11} - 742 x^{10} + 583 x^{9} + 984 x^{8} + 1484 x^{7} + 1498 x^{6} - 868 x^{5} - 1614 x^{4} - 396 x^{3} - 242 x^{2} - 180 x + 50$	$21$	[5,8]	$2^{8}\cdot 5^{2}\cdot 13^{6}\cdot 229^{6}\cdot 159191^{2}$	$5$	$46.6848227731$	$1641376.5539579347$			?	$C_3^7.C_2^6:A_7$ (as 21T148)	trivial	$2$	$12$	$5375052288.55$
21.21.122...944.1	$x^{21} - 7 x^{20} - x^{19} + 114 x^{18} - 219 x^{17} - 472 x^{16} + 1808 x^{15} - 333 x^{14} - 4832 x^{13} + 5022 x^{12} + 3881 x^{11} - 8733 x^{10} + 1621 x^{9} + 5276 x^{8} - 3399 x^{7} - 644 x^{6} + 1288 x^{5} - 333 x^{4} - 95 x^{3} + 69 x^{2} - 14 x + 1$	$21$	[21,0]	$2^{18}\cdot 13^{2}\cdot 73^{12}\cdot 347443^{2}$	$4$	$90.4845999233$	$864554.2095127514$			✓	$C_3^6.C_{21}:C_3$ (as 21T86)	trivial	$2$	$20$	$66161868019100$
21.19.460...104.1	$x^{21} - 45 x^{19} - 30 x^{18} + 729 x^{17} + 972 x^{16} - 4266 x^{15} - 9180 x^{14} - 6687 x^{13} - 2872 x^{12} + 131652 x^{11} + 443208 x^{10} + 46436 x^{9} - 1786608 x^{8} - 2821416 x^{7} - 29552 x^{6} + 4752864 x^{5} + 6645312 x^{4} + 4669568 x^{3} + 1886976 x^{2} + 419328 x + 39936$	$21$	[19,1]	$-\,2^{15}\cdot 3^{23}\cdot 13^{2}\cdot 313^{12}$	$4$	$186.079263523$					$C_3^7.C_2\wr C_7:C_3$ (as 21T137)	trivial	$2$	$19$	$681712691863000000$
21.15.283...256.1	$x^{21} - 6 x^{20} - 129 x^{19} + 738 x^{18} + 6841 x^{17} - 34182 x^{16} - 206917 x^{15} + 754770 x^{14} + 4078383 x^{13} - 7593138 x^{12} - 52093363 x^{11} + 8626390 x^{10} + 365734083 x^{9} + 439496302 x^{8} - 804532503 x^{7} - 2198991242 x^{6} - 1696579116 x^{5} - 3038803440 x^{4} - 11303652912 x^{3} - 18939196800 x^{2} - 14663981568 x - 4441714880$	$21$	[15,3]	$-\,2^{26}\cdot 13^{2}\cdot 73^{12}\cdot 1699^{2}\cdot 19440739^{2}$	$5$	$351.034784071$				?	$C_3^7.F_8:C_6$ (as 21T117)	$[3]$	$2$	$17$	$48439163443900000000$
22.0.233...016.1	$x^{22} + 58 x^{20} + 1489 x^{18} + 22320 x^{16} + 216663 x^{14} + 1424964 x^{12} + 6438231 x^{10} + 19757580 x^{8} + 39484992 x^{6} + 46601624 x^{4} + 25144376 x^{2} + 898976$	$22$	[0,11]	$-\,2^{45}\cdot 3^{28}\cdot 7^{4}\cdot 13\cdot 23^{4}\cdot 137^{16}\cdot 2161$	$7$	$2401.13774258$					$C_2^{11}.A_{11}$ (as 22T52)	not computed	$2$	$10$
22.14.935...064.1	$x^{22} - 58 x^{20} + 1489 x^{18} - 22320 x^{16} + 216663 x^{14} - 1424964 x^{12} + 6438231 x^{10} - 19757580 x^{8} + 39484992 x^{6} - 46601624 x^{4} + 25144376 x^{2} - 898976$	$22$	[14,4]	$2^{47}\cdot 3^{28}\cdot 7^{4}\cdot 13\cdot 23^{4}\cdot 137^{16}\cdot 2161$	$7$	$2557.31035725$					$C_2^{11}.A_{11}$ (as 22T52)	trivial	$2$	$17$	$10304301830700000000000000000000$
30.0.136...619.1	$x^{30} - 3 x + 3$	$30$	[0,15]	$-\,3^{30}\cdot 13\cdot 50\!\cdots\!87$	$3$	$86.6535707438$				✓	$S_{30}$ (as 30T5712)	$[2]$	$2$	$14$	$56438497078123610$
30.0.141...531.1	$x^{30} - x + 3$	$30$	[0,15]	$-\,13\cdot 179\cdot 560893979\cdot 1599364314633798641\cdot 6769077172765732520137982927$	$5$	$86.7637806276$	$1.1887130053860239e+29$			✓	$S_{30}$ (as 30T5712)	trivial	$2$	$14$	$256499963343328640$
30.2.239...125.1	$x^{30} - 5 x - 3$	$30$	[2,14]	$5^{30}\cdot 13\cdot 5801281\cdot 34\!\cdots\!09$	$4$	$129.604919856$				✓	$S_{30}$ (as 30T5712)	not computed	$2$	$15$
37.1.146...709.1	$x^{37} + 2 x - 1$	$37$	[1,18]	$13\cdot 79\cdot 3203\cdot 230203\cdot 34944191\cdot 52002217\cdot 4124383231\cdot 25\!\cdots\!59$	$8$	$65.3537130156$	$3.823841953282166e+33$			✓	$S_{37}$ (as 37T11)	trivial	$2$	$18$	$9551296549801247000$
37.1.739...704.1	$x^{37} + 2 x - 2$	$37$	[1,18]	$2^{36}\cdot 11\cdot 13\cdot 29\cdot 8111\cdot 32\!\cdots\!17$	$6$	$72.6657957379$	$2.0368533035272427e+29$			✓	$S_{37}$ (as 37T11)	trivial	$2$	$18$	$109736008063969670000$
37.1.124...256.1	$x^{37} + 2 x - 4$	$37$	[1,18]	$2^{70}\cdot 13\cdot 137\cdot 195791\cdot 10489284688357\cdot 5723750340436657\cdot 504174169295944373011$	$7$	$137.314984457$				?	$S_{37}$ (as 37T11)	not computed	$2$	$18$
38.0.195...488.1	$x^{38} - 2 x + 5$	$38$	[0,19]	$-\,2^{39}\cdot 13\cdot 35869\cdot 88799\cdot 604309\cdot 6594677\cdot 27890279\cdot 25456155281264080123\cdot 303856164543774260275357$	$9$	$175.59654618$				?	$S_{38}$ (as 38T76)	not computed	$2$	$18$