Global number field search results

Further refine search

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 1191)

Label	Polynomial	Discriminant	Galois group	Class group
32.0.14648040110065267094876580444599852735215435776.1	x^32 - x^16 + 1	\( 2^{128}\cdot 3^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[3, 3]$ (GRH)
32.0.51922968585348276285304963292200960000000000000000.1	x^32 + 2207x^16 + 1	\( 2^{128}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[17]$ (GRH)
32.0.5241670721450327242974152113348873388724842246701056.1	x^32 - 15x^30 + 134x^28 - 793x^26 + 3496x^24 - 11638x^22 + 30241x^20 - 60672x^18 + 94862x^16 - 111861x^14 + 99380x^12 - 61666x^10 + 26973x^8 - 6636x^6 + 1086x^4 - 36x^2 + 1	\( 2^{32}\cdot 3^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[40]$ (GRH)
32.0.11308580273943039971119355619759072515285051093549056.1	x^32 + 449x^16 + 65536	\( 2^{128}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[136]$ (GRH)
32.0.186221552718646678775874367536462493032617340087890625.1	x^32 - x^31 + 23x^30 - 12x^29 + 329x^28 - 122x^27 + 2779x^26 - 327x^25 + 16520x^24 - 338x^23 + 64543x^22 + 7650x^21 + 180555x^20 + 24855x^19 + 346044x^18 + 50946x^17 + 490499x^16 + 64136x^15 + 494181x^14 + 64009x^13 + 369102x^12 + 46478x^11 + 187873x^10 + 28296x^9 + 67299x^8 + 9995x^7 + 13558x^6 + 2674x^5 + 1791x^4 + 184x^3 + 62x^2 - 4x + 1	\( 3^{16}\cdot 5^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[2040]$ (GRH)
32.0.522985347130850714438199116261670575164549527299424256.1	x^32 + 43x^28 + 691x^24 + 5146x^20 + 17903x^16 + 25954x^12 + 11826x^8 + 876x^4 + 1	\( 2^{64}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[24, 24]$ (GRH)
32.0.15635882837354065773928209678057089399596629842162876416.1	x^32 - 353x^16 + 43046721	\( 2^{128}\cdot 11^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.0.18580171965640016453782803163423074549760000000000000000.1	x^32 + 45x^30 + 862x^28 + 9243x^26 + 61576x^24 + 268554x^22 + 790441x^20 + 1599264x^18 + 2244206x^16 + 2182743x^14 + 1454308x^12 + 646998x^10 + 183789x^8 + 30996x^6 + 2766x^4 + 108x^2 + 1	\( 2^{32}\cdot 5^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[8, 40, 40]$ (GRH)
32.0.20282409603651670423947251286016000000000000000000000000.2	x^32 + 29375x^16 + 390625	\( 2^{128}\cdot 5^{24} \)	$C_2^2\times C_8$ (as 32T37)	$[3, 246]$ (GRH)
32.0.40558185231562030583545760465225948212199635509568684161.1	x^32 - x^31 - 22x^30 + 9x^29 + 266x^28 - 2x^27 - 2597x^26 - 54x^25 + 20774x^24 + 1099x^23 - 128438x^22 - 27858x^21 + 651009x^20 + 153366x^19 - 2755230x^18 - 386184x^17 + 9170393x^16 + 1793642x^15 - 23184576x^14 - 6931256x^13 + 46258944x^12 + 5607104x^11 - 67085888x^10 + 6766080x^9 + 65201664x^8 + 3431936x^7 - 34820096x^6 - 14815232x^5 + 13553664x^4 + 2523136x^3 - 753664x^2 + 131072x + 65536	\( 3^{16}\cdot 7^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[15, 15]$ (GRH)
32.0.139694596386578246067777447172163512565760000000000000000.1	x^32 - 24x^30 + 372x^28 - 3360x^26 + 21794x^24 - 91200x^22 + 277384x^20 - 571296x^18 + 868896x^16 - 931104x^14 + 740368x^12 - 405120x^10 + 161928x^8 - 41472x^6 + 7072x^4 - 384x^2 + 16	\( 2^{124}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[340]$ (GRH)
32.0.139694596386578246067777447172163512565760000000000000000.2	x^32 + 24x^30 + 372x^28 + 3360x^26 + 21794x^24 + 91200x^22 + 277384x^20 + 571296x^18 + 868896x^16 + 931104x^14 + 740368x^12 + 405120x^10 + 161928x^8 + 41472x^6 + 7072x^4 + 384x^2 + 16	\( 2^{124}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[21, 840]$ (GRH)
32.0.226429538761357513323150294281958672053835192027364458496.1	x^32 + 625279x^16 + 43046721	\( 2^{128}\cdot 13^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.0.343518132400968646195554032900431766403471261479800406016.1	x^32 - 30x^30 + 536x^28 - 6344x^26 + 55936x^24 - 372416x^22 + 1935424x^20 - 7766016x^18 + 24284672x^16 - 57272832x^14 + 101765120x^12 - 126291968x^10 + 110481408x^8 - 54362112x^6 + 17793024x^4 - 1179648x^2 + 65536	\( 2^{48}\cdot 3^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[3, 120]$ (GRH)
32.0.343518132400968646195554032900431766403471261479800406016.2	x^32 + 30x^30 + 536x^28 + 6344x^26 + 55936x^24 + 372416x^22 + 1935424x^20 + 7766016x^18 + 24284672x^16 + 57272832x^14 + 101765120x^12 + 126291968x^10 + 110481408x^8 + 54362112x^6 + 17793024x^4 + 1179648x^2 + 65536	\( 2^{48}\cdot 3^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[8, 1640]$ (GRH)
32.0.2235113542185251937084439154754616201052160000000000000000.1	x^32 - 390625x^16 + 152587890625	\( 2^{128}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.32.2235113542185251937084439154754616201052160000000000000000.1	x^32 - 48x^30 + 984x^28 - 11328x^26 + 81260x^24 - 382560x^22 + 1217920x^20 - 2670144x^18 + 4065711x^16 - 4291632x^14 + 3096208x^12 - 1480992x^10 + 444972x^8 - 76608x^6 + 6448x^4 - 192x^2 + 1	\( 2^{128}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	Trivial (GRH)
32.0.2235113542185251937084439154754616201052160000000000000000.2	x^32 + 48x^30 + 984x^28 + 11328x^26 + 81260x^24 + 382560x^22 + 1217920x^20 + 2670144x^18 + 4065711x^16 + 4291632x^14 + 3096208x^12 + 1480992x^10 + 444972x^8 + 76608x^6 + 6448x^4 + 192x^2 + 1	\( 2^{128}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[42, 714]$ (GRH)
32.0.2235113542185251937084439154754616201052160000000000000000.3	x^32 - 223x^16 + 65536	\( 2^{128}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[3, 4080]$ (GRH)
32.0.2235113542185251937084439154754616201052160000000000000000.4	x^32 + 32x^30 + 464x^28 + 4032x^26 + 23400x^24 + 95680x^22 + 283360x^20 + 615296x^18 + 978421x^16 + 1101648x^14 + 711048x^12 - 239392x^10 - 1255068x^8 - 1437408x^6 - 736112x^4 - 140992x^2 + 4866436	\( 2^{128}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[7, 9520]$ (GRH)
32.0.2235113542185251937084439154754616201052160000000000000000.5	x^32 - 32x^30 + 464x^28 - 4032x^26 + 23400x^24 - 95680x^22 + 283360x^20 - 615296x^18 + 978421x^16 - 1101648x^14 + 711048x^12 + 239392x^10 - 1255068x^8 + 1437408x^6 - 736112x^4 + 140992x^2 + 4866436	\( 2^{128}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[3, 240]$ (GRH)
32.0.2235113542185251937084439154754616201052160000000000000000.6	x^32 - 16x^30 + 152x^28 - 960x^26 + 4524x^24 - 16160x^22 + 45184x^20 - 97984x^18 + 163951x^16 - 248976x^14 + 666768x^12 - 918880x^10 - 1388052x^8 + 2947392x^6 - 738128x^4 - 141376x^2 + 4879681	\( 2^{128}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[6, 102]$ (GRH)
32.0.2235113542185251937084439154754616201052160000000000000000.7	x^32 + 16x^30 + 152x^28 + 960x^26 + 4524x^24 + 16160x^22 + 45184x^20 + 97984x^18 + 163951x^16 + 248976x^14 + 666768x^12 + 918880x^10 - 1388052x^8 - 2947392x^6 - 738128x^4 + 141376x^2 + 4879681	\( 2^{128}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[14, 14]$ (GRH)
32.0.2235113542185251937084439154754616201052160000000000000000.8	x^32 - 16x^31 + 104x^30 - 320x^29 + 260x^28 + 1232x^27 - 3472x^26 + 208x^25 + 11050x^24 - 10400x^23 - 19240x^22 + 32240x^21 + 21840x^20 - 58800x^19 - 18600x^18 + 76960x^17 + 29237x^16 - 181936x^15 + 2343360x^14 - 14637840x^13 + 83608980x^12 - 315275168x^11 + 945709544x^10 - 2176666960x^9 + 3968694340x^8 - 5704396048x^7 + 6462476552x^6 - 5703032384x^5 + 3845008700x^4 - 1914237040x^3 + 663710864x^2 - 143187248x + 57526849	\( 2^{128}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.0.2235113542185251937084439154754616201052160000000000000000.9	x^32 - 81343x^16 + 4294967296	\( 2^{128}\cdot 3^{16}\cdot 5^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.0.4046674754963777806715657550724832045209369204607193972736.1	x^32 - 45x^30 + 991x^28 - 13806x^26 + 134311x^24 - 955614x^22 + 5086474x^20 - 20412324x^18 + 61603217x^16 - 138056868x^14 + 224682160x^12 - 255944832x^10 + 193736448x^8 - 88639488x^6 + 22093824x^4 - 1769472x^2 + 65536	\( 2^{32}\cdot 7^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[3, 120]$ (GRH)
32.0.16558545548645863110798599687464368531777983698317749518336.1	x^32 + 3437249x^16 + 4294967296	\( 2^{128}\cdot 17^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.0.30424831247408100720538934941471930111515239368421944590336.1	x^32 - 8x^31 + 4x^30 + 80x^29 + 234x^28 - 2264x^27 + 1136x^26 + 10616x^25 + 22459x^24 - 162808x^23 + 119568x^22 + 179256x^21 + 890618x^20 - 3819200x^19 + 4810220x^18 - 5531224x^17 + 16043315x^16 - 34704128x^15 + 51652776x^14 - 70800080x^13 + 94104568x^12 - 109734560x^11 + 111890280x^10 - 102977936x^9 + 84840210x^8 - 61558848x^7 + 39138560x^6 - 21489824x^5 + 9918048x^4 - 3743168x^3 + 1107472x^2 - 230048x + 24964	\( 2^{124}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[584]$ (GRH)
32.0.30424831247408100720538934941471930111515239368421944590336.2	x^32 - 16x^31 + 168x^30 - 1280x^29 + 7916x^28 - 40992x^27 + 183240x^26 - 716976x^25 + 2483598x^24 - 7665216x^23 + 21161272x^22 - 52347824x^21 + 115997916x^20 - 229791536x^19 + 405338832x^18 - 632761344x^17 + 866628755x^16 - 1028800288x^15 + 1041246888x^14 - 878355456x^13 + 599463788x^12 - 322075968x^11 + 142388096x^10 - 73052800x^9 + 58308178x^8 - 43372256x^7 + 18813856x^6 - 1013184x^5 - 2770312x^4 + 344192x^3 + 226720x^2 + 172032x + 116092	\( 2^{124}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[3, 408]$ (GRH)
32.0.56078041364540796715130003864299185186303615574764488400321.1	x^32 - 6x^31 + 12x^30 - 8x^29 - 61x^28 + 506x^27 - 1228x^26 + 369x^25 + 4169x^24 - 17726x^23 + 39027x^22 - 19516x^21 - 109778x^20 + 448827x^19 - 649829x^18 - 336490x^17 + 1298951x^16 - 2098612x^15 + 7358296x^14 - 9364589x^13 - 18829429x^12 + 74949056x^11 + 31923685x^10 - 307629712x^9 - 163392606x^8 + 1472291823x^7 - 87681207x^6 - 5684845246x^5 + 4210930219x^4 + 12988964210x^3 - 17053058431x^2 - 12778402507x + 23670130201	\( 3^{16}\cdot 11^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.0.72742794030721358896825924818930661340866148471832275390625.2	x^32 - x^31 - 11x^30 + 22x^29 + 125x^28 - 275x^27 - 94x^26 + 1509x^25 + 761x^24 - 9994x^23 + 7117x^22 + 14365x^21 - 21524x^20 - 49605x^19 + 175483x^18 - 33646x^17 + 320975x^16 + 904191x^15 - 1392802x^14 - 8705985x^13 - 464629x^12 + 21128450x^11 + 15851367x^10 - 21617481x^9 - 24556589x^8 - 1571294x^7 + 11656076x^6 + 28090720x^5 + 24696960x^4 - 3964352x^3 + 7184704x^2 + 33890176x + 18800896	\( 3^{16}\cdot 5^{24}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[2, 8760]$ (GRH)
32.0.98151526926811424140342224755366174047996680049191641153536.1	x^32 - 697729x^16 + 152587890625	\( 2^{128}\cdot 19^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.0.143766767556164787106199922232179916833038973486480712890625.1	x^32 - 14x^31 + 78x^30 - 188x^29 + 49x^28 + 296x^27 + 3226x^26 - 21675x^25 + 63975x^24 - 129988x^23 + 275925x^22 - 780056x^21 + 2403348x^20 - 6843359x^19 + 18026035x^18 - 44145382x^17 + 102440247x^16 - 225677648x^15 + 478360878x^14 - 961434547x^13 + 1830768541x^12 - 3240171528x^11 + 5352278301x^10 - 8101027726x^9 + 11338690706x^8 - 14331413831x^7 + 16632009985x^6 - 17012899062x^5 + 15839257061x^4 - 12277480374x^3 + 8585381539x^2 - 4158477603x + 1842570739	\( 5^{16}\cdot 7^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[3, 182040]$ (GRH)
32.0.486797299958529611528622959063550881784243829894751113445376.1	x^32 + 13590431x^16 + 152587890625	\( 2^{128}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.32.486797299958529611528622959063550881784243829894751113445376.1	x^32 - 64x^30 + 1856x^28 - 32256x^26 + 374400x^24 - 3061760x^22 + 18135040x^20 - 78757888x^18 + 251040319x^16 - 582109152x^14 + 962963040x^12 - 1099478272x^10 + 820815552x^8 - 364686336x^6 + 79473664x^4 - 4710400x^2 + 37249	\( 2^{128}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	Trivial (GRH)
32.0.486797299958529611528622959063550881784243829894751113445376.2	x^32 + 277727x^16 + 1	\( 2^{128}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[24, 816]$ (GRH)
32.0.486797299958529611528622959063550881784243829894751113445376.3	x^32 - 5764801x^16 + 33232930569601	\( 2^{128}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.0.486797299958529611528622959063550881784243829894751113445376.4	x^32 - 16x^31 + 184x^30 - 1520x^29 + 10332x^28 - 58576x^27 + 287336x^26 - 1231568x^25 + 4678390x^24 - 15845360x^23 + 48150984x^22 - 131699184x^21 + 325050908x^20 - 724744720x^19 + 1460287592x^18 - 2657464016x^17 + 4362326951x^16 - 6446364592x^15 + 8552171016x^14 - 10150858480x^13 + 10733886004x^12 - 10060579408x^11 + 8306946984x^10 - 5997987856x^9 + 3753175770x^8 - 2012511408x^7 + 911516648x^6 - 342110896x^5 + 103611084x^4 - 24348880x^3 + 4169416x^2 - 463120x + 25054	\( 2^{128}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[4, 24, 24]$ (GRH)
32.0.486797299958529611528622959063550881784243829894751113445376.5	x^32 + 64x^30 + 1856x^28 + 32256x^26 + 374400x^24 + 3061760x^22 + 18135040x^20 + 78757888x^18 + 251040319x^16 + 582109152x^14 + 962963040x^12 + 1099478272x^10 + 820815552x^8 + 364686336x^6 + 79473664x^4 + 4710400x^2 + 37249	\( 2^{128}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[2, 2, 6, 7446]$ (GRH)
32.0.486797299958529611528622959063550881784243829894751113445376.6	x^32 + 48x^30 + 1128x^28 + 16800x^26 + 175124x^24 + 1338720x^22 + 7679056x^20 + 33321408x^18 + 109128129x^16 + 266433984x^14 + 474418816x^12 + 595027968x^10 + 501224448x^8 + 258048000x^6 + 68485120x^4 + 3145728x^2 + 65536	\( 2^{128}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[8, 8, 19856]$ (GRH)
32.0.486797299958529611528622959063550881784243829894751113445376.7	x^32 - 32x^30 + 608x^28 - 7680x^26 + 72384x^24 - 517120x^22 + 2891776x^20 - 12541952x^18 + 42535999x^16 - 109410336x^14 + 213070656x^12 - 292113152x^10 + 276113088x^8 - 134830080x^6 + 46443520x^4 - 7872512x^2 + 923521	\( 2^{128}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[8, 272]$ (GRH)
32.0.486797299958529611528622959063550881784243829894751113445376.8	x^32 + 32x^30 + 608x^28 + 7680x^26 + 72384x^24 + 517120x^22 + 2891776x^20 + 12541952x^18 + 42535999x^16 + 109410336x^14 + 213070656x^12 + 292113152x^10 + 276113088x^8 + 134830080x^6 + 46443520x^4 + 7872512x^2 + 923521	\( 2^{128}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.0.486797299958529611528622959063550881784243829894751113445376.9	x^32 - 16x^31 + 152x^30 - 1040x^29 + 5660x^28 - 25648x^27 + 99848x^26 - 340496x^25 + 1032070x^24 - 2809040x^23 + 6920264x^22 - 15521584x^21 + 31841628x^20 - 59944080x^19 + 103821240x^18 - 165701168x^17 + 243967235x^16 - 331507312x^15 + 412923000x^14 - 461181840x^13 + 521407068x^12 - 811933616x^11 + 915761288x^10 + 616194800x^9 - 2353432250x^8 + 200955248x^7 + 3097052168x^6 - 1972643120x^5 - 538044580x^4 + 656503280x^3 - 66006472x^2 - 29392688x + 46058146	\( 2^{128}\cdot 3^{16}\cdot 7^{16} \)	$C_2^2\times C_8$ (as 32T37)	$[2, 6, 1752]$ (GRH)
32.0.812088781483990309128958174884497308062548741403852104148801.1	x^32 - 6x^31 + 60x^30 - 224x^29 + 1535x^28 - 4738x^27 + 25964x^26 - 65115x^25 + 297875x^24 - 640430x^23 + 2525043x^22 - 4605832x^21 + 15332596x^20 - 24484833x^19 + 69153169x^18 - 95340760x^17 + 215848229x^16 - 262803136x^15 + 483174616x^14 - 502558589x^13 + 676121303x^12 - 589256116x^11 + 629711197x^10 - 456787822x^9 + 331102182x^8 - 161825433x^7 + 79124517x^6 - 28239532x^5 + 11237683x^4 - 3082612x^3 + 787679x^2 - 101101x + 10201	\( 3^{16}\cdot 13^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.32.1217670149940184118315109788118094613693071360000000000000000.1	x^32 - 2x^31 - 75x^30 + 138x^29 + 2388x^28 - 4028x^27 - 42773x^26 + 66098x^25 + 481690x^24 - 682632x^23 - 3607182x^22 + 4693052x^21 + 18500129x^20 - 22098426x^19 - 65844764x^18 + 72088572x^17 + 162802674x^16 - 162666214x^15 - 276907093x^14 + 250455230x^13 + 317228010x^12 - 256163602x^11 - 236469810x^10 + 166790036x^9 + 108780553x^8 - 64933250x^7 - 28450908x^6 + 13786936x^5 + 3719918x^4 - 1375256x^3 - 182100x^2 + 44248x + 1361	\( 2^{48}\cdot 5^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	Trivial (GRH)
32.0.1217670149940184118315109788118094613693071360000000000000000.1	x^32 - 2x^31 - 11x^30 + 18x^29 + 160x^28 - 204x^27 - 85x^26 - 478x^25 + 6534x^24 - 6664x^23 + 40562x^22 - 44612x^21 + 393657x^20 - 342938x^19 + 2686108x^18 - 1863692x^17 + 16372434x^16 - 7017350x^15 + 81158763x^14 - 18587306x^13 + 328619726x^12 - 26993986x^11 + 1066070798x^10 + 3685932x^9 + 2730786641x^8 + 132064062x^7 + 5372660276x^6 + 339375200x^5 + 7725637406x^4 + 460160520x^3 + 7334969884x^2 + 342344184x + 3492717761	\( 2^{48}\cdot 5^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[12, 48, 1968]$ (GRH)
32.0.2086819187651930534747998459703375504007855816232843362697216.1	x^32 - 3322751x^16 + 2821109907456	\( 2^{128}\cdot 23^{16} \)	$C_2^2\times C_8$ (as 32T37)	n/a
32.0.5595161445268686921572205116053290617295140691904726508240896.1	x^32 - 12x^30 + 218x^28 - 2352x^26 + 24189x^24 - 202718x^22 + 1499568x^20 - 9556173x^18 + 52856810x^16 - 251354668x^14 + 1019045945x^12 - 3471939654x^10 + 9723925436x^8 - 21689088233x^6 + 36301701182x^4 - 41004582111x^2 + 23670130201	\( 2^{32}\cdot 11^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[17, 136]$ (GRH)
32.0.7257879674078131427258907485712138496000000000000000000000000.3	x^32 - 23x^30 + 114x^28 + 675x^26 - 5812x^24 + 2385x^22 + 62416x^20 - 141927x^18 + 763268x^16 - 6766397x^14 + 26657386x^12 - 48774875x^10 + 42559893x^8 - 31754380x^6 + 49669184x^4 - 46720448x^2 + 18800896	\( 2^{32}\cdot 5^{24}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[2, 4, 4, 584]$ (GRH)
32.32.22512804325029881197071829100162696243017892592340199408664576.1	x^32 - 60x^30 + 1499x^28 - 20332x^26 + 164371x^24 - 824692x^22 + 2624266x^20 - 5396088x^18 + 7298927x^16 - 6560964x^14 + 3912050x^12 - 1521784x^10 + 372978x^8 - 54264x^6 + 4236x^4 - 144x^2 + 1	\( 2^{64}\cdot 3^{16}\cdot 17^{28} \)	$C_2^2\times C_8$ (as 32T37)	$[2]$ (GRH)