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Label Polynomial Discriminant Galois group Class group
25.5.190...049.1 x25 - 4x24 + 4x23 + 5x22 - 20x21 + 18x20 + 19x19 - 28x18 - 2x16 + 2x15 - 28x14 - 29x13 + 120x12 + 59x11 - 112x10 - 35x9 + 16x8 - 23x7 + 29x6 + 32x5 - 21x4 - 12x3 + 7x2 + 2x - 1 \( 7^{10}\cdot 11^{20} \) $C_5\times D_5$ (as 25T3) trivial (GRH)
25.5.722...624.1 x25 - 3x24 + 4x23 - 7x22 + 5x21 - 6x20 + 28x19 - 37x18 + 24x17 + 60x15 - 133x14 + 74x13 + 37x12 - 24x11 - 112x10 + 155x9 - 56x8 - 45x7 + 51x6 - 17x5 + 3x4 - 3x3 + 3x - 1 \( 2^{30}\cdot 11^{20} \) $C_5\times D_5$ (as 25T3) trivial (GRH)
25.1.145...641.1 x25 - 3x24 + 9x23 - 22x22 + 41x21 - 60x20 + 66x19 - 47x18 + 6x17 + 48x16 - 82x15 + 76x14 + 11x13 - 138x12 + 280x11 - 336x10 + 317x9 - 205x8 + 144x7 - 109x6 + 126x5 - 104x4 + 76x3 - 23x2 + 10x + 1 \( 479^{12} \) $D_{25}$ (as 25T4) trivial (GRH)
25.1.213...801.1 x25 - 2x24 - x23 + 8x22 + 6x21 - 17x20 - 5x19 + 32x18 - 13x17 - 36x16 + 22x15 + 58x14 - 6x13 - 71x12 + 35x10 - 24x9 - 66x8 + 28x7 + 63x6 + 92x5 - 82x4 - 3x3 + 25x2 + 16x - 1 \( 599^{12} \) $D_{25}$ (as 25T4) trivial (GRH)
25.5.953...000.1 x25 - 5x24 + 10x23 - 10x22 + 17x20 - 25x19 + 10x18 + 55x17 - 150x16 + 156x15 - 100x14 + 115x13 - 60x12 - 175x11 + 208x10 + 70x9 - 80x8 - 70x7 - 25x6 + 20x5 + 15x4 + 15x3 + 10x2 - 1 \( 2^{20}\cdot 5^{40} \) $C_5\times D_5$ (as 25T3) trivial (GRH)
25.5.396...449.1 x25 - 3x24 + x23 - 3x22 + 19x21 - 17x20 - 8x19 - 27x18 + 13x17 + 72x16 + 7x15 + 58x14 - 37x13 - 186x12 + 151x11 - 314x10 + 404x9 - 330x8 + 297x7 - 201x6 + 123x5 - 65x4 + 32x3 - 18x2 + 7x - 1 \( 3^{10}\cdot 31^{20} \) $C_5\times D_5$ (as 25T3) trivial (GRH)
25.1.874...849.1 x25 - x - 1 \( 10667\cdot 282401201\cdot 925997749\cdot 31362479733103 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.901...401.1 x25 + x - 1 \( 13\cdot 2957\cdot 8969\cdot 6212881\cdot 42086382270382828249 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.425...361.1 x25 - 2x24 - x23 + 13x22 + 50x21 + 3x20 - 29x19 - 5x18 + 128x17 - 146x16 - 239x15 + 32x14 + 747x13 - 262x12 - 1333x11 - 456x10 + 1762x9 + 962x8 - 1685x7 - 1308x6 + 1439x5 + 1916x4 - 95x3 - 410x2 + 94x - 1 \( 1367^{12} \) $D_{25}$ (as 25T4) $[2, 2]$ (GRH)
25.5.188...376.1 x25 - 2x24 - 2x23 - 10x22 + 33x21 + 5x20 - 6x19 - 115x18 - 16x17 + 168x16 + 250x15 - 16x14 + 291x13 - 1042x12 + 750x11 - 1666x10 + 1541x9 - 903x8 + 418x7 + 161x6 - 27x5 + 92x4 + 3x3 + 8x2 + 4x - 1 \( 2^{20}\cdot 41^{20} \) $C_5\times D_5$ (as 25T3) trivial (GRH)
25.1.114...401.1 x25 - 4x24 + x23 + 2x22 + 5x21 + 38x20 + 24x19 - 79x18 - 45x17 - 175x16 - 246x15 + 78x14 + 160x13 + 28x12 + 1032x11 + 953x10 + 967x9 + 1690x8 + 1081x7 - 1035x6 - 715x5 - 2390x4 - 2966x3 - 1925x2 - 720x - 1003 \( 7^{12}\cdot 257^{12} \) $D_{25}$ (as 25T4) trivial (GRH)
25.1.123...944.1 x25 - x - 2 \( 2^{24}\cdot 739\cdot 12239\cdot 2507149\cdot 272308609\cdot 118872926969 \) $S_{25}$ (as 25T211) trivial (GRH)
25.5.300...849.1 x25 - 3x24 + x23 - 15x22 + 13x21 - 5x20 + 130x19 - 132x18 - 21x17 + 437x16 - 1713x15 + 747x14 + 4817x13 - 3107x12 - 7887x11 + 4826x10 + 5380x9 - 3452x8 + 864x7 - 1052x6 + 266x5 - 67x4 + 75x3 - 10x2 + 9x - 1 \( 3^{10}\cdot 61^{20} \) $C_5\times D_5$ (as 25T3) trivial (GRH)
25.1.447...857.1 x25 + 2x - 1 \( 2377\cdot 5147\cdot 460493604849521\cdot 7943531120919741043 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.335...881.1 x25 - 5x24 + 18x23 - 53x22 + 184x21 - 519x20 + 1425x19 - 2994x18 + 4254x17 - 2567x16 - 3146x15 + 8388x14 - 11301x13 - 6966x12 + 13530x11 + 11956x10 + 18271x9 + 21048x8 - 41862x7 - 65478x6 - 1959x5 + 35311x4 + 17869x3 - 2655x2 - 3850x - 2125 \( 2887^{12} \) $D_{25}$ (as 25T4) trivial (GRH)
25.1.121...625.1 x25 - 11x24 + 42x23 - 37x22 - 156x21 + 345x20 + 267x19 - 2248x18 + 5531x17 - 338x16 - 41434x15 + 71882x14 + 112392x13 - 407865x12 + 80824x11 + 717928x10 - 228258x9 - 1185331x8 + 280801x7 + 1733675x6 - 74160x5 - 2202750x4 - 202350x3 + 1981500x2 + 536000x - 1401875 \( 5^{12}\cdot 643^{12} \) $D_{25}$ (as 25T4) trivial (GRH)
25.1.140...536.1 x25 - 4x - 4 \( 2^{24}\cdot 7\cdot 19\cdot 2579\cdot 1081796927611\cdot 224982529004839973 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.144...768.1 x25 - 2x - 2 \( 2^{24}\cdot 86150370416311954984992370501578073 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.149...464.1 x25 - x - 4 \( 2^{24}\cdot 389\cdot 766126533933601\cdot 298023226053735461 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.149...000.1 x25 - 2 \( 2^{24}\cdot 5^{50} \) $D_{25}.C_{10}$ (as 25T40) trivial (GRH)
25.1.153...232.1 x25 + 2x - 2 \( 2^{24}\cdot 11\cdot 83\cdot 139\cdot 177347\cdot 386150417\cdot 10526535234089689 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.157...464.1 x25 + 4x - 4 \( 2^{24}\cdot 8054869\cdot 11688928159776857914348061941 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.106...201.1 x25 - 10x24 + 41x23 - 105x22 + 177x21 - 437x20 + 1470x19 - 3743x18 + 4598x17 - 1850x16 + 3734x15 - 33702x14 + 37801x13 + 70620x12 - 146863x11 - 115089x10 + 114649x9 + 185307x8 - 74232x7 - 239939x6 - 516736x5 - 486684x4 - 187312x3 - 162320x2 + 32064x - 22784 \( 3851^{12} \) $D_{25}$ (as 25T4) trivial (GRH)
25.1.397...641.1 x25 - x24 + 2x23 - 2x22 + 114x21 + 14x20 + 388x19 + 1085x18 + 7513x17 + 4819x16 + 1219x15 - 640x14 + 110085x13 + 396579x12 + 932255x11 + 3052375x10 + 5536096x9 + 12433767x8 + 17351055x7 + 27726417x6 + 30856797x5 + 36500635x4 + 30496620x3 + 26587890x2 + 14289723x + 8362683 \( 11^{20}\cdot 79^{12} \) $D_{25}$ (as 25T4) $[5]$ (GRH)
25.3.113...143.1 x25 - 3x - 1 \( -\,131\cdot 13259\cdot 3933670000864773133\cdot 165394543991056112099 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.113...393.1 x25 + 3x - 1 \( 7\cdot 14691751\cdot 10988276266833335135516653653549317449 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.113...768.1 x25 + 3x - 2 \( 2^{24}\cdot 7\cdot 1777\cdot 19854823\cdot 273087660366642710101853209 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.118...921.1 x25 - x24 - 19x23 - 76x22 + 156x21 + 1005x20 + 1755x19 - 1564x18 - 17480x17 + 14003x16 - 40555x15 + 158147x14 - 336486x13 - 456783x12 + 2807964x11 - 9825280x10 + 32382901x9 - 51222985x8 + 76250162x7 - 82760080x6 + 46691010x5 + 4604688x4 - 3014982x3 - 12748972x2 + 5156073x + 1384173 \( 11^{20}\cdot 127^{12} \) $D_{25}$ (as 25T4) $[5]$ (GRH)
25.1.171...161.1 x25 + 18x23 - 17x22 + 163x21 + 778x20 + 668x19 + 6093x18 + 8161x17 - 16824x16 + 24958x15 + 156175x14 + 317021x13 + 1220510x12 + 3228424x11 + 5166827x10 + 7607147x9 + 10396892x8 + 8655374x7 + 3386053x6 + 971637x5 + 379214x4 - 252700x3 + 96379x2 - 14488x + 1088 \( 11^{20}\cdot 131^{12} \) $D_{25}$ (as 25T4) $[5]$ (GRH)
25.1.239...857.1 x25 - 3x - 3 \( 3^{24}\cdot 102715785599666749\cdot 825740991458053453 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.250...393.1 x25 - 2x - 3 \( 3^{24}\cdot 4213063\cdot 105716820911311\cdot 199414803057521 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.250...849.1 x25 - x - 3 \( 3^{25}\cdot 2351\cdot 126764421589739\cdot 99341097532143287 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.250...625.1 x25 - 3 \( 3^{24}\cdot 5^{50} \) $D_{25}.C_{10}$ (as 25T40) trivial (GRH)
25.1.250...401.1 x25 + x - 3 \( 3^{24}\cdot 13\cdot 2298962364929\cdot 2971837118443792802173 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.262...393.1 x25 + 3x - 3 \( 3^{24}\cdot 7\cdot 67\cdot 197908420683503999162553897368437 \) $S_{25}$ (as 25T211) trivial (GRH)
25.25.338...625.1 x25 - 50x23 + 1025x21 - 11250x19 - 125x18 + 72525x17 + 3100x16 - 283885x15 - 28375x14 + 674550x13 + 121800x12 - 942450x11 - 261005x10 + 718625x9 + 269475x8 - 258425x7 - 117125x6 + 33010x5 + 16625x4 - 1100x3 - 650x2 - 50x - 1 \( 5^{68} \) $C_{25}$ (as 25T1) trivial (GRH)
25.25.126...401.1 x25 - x24 - 48x23 + 43x22 + 946x21 - 752x20 - 9993x19 + 6962x18 + 62052x17 - 37341x16 - 234195x15 + 119366x14 + 538390x13 - 226505x12 - 737819x11 + 249907x10 + 571793x9 - 151052x8 - 224456x7 + 42136x6 + 35494x5 - 2561x4 - 1633x3 + 57x2 + 19x - 1 \( 101^{24} \) $C_{25}$ (as 25T1) trivial (GRH)
25.3.150...224.1 x25 - 4x - 2 \( -\,2^{24}\cdot 7\cdot 11\cdot 173\cdot 431\cdot 2029499\cdot 218979707\cdot 3166728751\cdot 11077240423 \) $S_{25}$ (as 25T211) trivial (GRH)
25.3.150...599.1 x25 - 4x - 1 \( -\,7\cdot 53\cdot 3847\cdot 1012717\cdot 140141898521\cdot 847814229733\cdot 8744131694867 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.150...849.1 x25 + 4x - 1 \( 38117394317861\cdot 39395478462830178925440533821507109 \) $S_{25}$ (as 25T211) $[2]$ (GRH)
25.1.150...224.1 x25 + 4x - 2 \( 2^{24}\cdot 29\cdot 11136449\cdot 3349154609\cdot 82750417248561907056701 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.152...849.1 x25 + 4x - 3 \( 3^{24}\cdot 5405729825109676014849118774568643929 \) $S_{25}$ (as 25T211) trivial (GRH)
25.25.611...625.1 x25 - 5x24 - 60x23 + 290x22 + 1490x21 - 6836x20 - 20165x19 + 85905x18 + 165640x17 - 634300x16 - 876915x15 + 2860245x14 + 3104180x13 - 7920370x12 - 7429455x11 + 13143679x10 + 11662900x9 - 12187240x8 - 11034960x7 + 5336420x6 + 5352834x5 - 670950x4 - 973795x3 - 7365x2 + 53905x + 4751 \( 5^{40}\cdot 11^{20} \) $C_5^2$ (as 25T2) trivial (GRH)
25.1.624...192.1 x25 - 2x - 4 \( 2^{46}\cdot 13751\cdot 431377\cdot 76457289497\cdot 195834881900887 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.625...808.1 x25 + 2x - 4 \( 2^{46}\cdot 88817842129006217640672221714148697 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.125...521.1 x25 - 6x24 - 11x23 + 373x22 - 2123x21 + 6909x20 - 14504x19 + 11689x18 + 26637x17 - 134028x16 + 212769x15 - 8645x14 - 228977x13 + 2110377x12 + 2314970x11 + 6611519x10 + 25497478x9 + 45079364x8 + 81358720x7 + 135641936x6 + 134356064x5 + 105811904x4 + 91282176x3 + 70338560x2 + 75878400x + 47071232 \( 11^{20}\cdot 227^{12} \) $D_{25}$ (as 25T4) $[5]$ (GRH)
25.3.158...375.1 x25 - 5x - 3 \( -\,3^{24}\cdot 5^{23}\cdot 409\cdot 11545399656835619219 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.233...921.1 x25 - 7x24 + 49x23 - 283x22 + 1302x21 - 5636x20 + 22809x19 - 80739x18 + 282358x17 - 893429x16 + 2621604x15 - 6788665x14 + 15933765x13 - 33100241x12 + 60008112x11 - 95295391x10 + 131154926x9 - 150037171x8 + 139788299x7 - 104949621x6 + 56076967x5 - 27454311x4 + 20655635x3 - 14146574x2 + 4203471x - 447083 \( 11^{20}\cdot 239^{12} \) $D_{25}$ (as 25T4) $[5]$ (GRH)
25.1.249...232.1 x25 - 3x - 4 \( 2^{48}\cdot 4813\cdot 18452904050171902358151509294269 \) $S_{25}$ (as 25T211) trivial (GRH)
25.1.250...776.1 x25 + x - 4 \( 2^{48}\cdot 13\cdot 5969653\cdot 175300357\cdot 544585241\cdot 11988341597 \) $S_{25}$ (as 25T211) trivial (GRH)
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