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Label Polynomial Discriminant Galois group Class group
15.3.227131131690502261690628246149441.1 x15 - 3x14 - 81x13 + 482x12 + 1855x11 - 20398x10 - 17885x9 + 216818x8 - 344645x7 - 1939966x6 - 1313053x5 + 4806214x4 - 16258641x3 - 76618654x2 - 46619874x + 86089913 \( 7^{12}\cdot 71^{12} \) $(C_5^2 : C_3):C_2$ (as 15T12) $[5, 5]$ (GRH)
15.1.163587563515302975177730470000000000.1 x15 - 7x14 - 28x13 - 144x12 + 2095x11 + 337x10 - 19903x9 - 160455x8 + 1090677x7 - 522869x6 - 10364275x5 + 26986175x4 + 362562x3 - 96560678x2 + 149601655x - 74596195 \( -\,2^{10}\cdot 3^{13}\cdot 5^{10}\cdot 29^{13} \) $F_5 \times S_3$ (as 15T11) $[30]$ (GRH)
15.5.337135860780576171875000000000000000.1 x15 - 110x13 - 330x12 + 6050x11 + 25674x10 - 442200x9 - 2425610x8 + 6912345x7 + 36375350x6 - 70930618x5 - 40668100x4 + 762404060x3 - 1733605720x2 - 2315335000x + 7384846832 \( -\,2^{15}\cdot 5^{25}\cdot 11^{13} \) $S_3 \times C_5$ (as 15T4) $[5, 5]$ (GRH)
15.1.988623217530364550400000000000000000.1 x15 - 5124x10 + 12993792x5 + 398297088 \( -\,2^{23}\cdot 3^{13}\cdot 5^{17}\cdot 7^{13} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.32192049904498705314600000000000000000.1 x15 - 5x14 - 5x13 - 15x12 + 265x11 - 1927x10 + 6615x9 - 51485x8 - 790005x7 + 1814005x6 - 636307x5 - 19232005x4 + 56139395x3 - 238258865x2 + 169553865x - 501418879 \( -\,2^{18}\cdot 3^{12}\cdot 5^{17}\cdot 13^{13} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.1124406965607900390625000000000000000000.1 x15 - 5x14 + 10x13 + 100x12 - 435x11 + 629x10 + 4500x9 - 14610x8 + 34520x7 + 55340x6 - 165340x5 - 570520x4 + 2047880x3 - 1493480x2 + 1602100x + 4631132 \( -\,2^{18}\cdot 5^{28}\cdot 11^{5}\cdot 59^{5} \) $F_5 \times S_3$ (as 15T11) $[14]$ (GRH)
15.15.1586393893300992738237335763411468444721.1 x15 - x14 - 294x13 + 127x12 + 29253x11 - 353x10 - 1219824x9 - 638978x8 + 22372090x7 + 22528734x6 - 165257997x5 - 237407410x4 + 304223819x3 + 487995784x2 - 67361473x - 110965429 \( 631^{14} \) $C_{15}$ (as 15T1) $[11]$ (GRH)
15.1.2581452668046920778582615126630000000000.1 x15 - 5x14 - 45x13 + 135x12 + 1185x11 + 1086x10 - 22575x9 + 75600x8 + 767775x7 - 71525x6 + 2047624x5 + 13641630x4 + 69494445x3 - 277582410x2 + 519196590x - 280715886 \( -\,2^{10}\cdot 3^{13}\cdot 5^{10}\cdot 61^{13} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.2890088708537260245720054366720000000000.1 x15 - x14 + 203x13 + 249x12 + 14443x11 + 27391x10 + 434633x9 + 784389x8 + 4734027x7 + 2940961x6 - 15645211x5 - 122910997x4 - 309285975x3 - 271954775x2 + 1392333871x + 4737567935 \( -\,2^{18}\cdot 3^{13}\cdot 5^{10}\cdot 11^{13}\cdot 29^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.3090436790831875710201600000000000000000.1 x15 - 5x14 - 25x13 + 705x12 - 1235x11 - 16633x10 + 277655x9 + 231705x8 - 3692325x7 + 28332665x6 + 132709223x5 - 125865275x4 + 203969475x3 + 6121946705x2 + 13423647535x + 5856994189 \( -\,2^{23}\cdot 3^{13}\cdot 5^{17}\cdot 13^{13} \) $F_5 \times S_3$ (as 15T11) $[2, 10]$ (GRH)
15.1.3674682958567667934420285323670000000000.1 x15 - 5x14 + 5x13 + 285x12 - 1115x11 + 242x10 + 33455x9 - 95580x8 + 490815x7 + 670115x6 - 2042470x5 - 42451640x4 + 102976665x3 - 43337470x2 + 183470980x + 425268514 \( -\,2^{10}\cdot 3^{13}\cdot 5^{10}\cdot 11^{12}\cdot 149^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 15]$ (GRH)
15.1.4531843153076980395001600000000000000000.1 x15 - 15708x10 - 101662x5 - 234256 \( -\,2^{23}\cdot 5^{17}\cdot 11^{13}\cdot 29^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 10]$ (GRH)
15.3.6325478008948059728518400000000000000000.1 x15 - 55000x10 - 254375000x5 - 187404800000 \( 2^{23}\cdot 5^{17}\cdot 11^{13}\cdot 31^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 15]$ (GRH)
15.1.6362366218401470792736132808704000000000.1 x15 - 2x14 + 97x13 + 812x12 - 304x11 + 6410x10 + 49272x9 - 115242x8 - 526083x7 - 248742x6 - 3669519x5 - 17515380x4 - 30340590x3 + 136789686x2 + 504130986x + 1005343698 \( -\,2^{23}\cdot 3^{13}\cdot 5^{9}\cdot 37^{13} \) $F_5 \times S_3$ (as 15T11) $[3, 6]$ (GRH)
15.1.10788347544978437500000000000000000000000.1 x15 - 5500x10 + 6201250x5 + 10648000000 \( -\,2^{23}\cdot 5^{28}\cdot 11^{13} \) $F_5 \times S_3$ (as 15T11) $[40]$ (GRH)
15.1.19194711673970613594516583376070000000000.1 x15 - x14 + 80x13 + 48x12 + 1585x11 + 16969x10 - 6733x9 + 126897x8 - 167121x7 - 6668441x6 - 1834549x5 - 49323325x4 - 48976404x3 - 38132480x2 - 21240983x - 28629151 \( -\,2^{10}\cdot 3^{13}\cdot 5^{10}\cdot 19^{13}\cdot 31^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.32479853059663365203857421875000000000000.1 x15 + 55x13 - 100x12 + 1210x11 - 4280x10 + 17310x9 - 79200x8 + 277205x7 - 515600x6 + 1485851x5 - 531700x4 + 7708000x3 - 2431800x2 + 20860000x + 14746040 \( -\,2^{12}\cdot 5^{27}\cdot 29^{5}\cdot 139^{5} \) $F_5 \times S_3$ (as 15T11) $[14]$ (GRH)
15.1.41028151731920370720386831073280000000000.1 x15 - 5x14 + 23x13 - 761x12 + 6803x11 - 4453x10 - 11163x9 - 387685x8 + 3700959x7 - 4879383x6 - 8035207x5 + 88209781x4 - 169248627x3 + 355869121x2 - 496934421x + 1022287273 \( -\,2^{23}\cdot 5^{10}\cdot 29^{5}\cdot 31^{13} \) $F_5 \times S_3$ (as 15T11) $[55]$ (GRH)
15.3.101063018004202830052166400000000000000000.1 x15 - 5x14 - 20x13 + 500x12 - 2395x11 + 8033x10 - 134070x9 + 154410x8 - 4697580x7 - 21172140x6 - 190329732x5 - 557303040x4 - 3522839040x3 - 15893213040x2 - 67359711780x - 164654741844 \( 2^{23}\cdot 3^{13}\cdot 5^{17}\cdot 17^{13} \) $F_5 \times S_3$ (as 15T11) $[5, 20]$ (GRH)
15.1.106472941783456130152543427343750000000000.1 x15 - 53559x10 - 21386673x5 - 2593609227 \( -\,2^{10}\cdot 3^{13}\cdot 5^{17}\cdot 11^{13}\cdot 19^{5} \) $F_5 \times S_3$ (as 15T11) $[15]$ (GRH)
15.1.172832712591425821508917768538520000000000.1 x15 - 5x14 - 45x13 + 60x12 + 1485x11 + 1893x10 - 18615x9 - 115260x8 - 338145x7 + 1456855x6 + 1635325x5 - 17048850x4 + 2426400x3 - 18672300x2 - 80668500x - 122095500 \( -\,2^{12}\cdot 3^{13}\cdot 5^{10}\cdot 11^{13}\cdot 151^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.210051400399105472360464905891352000000000.1 x15 - 5x14 - 40x13 - 190x12 + 2225x11 + 9591x10 + 8390x9 - 366980x8 - 2261440x7 + 2732880x6 + 18555360x5 - 81164320x4 + 192419200x3 - 419916800x2 - 3039303680x - 2807964928 \( -\,2^{12}\cdot 5^{9}\cdot 11^{13}\cdot 3769^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.219387435712728438617734525000000000000000.1 x15 - 5x14 - 205x13 + 2285x12 + 11465x11 - 292788x10 + 818485x9 + 14288760x8 - 119368045x7 - 8391805x6 + 4295896648x5 - 19651259480x4 - 11485832055x3 + 402491806260x2 - 1460294354910x + 1953811463264 \( -\,2^{15}\cdot 5^{17}\cdot 11^{13}\cdot 191^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.305908393993716440346185189875000000000000.1 x15 - 5x14 + 60x13 - 370x12 + 1945x11 - 10297x10 + 42250x9 - 178520x8 + 856800x7 - 2144000x6 + 4659456x5 - 404560x4 + 10719680x3 - 15785600x2 + 89744320x + 4649536 \( -\,2^{12}\cdot 5^{15}\cdot 11^{13}\cdot 19^{5}\cdot 31^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.3.308982052185601664705132225000000000000000.1 x15 - 5x14 - 80x13 + 460x12 + 2265x11 - 16564x10 - 20720x9 + 294580x8 - 241460x7 - 2045090x6 + 4494657x5 + 2985455x4 - 24629270x3 + 43193990x2 - 17766115x - 27711922 \( 2^{15}\cdot 5^{17}\cdot 19^{12}\cdot 89^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 10]$ (GRH)
15.1.505587397847240362501152000000000000000000.1 x15 - 15x13 - 30x12 + 75x11 + 2880x10 - 36275x9 - 455490x8 + 794220x7 + 7999460x6 - 29685606x5 - 73095900x4 + 981089960x3 + 5043879720x2 + 10724525400x + 9378358624 \( -\,2^{23}\cdot 3^{20}\cdot 5^{18}\cdot 1459^{4} \) 15T40 $[15]$ (GRH)
15.1.541731882746046925621032714843750000000000.1 x15 - 5775x10 - 31515x5 - 50625 \( -\,2^{10}\cdot 3^{13}\cdot 5^{28}\cdot 389^{5} \) $F_5 \times S_3$ (as 15T11) $[3, 6]$ (GRH)
15.1.654503601162655079739525888000000000000000.1 x15 - 420x10 + 35868x5 + 7112448 \( -\,2^{23}\cdot 3^{13}\cdot 5^{15}\cdot 7^{12}\cdot 41^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.1036257839565777636208518400000000000000000.1 x15 - 5x14 - 105x13 + 185x12 + 5665x11 + 6647x10 - 147465x9 - 703515x8 - 21445x7 + 13204145x6 + 23655453x5 - 136700405x4 - 387843005x3 - 592258115x2 - 600143435x - 1744422601 \( -\,2^{23}\cdot 5^{17}\cdot 61^{13} \) $F_5 \times S_3$ (as 15T11) $[10, 10]$ (GRH)
15.1.1152275901087640214484331783593750000000000.1 x15 - 5x14 - 5x13 - 265x12 + 1265x11 - 8284x10 + 62805x9 - 340470x8 - 18871785x7 + 41596335x6 - 14726448x5 - 1841961870x4 + 3220463205x3 - 21861208260x2 + 1653437610x - 48460084002 \( -\,2^{10}\cdot 3^{13}\cdot 5^{17}\cdot 41^{13} \) $F_5 \times S_3$ (as 15T11) $[5, 15]$ (GRH)
15.1.1956208803104312462005615234375000000000000.1 x15 - 5x14 + 105x13 - 340x12 + 3985x11 - 7051x10 + 68715x9 - 29340x8 + 545195x7 + 913895x6 + 1981059x5 + 7949350x4 + 1415200x3 + 22609900x2 - 20821100x + 59344580 \( -\,2^{12}\cdot 5^{28}\cdot 19^{5}\cdot 349^{5} \) $F_5 \times S_3$ (as 15T11) $[21]$ (GRH)
15.1.2159687645407390587226247752000000000000000.1 x15 - 5x14 - 50x13 + 400x12 + 405x11 - 10957x10 + 21460x9 + 138610x8 - 862280x7 + 954040x6 + 3131424x5 + 20480x4 - 22766960x3 + 50225840x2 - 74460160x + 93869216 \( -\,2^{18}\cdot 5^{15}\cdot 11^{13}\cdot 379^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.4187841625991756164549900032000000000000000.1 x15 - 46980x10 - 113400324x5 - 131995609344 \( -\,2^{23}\cdot 3^{13}\cdot 5^{15}\cdot 29^{13} \) $F_5 \times S_3$ (as 15T11) $[2, 10]$ (GRH)
15.3.6484622183937592099059160665866970000000000.1 x15 - 5x14 - 115x13 + 675x12 + 4765x11 - 35470x10 - 69745x9 + 926130x8 - 763005x7 - 9133825x6 + 22965638x5 + 21244810x4 - 195801075x3 + 409630610x2 - 163462160x - 398276804 \( 2^{10}\cdot 3^{13}\cdot 5^{10}\cdot 19^{12}\cdot 179^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.7512388954787337016979704576000000000000000.1 x15 - 12740x10 + 32336668x5 - 860204310784 \( -\,2^{23}\cdot 5^{15}\cdot 7^{13}\cdot 13^{13} \) $F_5 \times S_3$ (as 15T11) $[10, 10]$ (GRH)
15.1.8435805927443939947156293677343750000000000.1 x15 - 20349x10 + 174065517x5 - 23085974187 \( -\,2^{10}\cdot 3^{13}\cdot 5^{17}\cdot 11^{5}\cdot 19^{13} \) $F_5 \times S_3$ (as 15T11) $[30]$ (GRH)
15.1.11274121380851814944915771484375000000000000.1 x15 - 5x14 + 55x13 - 460x12 + 2165x11 - 9901x10 + 55665x9 - 418770x8 + 7842555x7 - 17116785x6 + 19156149x5 + 446434740x4 - 768468060x3 - 1472601870x2 + 5757007770x + 5802471126 \( -\,2^{12}\cdot 3^{13}\cdot 5^{28}\cdot 541^{5} \) $F_5 \times S_3$ (as 15T11) $[15]$ (GRH)
15.3.18077489127555014674740676881656250000000000.1 x15 - 5x14 - 105x13 + 675x12 + 3705x11 - 33870x10 - 27435x9 + 937980x8 - 2743665x7 - 2066285x6 + 20814100x5 + 20538450x4 - 294061995x3 + 805024170x2 + 284948010x - 624218022 \( 2^{10}\cdot 3^{13}\cdot 5^{15}\cdot 11^{13}\cdot 101^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.21919782836729069869914926177537862000000000.1 x15 - 5x14 + 135x13 - 465x12 + 6825x11 - 14202x10 + 161325x9 - 171900x8 + 1776615x7 + 2275555x6 + 6608476x5 + 35139510x4 - 35275635x3 + 237235950x2 - 216139110x + 963981822 \( -\,2^{10}\cdot 3^{12}\cdot 5^{9}\cdot 31^{13}\cdot 61^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 15]$ (GRH)
15.3.31181432989778750343506297600000000000000000.1 x15 - 40812x10 + 563198x5 + 2085136 \( 2^{23}\cdot 5^{17}\cdot 19^{13}\cdot 41^{5} \) $F_5 \times S_3$ (as 15T11) $[2, 2, 10]$ (GRH)
15.1.34898680216597968037915833600000000000000000.1 x15 - 5x14 - 30x13 + 10x12 + 965x11 - 2819x10 + 7380x9 - 273620x8 - 3835960x7 + 7674660x6 - 2572288x5 - 189916220x4 + 592975880x3 - 2416077960x2 + 2563933460x - 8065689292 \( -\,2^{23}\cdot 3^{12}\cdot 5^{17}\cdot 29^{13} \) $F_5 \times S_3$ (as 15T11) $[5, 10]$ (GRH)
15.1.64007262884567863139459214673592320000000000.1 x15 - x14 + 115x13 + 233x12 + 3215x11 + 47979x10 - 31523x9 - 60303x8 - 1140151x7 - 60011861x6 - 12647679x5 - 566354805x4 - 760159369x3 - 600364745x2 - 456912753x - 844596301 \( -\,2^{23}\cdot 5^{10}\cdot 41^{13}\cdot 61^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 15]$ (GRH)
15.1.81768020500282951857411490366375000000000000.1 x15 - 5x14 + 40x13 + 130x12 - 495x11 + 6533x10 + 10770x9 - 9120x8 + 560000x7 + 422300x6 + 552212x5 + 7024160x4 + 37747640x3 - 2612120x2 + 280653460x + 350125148 \( -\,2^{12}\cdot 5^{15}\cdot 11^{13}\cdot 1801^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.212109976697868913424682627876372480000000000.1 x15 - 6x14 + 115x13 - 552x12 + 7120x11 + 4644x10 + 90422x9 + 2742312x8 - 9952441x7 + 45129354x6 + 982709201x5 - 1851693840x4 - 1739418204x3 + 69424749540x2 + 93251552652x + 69750425364 \( -\,2^{23}\cdot 3^{12}\cdot 5^{10}\cdot 19^{13}\cdot 41^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.3.322947060137321101063230598400000000000000000.1 x15 - 40216x10 - 675375448x5 + 4640328378752 \( 2^{23}\cdot 5^{17}\cdot 11^{13}\cdot 271^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.3.328796742550936048048723892663067930000000000.1 x15 - x14 - 130x13 + 1038x12 + 3775x11 - 126671x10 - 27463x9 + 6419037x8 + 2668689x7 - 127033781x6 - 34006219x5 + 812573375x4 - 911101734x3 - 767195780x2 + 512296117x - 844596301 \( 2^{10}\cdot 3^{13}\cdot 5^{10}\cdot 31^{13}\cdot 61^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.1.343324018227307701093486021364843750000000000.1 x15 - 64713x10 - 492877x5 - 1874161 \( -\,2^{10}\cdot 5^{17}\cdot 37^{13}\cdot 71^{5} \) $F_5 \times S_3$ (as 15T11) $[2, 6]$ (GRH)
15.1.534359547919362296589172482600000000000000000.1 x15 + 125x13 - 550x12 + 6250x11 - 52732x10 + 277250x9 - 2346000x8 + 18512525x7 - 38235000x6 + 207170233x5 + 472707250x4 + 3376407000x3 - 1867556300x2 + 43463765000x + 28154663716 \( -\,2^{18}\cdot 3^{12}\cdot 5^{17}\cdot 7^{13}\cdot 139^{5} \) $F_5 \times S_3$ (as 15T11) $[15]$ (GRH)
15.1.715448845372327674720280403400000000000000000.1 x15 - 5x14 - 130x13 + 210x12 + 8365x11 + 8327x10 - 246940x9 - 1889940x8 - 6949920x7 + 27969920x6 + 46028768x5 - 1020183680x4 - 438343680x3 - 5489655040x2 + 21933571840x - 50114084096 \( -\,2^{18}\cdot 3^{13}\cdot 5^{17}\cdot 11^{12}\cdot 59^{5} \) $F_5 \times S_3$ (as 15T11) $[5, 5]$ (GRH)
15.3.791180428866728914712562561035156250000000000.1 x15 - 110x13 - 30x12 + 4840x11 + 2595x10 - 106120x9 - 92070x8 + 1139420x7 + 1130400x6 - 4659937x5 - 5408340x4 - 4599000x3 - 18298740x2 + 5689440x + 75838029 \( 2^{10}\cdot 3^{12}\cdot 5^{28}\cdot 2081^{5} \) $F_5 \times S_3$ (as 15T11) $[15]$ (GRH)
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