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Results (displaying all 21 matches)

Label Polynomial Discriminant Galois group Class group
21.3.73661115700272446040000814818508518327.1 x21 - 57x14 + 495x7 + 1 \( -\,3^{28}\cdot 7^{29} \) $C_3\times F_7$ (as 21T9) $[21]$ (GRH)
21.3.20301208447174974342642532070159912109375.1 x21 - 6x19 - 96x18 - 6x17 + 648x16 + 2889x15 - 5685x14 - 28155x13 - 9420x12 + 241392x11 + 451815x10 - 1479827x9 - 510537x8 + 7030128x7 - 10608182x6 - 37483542x5 + 47557968x4 + 35144488x3 - 121483152x2 + 50031891x - 18017937 \( -\,3^{28}\cdot 5^{18}\cdot 7^{17} \) $C_3\times F_7$ (as 21T9) $[42]$ (GRH)
21.3.48958786234221774012025092444897160075327.1 x21 - 7x20 + 21x19 - 34x18 + 29x17 + 52x16 - 373x15 + 248x14 - 3577x13 + 42918x12 - 170639x11 + 225822x10 + 43556x9 + 105237x8 - 3230632x7 + 5161290x6 + 1287601x5 + 2320101x4 - 14827477x3 + 4310250x2 + 1634962x + 569387 \( -\,7^{17}\cdot 29^{18} \) $F_7$ (as 21T4) $[7, 7]$ (GRH)
21.3.48958786234221774012025092444897160075327.2 x21 - 7x20 + 21x19 - 34x18 + 116x17 + 545x16 - 2200x15 + 3148x14 - 14133x13 - 26711x12 - 65282x11 - 158805x10 + 228083x9 - 139668x8 - 1168123x7 + 426315x6 + 764470x5 - 1534666x4 - 486339x3 + 614026x2 - 225533x + 15197 \( -\,7^{17}\cdot 29^{18} \) $C_3\times D_7$ (as 21T3) $[7, 7]$ (GRH)
21.3.10818253163301189593225415258146650423071342592.2 x21 - 2018x14 + 6152x7 - 128 \( -\,2^{18}\cdot 7^{21}\cdot 43^{14} \) $C_3\times F_7$ (as 21T9) $[14]$ (GRH)
21.3.29588990284336432332939370460310604619437105887.1 x21 - 21x19 - 11x18 + 189x17 - 978x15 + 693x14 + 3759x13 + 2519x12 + 3213x11 - 30030x10 - 29151x9 + 12474x8 - 95907x7 + 698269x6 + 658350x5 - 1504272x4 - 8525x3 + 557865x2 - 85701x - 57365 \( -\,3^{28}\cdot 7^{17}\cdot 11^{18} \) $C_3\times F_7$ (as 21T9) $[21]$ (GRH)
21.3.489009118212301150746875247421551446873029171927.1 x21 - 7x20 + 21x19 - 34x18 - 326x17 - 2633x16 + 6276x15 - 262x14 - 62573x13 - 195159x12 + 556052x11 - 18483x10 + 1794625x9 + 26343578x8 + 40153179x7 - 162134041x6 - 214511808x5 + 867279238x4 + 2465480719x3 + 2567288464x2 + 1206871419x + 176307053 \( -\,7^{17}\cdot 71^{18} \) $C_3\times D_7$ (as 21T3) $[7, 7]$ (GRH)
21.3.674424743915820495717627003682966750085368250368.1 x21 - 77856x14 + 263505920x7 + 2097152 \( -\,2^{18}\cdot 7^{29}\cdot 19^{14} \) $C_3\times F_7$ (as 21T9) $[21]$ (GRH)
21.3.674424743915820495717627003682966750085368250368.2 x21 - 830x14 - 181248x7 + 2097152 \( -\,2^{18}\cdot 7^{29}\cdot 19^{14} \) $C_3\times F_7$ (as 21T9) $[21]$ (GRH)
21.3.31802469923372977610337732723351505277264012368687.1 x21 - 449x14 - 8521x7 + 1 \( -\,7^{29}\cdot 61^{14} \) $C_3\times F_7$ (as 21T9) $[21]$ (GRH)
21.3.677652621280228828828157332148396859511871800989727.1 x21 - 3915x14 - 19657534x7 + 17249876309 \( -\,7^{29}\cdot 29^{18} \) $C_3\times D_7$ (as 21T3) $[91]$ (GRH)
21.3.996726852728145413540441359277571789889580380640583.1 x21 - 103983x14 + 508304187x7 + 10460353203 \( -\,3^{18}\cdot 7^{29}\cdot 19^{14} \) $C_3\times F_7$ (as 21T9) $[21]$ (GRH)
21.3.996726852728145413540441359277571789889580380640583.2 x21 - 29403x14 + 214879311x7 + 10460353203 \( -\,3^{18}\cdot 7^{29}\cdot 19^{14} \) $C_3\times F_7$ (as 21T9) $[42]$ (GRH)
21.3.2137268649710710138161420639989505603645937518741543.2 x21 - 6237x14 - 38795193x7 - 10460353203 \( -\,3^{18}\cdot 7^{21}\cdot 61^{14} \) $C_3\times F_7$ (as 21T9) $[42]$ (GRH)
21.3.2676358627652966148624150642671926317530334055358005248.2 x21 - 6432x14 - 3778560x7 + 2097152 \( -\,2^{18}\cdot 3^{28}\cdot 7^{21}\cdot 19^{14} \) $C_3\times F_7$ (as 21T9) $[42]$ (GRH)
21.3.3273124848363888176455767741482926684693411707415817487.1 x21 - 5205x14 + 1057239x7 - 2187 \( -\,3^{18}\cdot 7^{21}\cdot 103^{14} \) $C_3\times F_7$ (as 21T9) $[14]$ (GRH)
21.21.7246641953163409527953772394951784818867805657911594619889.4 x21 - 903x19 - 2408x18 + 322371x17 + 1567608x16 - 57217692x15 - 384550677x14 + 5297604816x13 + 46019992039x12 - 239871482424x11 - 2894978733948x10 + 3238401809699x9 + 94345678493136x8 + 111760681819143x7 - 1405026978142459x6 - 4000967262399996x5 + 5000920037348550x4 + 31976002108505938x3 + 39769563390498270x2 + 15884115372049848x + 1731927086090117 \( 3^{28}\cdot 7^{14}\cdot 43^{20} \) $C_{21}$ (as 21T1) $[6, 6]$ (GRH)
21.21.32615044040601465591789077347406642010407599407890505169329.2 x21 - 3x20 - 234x19 + 373x18 + 22227x17 - 11901x16 - 1094568x15 - 107259x14 + 30750441x13 + 11716858x12 - 518275467x11 - 210631296x10 + 5345836461x9 + 1384500363x8 - 33101161890x7 - 481181304x6 + 113556752970x5 - 28704806013x4 - 175186581586x3 + 80675421420x2 + 58460165631x - 20341937701 \( 3^{28}\cdot 7^{14}\cdot 71^{18} \) $C_{21}$ (as 21T1) $[21]$ (GRH)
21.3.58922863816834248701730948403017453588761267745332101431343.1 x21 - 7x20 + 21x19 - 34x18 + 29x17 - 17000x16 + 76879x15 + 25168x14 - 3960985x13 - 7944166x12 + 40651037x11 + 81259502x10 - 506512648x9 - 2778664855x8 - 84195862092x7 + 400745644202x6 + 655623718393x5 - 7349761489371x4 + 529795117999x3 + 53152215171034x2 - 12893672008602x - 131863811763929 \( -\,7^{17}\cdot 293^{18} \) $F_7$ (as 21T4) $[7, 7]$ (GRH)
21.3.70488525434400042968409628831807900651401450217386256557463.1 x21 - 560857x14 + 65329261371x7 - 93206534790699 \( -\,7^{29}\cdot 11^{18}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) $[2, 6]$ (GRH)
21.13.3939527404840449202647348389943760445443805570249819965902848.1 x21 - 6x20 - 196x19 + 908x18 + 16298x17 - 38657x16 - 805846x15 - 121733x14 + 23579189x13 + 60920978x12 - 321396183x11 - 1963423184x10 - 1073818319x9 + 21446736466x8 + 79483877862x7 + 59509268311x6 - 426733627582x5 - 1804226819510x4 - 3692869755195x3 - 4543444380349x2 - 3247488161475x - 1051284118606 \( 2^{12}\cdot 7^{14}\cdot 19^{2}\cdot 79^{2}\cdot 173^{9}\cdot 967^{2}\cdot 2202121^{2} \) 21T133 $[3, 3, 3]$ (GRH)


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