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Label Polynomial Discriminant Galois group Class group
21.3.65701728236743660173798567.1 x21 - 4x20 + 12x19 - 22x18 + 41x17 - 54x16 + 79x15 - 60x14 + 57x13 + 46x12 - 70x11 + 222x10 - 182x9 + 306x8 - 168x7 + 207x6 - 48x5 + 42x4 + 5x3 - 17x2 - 15x - 1 \( -\,3^{24}\cdot 7^{17} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.108608979330127274981177223.1 x21 - 9x14 - 12x7 + 1 \( -\,3^{28}\cdot 7^{15} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.12777737809210143774260519108727.3 x21 - 9x14 + 15x7 + 1 \( -\,3^{28}\cdot 7^{21} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.1395088421598327334260620375359488.1 x21 - 6x20 + 27x19 - 106x18 + 291x17 - 654x16 + 1319x15 - 2328x14 + 3921x13 - 5612x12 + 7467x11 - 10410x10 + 10203x9 - 11046x8 + 13119x7 - 7050x6 + 8664x5 - 6660x4 + 2044x3 - 2778x2 + 1104x - 62 \( -\,2^{18}\cdot 3^{28}\cdot 7^{17} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.1395088421598327334260620375359488.2 x21 - 21x19 - 2x18 + 189x17 - 843x15 + 126x14 + 1869x13 - 1072x12 - 2457x11 + 7770x10 + 1395x9 - 24948x8 - 9723x7 + 52888x6 + 40320x5 - 48594x4 - 75620x3 - 9702x2 + 28266x + 11494 \( -\,2^{18}\cdot 3^{28}\cdot 7^{17} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.2199205295571527101158910284971023.1 x21 - 12x14 + 35x7 + 1 \( -\,7^{21}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.2199205295571527101158910284971023.2 x21 - 17x14 - 25x7 + 1 \( -\,7^{21}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.176088256709912967722303227668133447.1 x21 + 7x19 - 3x18 - 3x17 - 16x16 - 353x15 - 213x14 - 420x13 - 916x12 + 2308x11 + 2660x10 + 1560x9 + 6188x8 - 3301x7 - 10148x6 - 6715x5 + 1703x4 + 9951x3 + 12672x2 + 11237x + 7785 \( -\,7^{17}\cdot 31^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.240111817160475801918451219385024512.1 x21 - 7x20 + 27x19 - 19x18 - 185x17 + 661x16 + 75x15 - 4907x14 + 5248x13 + 17006x12 - 24814x11 - 42058x10 + 51928x9 + 130100x8 - 180216x7 - 69004x6 + 106640x5 + 97712x4 - 82628x3 - 16944x2 + 21492x + 2484 \( -\,2^{18}\cdot 7^{17}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.240111817160475801918451219385024512.2 x21 - 7x20 + 23x19 - 59x18 + 159x17 - 439x16 + 1181x15 - 2881x14 + 6088x13 - 11638x12 + 20752x11 - 35784x10 + 61024x9 - 90396x8 + 95820x7 - 47992x6 - 56240x5 + 172576x4 - 215232x3 + 149248x2 - 53248x + 5888 \( -\,2^{18}\cdot 7^{17}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.446281879718922006187614065613552847.1 x21 - 24x14 - 55x7 + 1 \( -\,7^{21}\cdot 19^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.446281879718922006187614065613552847.2 x21 - 17x14 + 71x7 + 1 \( -\,7^{21}\cdot 19^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.2096480451371533622031253968968078623.1 x21 - 9x20 + 41x19 - 132x18 + 322x17 - 791x16 + 1785x15 - 3220x14 + 3122x13 - 2044x12 + 2989x11 - 13769x10 + 24304x9 - 14945x8 + 6321x7 + 1372x6 - 4802x5 - 1029x4 + 8232x3 - 2401x2 - 1029x + 343 \( -\,7^{17}\cdot 37^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.48725579790519404577278592926363680768.1 x21 - 2x20 + 3x19 + 28x18 - 103x17 + 158x16 + 231x15 - 2386x14 + 4533x13 + 2060x12 - 26199x11 + 48058x10 + 15699x9 - 114172x8 + 99573x7 - 91574x6 - 382958x5 + 518290x4 + 2159304x3 - 2056094x2 - 3898716x + 3849502 \( -\,2^{18}\cdot 7^{17}\cdot 19^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.73661115700272446040000814818508518327.1 x21 - 57x14 + 495x7 + 1 \( -\,3^{28}\cdot 7^{29} \) $C_3\times F_7$ (as 21T9) $[21]$ (GRH)
21.3.354859304882011896712926901003999617447.1 x21 - x20 - 10x19 + 26x18 - 175x17 + 893x16 - 2535x15 + 4105x14 - 5396x13 + 15522x12 - 38866x11 + 99374x10 - 196980x9 + 167386x8 - 522437x7 + 1728873x6 - 1333540x5 - 718864x4 - 722371x3 + 4119359x2 - 3755923x + 1239967 \( -\,3^{18}\cdot 7^{17}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.354859304882011896712926901003999617447.2 x21 - 4x20 - 13x19 + 92x18 - 100x17 - 685x16 + 3114x15 - 6722x14 + 11287x13 - 27129x12 + 85460x11 - 229903x10 + 486885x9 - 823628x8 + 1106479x7 - 1124295x6 + 783536x5 - 296659x4 - 6943x3 + 57281x2 - 20482x + 2527 \( -\,3^{18}\cdot 7^{17}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.942050611570682143073376679874187231232.1 x21 - 318x14 + 1592x7 + 128 \( -\,2^{18}\cdot 7^{15}\cdot 31^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.942050611570682143073376679874187231232.2 x21 - 286x14 - 800x7 + 16384 \( -\,2^{18}\cdot 7^{15}\cdot 31^{14} \) $C_3\times F_7$ (as 21T9) $[7]$ (GRH)
21.3.5033649563743052226497040779492356773823.1 x21 - 33x14 + 215x7 + 1 \( -\,7^{21}\cdot 37^{14} \) $C_3\times F_7$ (as 21T9) $[7]$ (GRH)
21.3.5033649563743052226497040779492356773823.2 x21 - 44x14 - 181x7 + 1 \( -\,7^{21}\cdot 37^{14} \) $C_3\times F_7$ (as 21T9) $[7]$ (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)
21.3.30993803831664495838915372384842966866167.1 x21 - 89x14 + 959x7 + 1 \( -\,7^{15}\cdot 97^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.71307894054048265215993997676849365234375.1 x21 - 435x14 + 38375x7 - 78125 \( -\,5^{18}\cdot 7^{15}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.71307894054048265215993997676849365234375.2 x21 - 995x14 - 18500x7 + 78125 \( -\,5^{18}\cdot 7^{15}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.72011138722425633565208857577376396922983.1 x21 - 7x20 - 10x19 + 149x18 + 8x17 - 1375x16 + 513x15 + 1633x14 + 27157x13 - 52788x12 - 327079x11 + 1254566x10 + 736266x9 - 9563747x8 + 12752578x7 + 5924631x6 - 8676262x5 - 34239268x4 + 23180423x3 + 11077409x2 + 29642690x - 10983749 \( -\,3^{18}\cdot 7^{17}\cdot 19^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.91953634653088335584878879192739848388608.1 x21 - 1570x14 + 20744x7 + 128 \( -\,2^{18}\cdot 7^{15}\cdot 43^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.21.114573143280690357510711381762768711450624.1 x21 - 6x20 - 36x19 + 249x18 + 459x17 - 4095x16 - 2034x15 + 34362x14 - 5715x13 - 157734x12 + 90396x11 + 390069x10 - 341226x9 - 463293x8 + 549828x7 + 168453x6 - 342792x5 + 54675x4 + 31698x3 - 2349x2 - 891x - 27 \( 2^{27}\cdot 3^{34}\cdot 13^{15} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.5516663961752188429459704285256595202031087.1 x21 - 963x14 + 1439x7 + 2187 \( -\,7^{21}\cdot 61^{14} \) $C_3\times F_7$ (as 21T9) $[7]$ (GRH)
21.3.5516663961752188429459704285256595202031087.2 x21 - 1572x14 - 4591x7 - 2187 \( -\,7^{21}\cdot 61^{14} \) $C_3\times F_7$ (as 21T9) $[7]$ (GRH)
21.3.8666156601021353004160055862582708672653223.1 x21 - 72x14 - 435x7 + 1 \( -\,3^{28}\cdot 7^{35} \) $C_3\times F_7$ (as 21T9) $[2, 546]$ (GRH)
21.3.19309819514132220094709973599783097028313088.1 x21 - 14550x14 - 525816x7 + 2097152 \( -\,2^{18}\cdot 3^{28}\cdot 7^{29} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.19309819514132220094709973599783097028313088.2 x21 - 2592x14 - 620544x7 + 2097152 \( -\,2^{18}\cdot 3^{28}\cdot 7^{29} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.19309819514132220094709973599783097028313088.3 x21 - 1416x14 + 470784x7 + 2097152 \( -\,2^{18}\cdot 3^{28}\cdot 7^{29} \) $C_3\times F_7$ (as 21T9) $[6]$ (GRH)
21.21.19362861214436670419310223517907912235155456.1 x21 - 102x19 - 56x18 + 4023x17 + 3564x16 - 79386x15 - 79758x14 + 890316x13 + 906992x12 - 6031368x11 - 5993106x10 + 25202042x9 + 24195240x8 - 64326231x7 - 59521236x6 + 95913018x5 + 84833856x4 - 75336041x3 - 62360064x2 + 23653968x + 17535232 \( 2^{27}\cdot 3^{34}\cdot 13^{17} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.44370779853247226690909004342839318612788927.1 x21 - 177x14 - 1945x7 + 1 \( -\,7^{15}\cdot 163^{14} \) $C_3\times F_7$ (as 21T9) $[2, 2]$ (GRH)
21.3.110831312400679183450439693010518253567213568.1 x21 - 1882x14 - 17240x7 - 128 \( -\,2^{18}\cdot 7^{21}\cdot 31^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.110831312400679183450439693010518253567213568.2 x21 - 290x14 + 18072x7 - 16384 \( -\,2^{18}\cdot 7^{21}\cdot 31^{14} \) $C_3\times F_7$ (as 21T9) $[7]$ (GRH)
21.3.110831312400679183450439693010518253567213568.3 x21 - 560x14 - 167936x7 + 2097152 \( -\,2^{18}\cdot 7^{21}\cdot 31^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.110831312400679183450439693010518253567213568.4 x21 - 1056x14 + 149504x7 + 2097152 \( -\,2^{18}\cdot 7^{21}\cdot 31^{14} \) $C_3\times F_7$ (as 21T9) $[7]$ (GRH)
21.3.110831312400679183450439693010518253567213568.5 x21 - 4x14 - 70592x7 + 16384 \( -\,2^{18}\cdot 7^{21}\cdot 31^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.110831312400679183450439693010518253567213568.6 x21 - 358x14 + 19864x7 - 128 \( -\,2^{18}\cdot 7^{21}\cdot 31^{14} \) $C_3\times F_7$ (as 21T9) $[182]$ (GRH)
21.3.205986196435530872265507304901371119909816967.1 x21 - 89x14 - 625x7 + 1 \( -\,7^{21}\cdot 79^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.205986196435530872265507304901371119909816967.2 x21 - 72x14 + 701x7 + 1 \( -\,7^{21}\cdot 79^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.3.2437288133845320729958641787363924555521111847.1 x21 - 204x14 + 3239x7 + 1 \( -\,7^{29}\cdot 31^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.3323456621672145880164070108616782869016870912.1 x21 - 6024x14 - 3354880x7 + 2097152 \( -\,2^{18}\cdot 7^{29}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) $[6]$ (GRH)
21.3.3323456621672145880164070108616782869016870912.2 x21 - 47334x14 + 6588344x7 - 105413504 \( -\,2^{18}\cdot 7^{29}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.3323456621672145880164070108616782869016870912.3 x21 - 13674x14 + 1783064x7 - 2097152 \( -\,2^{18}\cdot 7^{29}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) $[6]$ (GRH)
21.3.3323456621672145880164070108616782869016870912.4 x21 - 2592x14 + 1587200x7 + 2097152 \( -\,2^{18}\cdot 7^{29}\cdot 13^{14} \) $C_3\times F_7$ (as 21T9) $[3]$ (GRH)
21.3.3646390026991496270952554645704390208837681383.1 x21 - 108x14 - 865x7 + 1 \( -\,7^{21}\cdot 97^{14} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
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