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Label Polynomial Discriminant Galois group Class group
21.1.238583305854552412020101.1 x21 - 6x18 - 6x16 + 8x15 - 8x14 + 17x13 - 3x12 + 23x11 - 28x10 - 11x9 - 45x8 - 14x7 - 44x6 - 17x5 - 21x4 - 4x3 - 8x2 - 1 \( 23^{7}\cdot 41227^{3} \) 21T62 Trivial (GRH)
21.3.3219905755813179726837607.1 x21 - 5x14 - 8x7 - 1 \( -\,7^{29} \) $C_3\times D_7$ (as 21T3) Trivial (GRH)
21.3.3960879820606443846053527.1 x21 - 5x20 + 11x19 - 20x18 + 37x17 - 68x16 + 120x15 - 168x14 + 237x13 - 331x12 + 362x11 - 431x10 + 452x9 - 381x8 + 350x7 - 238x6 + 169x5 - 90x4 + 43x3 + 6x2 + 27 \( -\,13^{2}\cdot 1801^{2}\cdot 193327^{3} \) 21T139 Trivial (GRH)
21.3.6826740523487474380439552.1 x21 - 2x20 - x19 - 3x18 + 10x17 + 13x16 + x15 - 27x14 - 16x13 - 20x12 + 55x11 - 4x10 + 8x9 - 32x8 - x7 + 70x6 - 52x5 - 4x4 + 6x3 + 2x2 - 6x + 1 \( -\,2^{21}\cdot 71^{10} \) $S_3\times D_7$ (as 21T8) Trivial (GRH)
21.3.7174552902718171733819392.1 x21 - 7x20 + 21x19 - 42x18 + 77x17 - 126x16 + 168x15 - 213x14 + 266x13 - 280x12 + 259x11 - 217x10 + 133x9 - 42x8 - 53x7 + 126x6 - 112x5 + 7x4 + 63x3 - 49x2 + 14x - 1 \( -\,2^{18}\cdot 7^{23} \) $F_7$ (as 21T4) Trivial (GRH)
21.3.9284127557257563917891699.1 x21 - 5x20 + 11x19 - 13x18 + 7x17 + 4x16 - 16x15 + 13x14 - 6x13 + 2x12 - 2x11 + 21x10 - 28x8 + 29x7 - 16x6 - 18x5 + 17x4 - 9x3 - 2x2 + 3x - 1 \( -\,11^{9}\cdot 13^{14} \) $F_7$ (as 21T4) Trivial (GRH)
21.3.10904210824444953500612167.1 x21 + x19 - 2x18 - 2x17 - 3x16 - x15 + 4x14 + 15x13 + 3x12 - 4x11 - 29x10 - 4x9 + 12x8 + 23x7 + 16x6 - 4x5 - 7x4 - 8x3 - x2 + 1 \( -\,31^{8}\cdot 67^{3}\cdot 349^{3} \) 21T74 Trivial (GRH)
21.5.16253945603436050603615041.1 x21 - x20 - 6x19 + 8x18 + 15x17 - 28x16 - 39x15 + 74x14 + 112x13 - 127x12 - 227x11 + 89x10 + 306x9 + x8 - 244x7 - 55x6 + 122x5 + 40x4 - 41x3 - 6x2 + 8x - 1 \( 13^{8}\cdot 109^{8} \) $\PSL(2,7)$ (as 21T14) Trivial (GRH)
21.1.21420980525151261442929721.1 x21 - x20 - x19 + 2x18 + 2x17 + x16 - 5x15 - x14 + 13x13 + 9x12 - 7x11 - 16x10 - x9 + 21x8 + 17x7 - 3x6 - 11x5 - 3x4 + 4x3 + 3x2 - 1 \( 23^{7}\cdot 184607^{3} \) 21T74 Trivial (GRH)
21.1.23714597990105054274863104.1 x21 + x19 - 5x18 + 8x17 - 5x16 + 11x15 - 40x14 + 33x13 + 2x12 + 62x11 - 87x10 - 12x9 - 43x8 + 76x7 + 27x6 - 15x5 - 7x4 - 10x3 + 2x2 + x + 1 \( 2^{14}\cdot 11^{8}\cdot 41^{3}\cdot 461^{3} \) 21T74 Trivial (GRH)
21.5.26730926988131422081122304.1 x21 - 5x20 + 11x19 - 16x18 + 25x17 - 38x16 + 36x15 - 25x14 + 18x13 - 4x12 - 3x11 - 17x10 - 23x9 - 12x8 + 55x7 + 18x6 - 46x5 - 17x4 + 19x3 + 9x2 - 2x - 1 \( 2^{18}\cdot 317^{8} \) $\PSL(2,7)$ (as 21T14) Trivial (GRH)
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)
21.1.75911839528959490356446229.1 x21 - x18 - 3x15 + 2x12 + 4x9 - x6 - 2x3 - 1 \( 3^{21}\cdot 193607^{3} \) 21T138 Trivial (GRH)
21.5.85594961606810871789418849.1 x21 - 4x19 + 23x17 - 4x16 - 54x15 + 19x14 + 94x13 - 41x12 - 115x11 + 59x10 + 30x9 - 81x8 + 20x7 + 46x6 - 18x5 - 5x4 + 13x3 - 3x2 + 1 \( 23^{8}\cdot 239^{3}\cdot 431^{3} \) 21T74 Trivial (GRH)
21.3.108608979330127274981177223.1 x21 - 9x14 - 12x7 + 1 \( -\,3^{28}\cdot 7^{15} \) $C_3\times F_7$ (as 21T9) Trivial (GRH)
21.1.156106141952973043121291857.1 x21 - x20 - x19 + 2x18 + 5x17 + 2x16 - 10x15 - 2x14 + 23x13 + 19x12 - 11x11 - 28x10 + 8x9 + 47x8 + 23x7 - 13x6 - 24x5 - 7x4 + 11x3 + 6x2 - 1 \( 23^{7}\cdot 71^{9} \) $S_3\times D_7$ (as 21T8) Trivial (GRH)
21.3.167297208611536987435565056.1 x21 - 7x20 + 23x19 - 46x18 + 59x17 - 38x16 - 51x15 + 276x14 - 725x13 + 1392x12 - 2056x11 + 2397x10 - 2311x9 + 1987x8 - 1615x7 + 1208x6 - 783x5 + 436x4 - 201x3 + 66x2 - 12x + 1 \( -\,2^{18}\cdot 17^{6}\cdot 31^{9} \) 21T57 Trivial (GRH)
21.3.188012010050973537326115059.1 x21 - 3x20 + 2x19 - 4x18 + 10x17 - 9x16 + 70x15 - 167x14 + 91x13 + 110x12 - 252x11 + 50x10 + 456x9 - 519x8 + x7 + 487x6 - 548x5 + 272x4 - 48x3 + x2 - 3x + 1 \( -\,59^{8}\cdot 10859^{3} \) 21T74 Trivial (GRH)
21.3.214407920026380373514939807.1 x21 - x20 - x19 + x18 - x17 + 6x16 - 7x15 + 2x14 - 4x13 + 5x12 + 9x11 - 17x10 + 11x9 - 4x8 - 3x7 + 9x6 - 6x5 - x4 + 3x3 - x2 - x + 1 \( -\,184607^{5} \) 21T38 Trivial (GRH)
21.3.270061427296836406180775407.1 x21 - 4x18 - x17 + x16 + 7x15 + x14 - 6x13 - 11x12 + 2x11 + 10x10 + 14x9 - 2x8 - 5x7 - 6x6 + 2x5 - 2x4 - 3x3 + 2x2 - 1 \( -\,193327^{5} \) 21T38 Trivial (GRH)
21.3.336444035684435024524918784.1 x21 - 5x20 + 11x19 - 5x18 - 29x17 + 64x16 - 22x15 - 117x14 + 218x13 - 124x12 - 76x11 + 132x10 - 38x9 + 31x8 - 168x7 + 204x6 - 47x5 - 120x4 + 134x3 - 63x2 + 13x - 1 \( -\,2^{14}\cdot 11^{13}\cdot 29^{6} \) 21T57 Trivial (GRH)
21.3.930871627030827422699634607.1 x21 - 5x20 + 36x18 - 35x17 - 108x16 + 155x15 + 176x14 - 338x13 - 129x12 + 413x11 - 50x10 - 234x9 + 162x8 - 66x7 - 51x6 + 196x5 - 92x4 - 98x3 + 71x2 - 10x - 25 \( -\,151^{2}\cdot 2377^{2}\cdot 193327^{3} \) 21T139 Trivial (GRH)
21.1.1261412107834594448324876441.1 x21 + 3x19 - x18 + x17 + 8x16 - 7x15 + 24x14 - 15x13 + 7x12 + 25x11 - 42x10 + 46x9 - 39x8 - 12x7 + 15x6 - 14x5 + x4 + 10x3 - x2 + 2x + 1 \( 31^{7}\cdot 71^{9} \) $S_3\times D_7$ (as 21T8) Trivial (GRH)
21.1.1901751171347368714361726129.1 x21 - x14 + 1 \( 7^{21}\cdot 23^{7} \) 21T29 Trivial (GRH)
21.9.2523828389200110188894232441.1 x21 - 9x19 + 3x17 + 66x15 - 75x14 - 90x13 + 198x12 - 21x11 + 63x9 - 177x8 + 54x7 + 45x6 - 51x5 + 18x4 - 8x3 - 3x2 + 3 \( 3^{34}\cdot 73^{6} \) 21T44 Trivial (GRH)
21.9.3326751700248238687839567609.1 x21 - 6x20 + 12x19 - 2x18 - 27x17 + 36x16 - 39x15 + 180x14 - 396x13 + 183x12 + 558x11 - 738x10 - 339x9 + 1035x8 + 27x7 - 936x6 + 27x5 + 621x4 + 99x3 - 189x2 - 81x - 9 \( 3^{36}\cdot 53^{6} \) 21T44 Trivial (GRH)
21.3.4266945093472415611428661007.1 x21 - x20 - 7x19 + 6x18 + 16x17 - 27x16 + 3x15 + 119x14 + 23x13 - 181x12 - 153x11 + 154x10 + 417x9 - 133x8 - 395x7 + 153x6 + 61x5 - 33x4 + 2x3 + 7x2 - 2x - 1 \( -\,7^{14}\cdot 184607^{3} \) 21T56 Trivial (GRH)
21.3.4297390112987454978404646912.1 x21 - x20 + 9x19 - 7x18 + 35x17 - 27x16 + 83x15 - 61x14 + 123x13 - 111x12 + 163x11 - 225x10 + 213x9 - 253x8 + 177x7 - 167x6 + 192x5 - 180x4 + 136x3 - 76x2 - 12x + 4 \( -\,2^{38}\cdot 3^{18}\cdot 7^{9} \) $SO(3,7)$ (as 21T20) Trivial (GRH)
21.3.4900609474961156001559784767.1 x21 - x20 - 2x19 + 9x18 - 8x17 - 16x16 + 40x15 + 25x14 - 4x13 - 178x12 - 112x11 + 286x10 + 394x9 - 392x8 - 175x7 + 201x6 - 68x5 - 36x4 + 30x3 - 4x2 - 4x + 1 \( -\,7^{14}\cdot 193327^{3} \) 21T56 Trivial (GRH)
21.1.5737729418385982521381124421.1 x21 - x - 1 \( 1137694897331\cdot 5043293621028391 \) 21T164 Trivial (GRH)
21.1.5947444618385982521381124421.1 x21 + x - 1 \( 11\cdot 17\cdot 1033\cdot 1583\cdot 159503\cdot 121937899012999 \) 21T164 Trivial (GRH)
21.3.7146646609494406531041460224.1 x21 - 3x20 - 4x19 + 16x18 - 9x17 - 33x16 + 52x15 + 12x14 - 136x13 + 96x12 + 180x11 - 260x10 - 144x9 + 312x8 + 44x7 - 220x6 + 15x5 + 59x4 - 16x3 + 36x2 - 31x + 1 \( -\,2^{64}\cdot 3^{18} \) $SO(3,7)$ (as 21T20) Trivial (GRH)
21.1.7399096241029480225646983928.1 x21 - 2x20 - x19 + 7x18 - 3x17 - 13x16 + 14x15 + 13x14 - 28x13 - 2x12 + 34x11 - 15x10 - 25x9 + 24x8 + 7x7 - 21x6 + 6x5 + 8x4 - 7x3 + 2x - 1 \( 2^{3}\cdot 101\cdot 1951\cdot 7481\cdot 35629381\cdot 17609300881 \) 21T164 Trivial (GRH)
21.3.8971378199137136745057872231.1 x21 - x20 + 3x19 + 4x18 + 8x17 - 12x16 + 9x15 + 113x14 - 287x13 + 404x12 - 526x11 + 1106x10 - 2438x9 + 2381x8 - 2385x7 + 3637x6 - 6756x5 + 4734x4 - 3615x3 + 1513x2 - 2017x - 1319 \( -\,7^{2}\cdot 13^{2}\cdot 71^{9}\cdot 4861^{2} \) 21T76 Trivial (GRH)
21.1.9900725472657912423302447104.1 x21 - 3x20 - 2x19 + 25x18 - 40x17 - 24x16 + 156x15 - 215x14 + 131x13 - 57x12 + 294x11 - 907x10 + 1374x9 - 1171x8 + 439x7 + 387x6 - 847x5 + 669x4 - 179x3 - 142x2 + 156x - 38 \( 2^{14}\cdot 11^{10}\cdot 13^{12} \) $D_{21}:C_3$ (as 21T10) Trivial (GRH)
21.3.10367263422675536780303271503.1 x21 - 6x20 - x19 + 72x18 - 100x17 - 299x16 + 733x15 + 386x14 - 2195x13 + 634x12 + 3126x11 - 2357x10 - 2090x9 + 2868x8 + 87x7 - 1535x6 + 673x5 + 170x4 - 243x3 + 89x2 - 15x + 1 \( -\,11^{4}\cdot 103^{4}\cdot 184607^{3} \) 21T130 Trivial (GRH)
21.5.12329728569841547876503864001.1 x21 - 2x19 - x18 - 8x17 + 16x15 + 16x14 + 21x13 - 27x12 - 29x11 - 63x10 - 3x9 + 86x8 + 60x7 + 11x6 - 69x5 - 49x4 + 30x3 + 16x2 - 6x - 1 \( 7^{9}\cdot 12503^{5} \) 21T38 Trivial (GRH)
21.1.15367056821818447650208822777.1 x21 + x7 - 1 \( 7^{21}\cdot 31^{7} \) 21T29 Trivial (GRH)
21.9.18453551447289410297167049873.1 x21 - 2x20 - 2x19 + 12x18 - 25x17 + x16 + 48x15 - 91x14 + 103x13 - 12x12 - 110x11 + 272x10 - 277x9 - 78x8 + 278x7 - 46x6 + 11x5 - 114x4 + 3x3 + 93x2 - 19x - 23 \( 71^{3}\cdot 8623^{3}\cdot 283573^{2} \) 21T139 Trivial (GRH)
21.3.19019216778782670169504453271.1 x21 - 9x20 + 23x19 + 24x18 - 196x17 + 152x16 + 587x15 - 1008x14 - 562x13 + 2180x12 - 404x11 - 2259x10 + 1317x9 + 1079x8 - 1081x7 - 177x6 + 477x5 - 106x4 - 81x3 + 53x2 - 12x + 1 \( -\,67^{2}\cdot 71^{9}\cdot 9613^{2} \) 21T76 Trivial (GRH)
21.3.20735011601517857380131405824.1 x21 - 4x20 + 8x19 - 12x18 + 12x17 - 16x16 + 44x15 - 94x14 + 160x13 - 200x12 + 184x11 - 132x10 + 52x9 - 8x7 + 4x6 + 16x4 - 36x3 + 32x2 - 16x + 4 \( -\,2^{20}\cdot 11^{7}\cdot 317^{6} \) 21T27 Trivial (GRH)
21.3.20735011601517857380131405824.2 x21 - 2x20 + 2x19 - 4x16 - 6x15 + 8x14 - 16x13 + 30x12 - 24x11 + 22x10 - 48x9 - 4x8 - 30x7 + 8x6 - 4x5 - 12x4 - 10x3 + 12x2 - 4x + 2 \( -\,2^{20}\cdot 11^{7}\cdot 317^{6} \) 21T27 Trivial (GRH)
21.5.27984468103350046268523020288.1 x21 - 2x19 - 7x18 - 5x17 + 11x16 + 17x15 + 34x14 - 32x13 - 19x12 - 120x11 - 65x10 - 276x9 + 43x8 + 539x7 + 983x6 + 606x5 + 280x4 + 121x3 + 40x2 - 13x - 5 \( 2^{27}\cdot 181^{9} \) $SO(3,7)$ (as 21T20) Trivial (GRH)
21.3.31095511042786085990206459319.1 x21 - x20 - 7x19 + 6x18 + 3x17 - 30x16 + 72x15 + 134x14 - 49x13 - 195x12 - 375x11 + 190x10 + 878x9 - 233x8 - 491x7 + 177x6 + 32x5 - 47x4 + 21x3 + 10x2 - 4x - 1 \( -\,7^{14}\cdot 71^{9} \) $C_3\times D_7$ (as 21T3) Trivial (GRH)
21.1.34154868120917133312000000000.1 x21 - 10x18 + 36x15 - 76x12 - 224x9 - 144x6 - 32x3 - 16 \( 2^{20}\cdot 3^{34}\cdot 5^{9} \) $S_3\times F_7$ (as 21T15) Trivial (GRH)
21.5.34815740375535437995421466177.1 x21 - 2x20 - 5x18 + 12x17 - 5x16 + 4x15 - 27x14 + 16x13 - 8x12 + 8x11 - 22x10 - 8x9 - 2x8 + 9x7 + 15x6 + 12x5 + 13x4 + 2x3 - x2 - 2x - 1 \( 3^{8}\cdot 37^{5}\cdot 2381^{5} \) 21T38 Trivial (GRH)
21.5.41784109442335295334261365153.1 x21 - 3x19 - 2x18 + 15x17 + 6x16 - 23x15 - 30x14 + 23x13 + 44x12 + 12x11 - 43x10 - 61x9 + 51x8 + 34x7 - 5x6 - 30x5 - 9x4 + 13x3 + 7x2 - 1 \( 23^{7}\cdot 107^{3}\cdot 21557^{3} \) 21T74 Trivial (GRH)
21.1.75375354289024738220986584068.1 x21 - 2x20 - x19 + 7x18 - 3x17 - 13x16 + 14x15 + 13x14 - 28x13 - 2x12 + 34x11 - 15x10 - 25x9 + 25x8 + 7x7 - 22x6 + 6x5 + 8x4 - 7x3 + 2x - 1 \( 2^{2}\cdot 11\cdot 29\cdot 1447\cdot 2579\cdot 4423\cdot 3578836676945557 \) 21T164 Trivial (GRH)
21.9.77814973866654515283350056553.1 x21 - 8x20 + 15x19 + 42x18 - 181x17 + 43x16 + 664x15 - 785x14 - 999x13 + 2386x12 - 12x11 - 3337x10 + 2186x9 + 1818x8 - 2845x7 + 445x6 + 1349x5 - 754x4 - 347x3 + 279x2 + 76x + 1 \( 71^{3}\cdot 157^{2}\cdot 3709^{2}\cdot 8623^{3} \) 21T139 Trivial (GRH)
21.7.105070765003019731854543276767.1 x21 - x20 - 6x19 + 11x18 + 47x17 - 45x16 - 170x15 + 162x14 + 400x13 - 307x12 - 750x11 + 395x10 + 733x9 - 371x8 - 425x7 + 197x6 + 204x5 - 78x4 - 36x3 + 17x2 - 1 \( -\,17^{3}\cdot 23^{8}\cdot 64879^{3} \) 21T74 Trivial (GRH)

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