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Label Polynomial Discriminant Galois group Class group
21.3.123150719151859535557398786815169892171776.1 x21 + 24x19 - 16x18 + 270x17 - 360x16 + 2820x15 - 5400x14 + 36081x13 - 87416x12 + 190863x11 - 385986x10 + 120545x9 + 1087884x8 - 8079579x7 + 29377014x6 - 55677564x5 + 60990264x4 - 40506896x3 + 16190496x2 - 3597888x + 342656 \( -\,2^{14}\cdot 3^{28}\cdot 71^{9}\cdot 2677^{2} \) 21T122 Trivial (GRH)
21.3.241787774691530742888323503970893214367744.1 x21 - 24x19 - 34x18 + 9x17 + 480x16 + 2410x15 + 2646x14 - 453x13 - 31052x12 + 16326x11 - 187728x10 - 267343x9 + 719244x8 - 6331761x7 - 8237756x6 - 12927024x5 - 9316032x4 - 7774096x3 - 4321152x2 - 1440384x - 480128 \( -\,2^{14}\cdot 3^{28}\cdot 11^{4}\cdot 31^{2}\cdot 71^{9} \) 21T122 $[3]$ (GRH)
21.13.83737838586499625317207823358068174759018496.1 x21 - 27x19 - 18x18 + 171x17 + 228x16 + 589x15 + 1026x14 - 5067x13 - 15184x12 - 15093x11 - 6006x10 + 26188x9 + 105696x8 + 177387x7 + 165758x6 + 98172x5 + 43416x4 + 17424x3 + 6048x2 + 1344x + 128 \( 2^{14}\cdot 3^{31}\cdot 587^{9} \) 21T122 Trivial (GRH)
21.13.6782764925506469650693833692003522155480498176.1 x21 - 6x19 - 4x18 - 126x17 - 168x16 + 322x15 + 756x14 + 4554x13 + 10912x12 + 5454x11 - 13020x10 - 60139x9 - 164556x8 - 259701x7 - 251642x6 - 171396x5 - 97416x4 - 48624x3 - 18144x2 - 4032x - 384 \( 2^{14}\cdot 3^{35}\cdot 587^{9} \) 21T122 Trivial (GRH)
21.17.10322551559300386187871072331953642204421617893376.1 x21 - 48x19 - 32x18 + 846x17 + 1128x16 - 5726x15 - 12204x14 - 3924x13 + 9424x12 + 186678x11 + 589812x10 - 71609x9 - 2888964x8 - 4329267x7 + 474058x6 + 8477028x5 + 11551176x4 + 8074864x3 + 3259872x2 + 724416x + 68992 \( 2^{14}\cdot 3^{22}\cdot 7^{4}\cdot 11^{2}\cdot 1601^{9} \) 21T122 Trivial (GRH)
21.9.1750441539883089176601466819028470407898038292856832.1 x21 + 87x19 - 58x18 + 2538x17 - 3384x16 + 23268x15 - 44280x14 - 166662x13 + 516592x12 - 4292082x11 + 12795612x10 - 24847918x9 + 43400664x8 - 1311111x7 - 213707802x6 + 500038164x5 - 575760456x4 + 387377584x3 - 155234016x2 + 34496448x - 3285376 \( 2^{14}\cdot 3^{28}\cdot 577^{9}\cdot 25667^{2} \) 21T122 Trivial (GRH)
21.21.3793483076351788784186108732872148040652017859086592000000.1 x21 - 8x20 - 233x19 + 2271x18 + 14055x17 - 161041x16 - 485290x15 + 5398226x14 + 13931443x13 - 95749463x12 - 315559277x11 + 718427602x10 + 4151473307x9 + 2527041973x8 - 18494956965x7 - 54137613220x6 - 73425815916x5 - 59163722754x4 - 29842819052x3 - 9275792049x2 - 1629072398x - 123950137 \( 2^{14}\cdot 5^{6}\cdot 29^{4}\cdot 577^{9}\cdot 3271^{2}\cdot 525571^{2} \) 21T122 $[3]$ (GRH)


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