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Label Polynomial Discriminant Galois group Class group Regulator
12.8.1130350095703125.1 $x^{12} - 6 x^{11} + 9 x^{10} + 9 x^{9} - 33 x^{8} + 30 x^{7} - 10 x^{6} - 48 x^{5} + 78 x^{4} + 3 x^{3} - 30 x^{2} - 3 x + 1$ $3^{14}\cdot 5^{9}\cdot 11^{2}$ $S_3^2:C_4$ (as 12T79) trivial $1589.3897461008255$
12.6.5135673858195456.1 $x^{12} - 6 x^{10} - 4 x^{9} + 3 x^{8} + 36 x^{7} - 4 x^{6} - 48 x^{5} - 6 x^{4} + 16 x^{3} + 24 x^{2} - 8$ $-\,2^{30}\cdot 3^{14}$ $\SOPlus(4,2)$ (as 12T35) trivial $12561.6080377$
12.4.10271347716390912.1 $x^{12} - 4 x^{9} + 12 x^{8} + 2 x^{6} - 72 x^{5} + 12 x^{4} + 100 x^{3} - 132 x^{2} + 96 x - 23$ $2^{31}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $5596.71858495$
12.2.20542695432781824.21 $x^{12} - 6 x^{10} - 16 x^{9} - 15 x^{8} - 24 x^{7} - 24 x^{6} - 24 x^{5} - 15 x^{4} - 16 x^{3} - 6 x^{2} + 1$ $-\,2^{32}\cdot 3^{14}$ $\SOPlus(4,2)$ (as 12T36) trivial $7694.69688611$
12.4.41085390865563648.1 $x^{12} + 6 x^{10} - 12 x^{9} + 3 x^{8} + 60 x^{7} - 136 x^{6} + 120 x^{5} - 24 x^{4} - 48 x^{3} + 24 x^{2} - 2$ $2^{33}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $12787.4664345$
12.0.41085390865563648.20 $x^{12} + 12 x^{10} - 8 x^{9} + 78 x^{8} - 72 x^{7} + 308 x^{6} - 288 x^{5} + 711 x^{4} - 592 x^{3} + 924 x^{2} - 816 x + 526$ $2^{33}\cdot 3^{14}$ $(C_3\times C_3):C_4$ (as 12T17) $[2]$ $6058.14180821$
12.6.82170781731127296.1 $x^{12} - 12 x^{10} + 48 x^{8} - 96 x^{6} + 108 x^{4} + 144 x^{2} - 144$ $-\,2^{34}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T201) trivial $25238.0448986$
12.6.82170781731127296.2 $x^{12} - 12 x^{10} + 42 x^{8} - 24 x^{6} - 81 x^{4} + 108 x^{2} - 36$ $-\,2^{34}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T201) trivial $52560.5798808$
12.6.82170781731127296.3 $x^{12} - 6 x^{10} + 3 x^{8} + 12 x^{6} + 9 x^{4} - 18 x^{2} - 9$ $-\,2^{34}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T201) trivial $66877.8468166$
12.6.82170781731127296.4 $x^{12} - 6 x^{10} - 15 x^{8} - 60 x^{6} - 9 x^{4} + 90 x^{2} - 9$ $-\,2^{34}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T201) trivial $31131.4421679$
12.2.82170781731127296.8 $x^{12} + 6 x^{10} - 3 x^{8} - 120 x^{6} - 288 x^{4} - 216 x^{2} - 36$ $-\,2^{34}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T201) trivial $7289.13047097$
12.2.82170781731127296.12 $x^{12} + 6 x^{10} - 15 x^{8} + 60 x^{6} - 9 x^{4} - 90 x^{2} - 9$ $-\,2^{34}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T200) $[2]$ $7078.46847361$
12.4.164341563462254592.1 $x^{12} - 6 x^{11} + 15 x^{10} - 6 x^{9} - 69 x^{8} + 204 x^{7} - 238 x^{6} - 36 x^{5} + 579 x^{4} - 1014 x^{3} + 879 x^{2} - 294 x - 23$ $2^{35}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $23998.7867955$
12.8.164341563462254592.1 $x^{12} - 18 x^{10} + 105 x^{8} - 228 x^{6} + 234 x^{4} - 108 x^{2} + 18$ $2^{35}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $43838.1438943$
12.4.164341563462254592.2 $x^{12} - 24 x^{9} - 12 x^{8} + 72 x^{7} + 188 x^{6} - 312 x^{5} - 123 x^{4} + 264 x^{3} - 204 x^{2} + 192 x - 14$ $2^{35}\cdot 3^{14}$ $C_2\times C_3^2:C_4$ (as 12T41) trivial $42465.0056166$
12.4.164341563462254592.5 $x^{12} - 6 x^{10} - 15 x^{8} + 156 x^{6} - 198 x^{4} - 180 x^{2} + 18$ $2^{35}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $69058.3330193$
12.4.164...592.19 $x^{12} - 12 x^{8} - 24 x^{6} + 18 x^{4} + 216 x^{2} + 72$ $2^{35}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $52482.0428066$
12.4.164...592.26 $x^{12} + 12 x^{10} + 42 x^{8} - 48 x^{6} - 288 x^{4} + 288$ $2^{35}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $35930.2072188$
12.4.164...592.27 $x^{12} - 12 x^{10} + 42 x^{8} + 48 x^{6} - 288 x^{4} + 288$ $2^{35}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $27696.4716677$
12.8.289369624500000000.1 $x^{12} - 3 x^{11} + 9 x^{10} + 19 x^{9} - 75 x^{8} + 192 x^{7} - 187 x^{6} - 204 x^{5} + 279 x^{4} + 11 x^{3} - 42 x^{2} + 1$ $2^{8}\cdot 3^{14}\cdot 5^{9}\cdot 11^{2}$ $C_3:S_3^3:C_4$ (as 12T245) trivial $23766.397630604413$
12.2.328683126924509184.1 $x^{12} - 6 x^{10} + 51 x^{8} - 132 x^{6} + 441 x^{4} + 54 x^{2} - 441$ $-\,2^{36}\cdot 3^{14}$ $(C_2^2\times A_4^2):C_4$ (as 12T241) trivial $20420.2934177$
12.6.328683126924509184.3 $x^{12} + 6 x^{10} + 3 x^{8} - 48 x^{6} + 72 x^{2} - 36$ $-\,2^{36}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T201) trivial $78015.7587989$
12.2.328683126924509184.3 $x^{12} + 12 x^{10} + 48 x^{8} + 96 x^{6} + 108 x^{4} - 144 x^{2} - 144$ $-\,2^{36}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T200) trivial $23300.3648249$
12.6.328683126924509184.4 $x^{12} - 6 x^{10} - 3 x^{8} + 120 x^{6} - 288 x^{4} + 216 x^{2} - 36$ $-\,2^{36}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T200) trivial $77919.347564$
12.6.328683126924509184.5 $x^{12} + 6 x^{10} - 39 x^{8} + 60 x^{6} - 81 x^{4} + 54 x^{2} - 9$ $-\,2^{36}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T201) trivial $59337.7423393$
12.2.328683126924509184.7 $x^{12} + 12 x^{10} + 42 x^{8} + 24 x^{6} - 81 x^{4} - 108 x^{2} - 36$ $-\,2^{36}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T200) trivial $34259.1560974$
12.2.328683126924509184.8 $x^{12} - 6 x^{10} + 3 x^{8} + 48 x^{6} - 72 x^{2} - 36$ $-\,2^{36}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T200) $[2]$ $12241.4549258$
12.2.328683126924509184.9 $x^{12} + 30 x^{8} - 12 x^{6} + 153 x^{4} - 36 x^{2} - 36$ $-\,2^{36}\cdot 3^{14}$ $C_6^2:C_4$ (as 12T82) trivial $37077.8687039$
12.2.328...184.13 $x^{12} + 30 x^{8} + 12 x^{6} + 153 x^{4} + 36 x^{2} - 36$ $-\,2^{36}\cdot 3^{14}$ $C_6^2:C_4$ (as 12T82) $[3]$ $14842.120621$
12.2.328...184.17 $x^{12} - 6 x^{10} - 39 x^{8} - 60 x^{6} - 81 x^{4} - 54 x^{2} - 9$ $-\,2^{36}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T200) $[4]$ $7633.31726175$
12.2.328...184.18 $x^{12} + 6 x^{10} + 15 x^{8} + 12 x^{6} - 27 x^{4} - 54 x^{2} - 9$ $-\,2^{36}\cdot 3^{14}$ $(C_2^2\times A_4^2):C_4$ (as 12T241) trivial $27291.4899343$
12.2.328...184.20 $x^{12} + 6 x^{10} + 3 x^{8} - 12 x^{6} + 9 x^{4} + 18 x^{2} - 9$ $-\,2^{36}\cdot 3^{14}$ $S_4\wr C_2$ (as 12T200) trivial $24880.321592$
12.8.657366253849018368.2 $x^{12} - 12 x^{10} + 42 x^{8} - 84 x^{6} + 225 x^{4} - 432 x^{2} + 288$ $2^{37}\cdot 3^{14}$ $S_3^2:C_4$ (as 12T79) trivial $153152.048963$
12.4.657366253849018368.5 $x^{12} - 24 x^{8} + 60 x^{6} - 27 x^{4} - 36 x^{2} + 18$ $2^{37}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $46081.8962216$
12.4.657366253849018368.6 $x^{12} - 24 x^{8} - 60 x^{6} - 27 x^{4} + 36 x^{2} + 18$ $2^{37}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $63915.9301504$
12.4.657366253849018368.7 $x^{12} + 6 x^{10} - 15 x^{8} - 156 x^{6} - 198 x^{4} + 180 x^{2} + 18$ $2^{37}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $48271.1258774$
12.0.657366253849018368.8 $x^{12} + 18 x^{10} + 105 x^{8} + 228 x^{6} + 234 x^{4} + 108 x^{2} + 18$ $2^{37}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) $[2]$ $11792.4560111$
12.4.657366253849018368.9 $x^{12} + 6 x^{10} - 39 x^{8} - 120 x^{6} + 360 x^{4} - 864 x^{2} + 72$ $2^{37}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $58908.8441685$
12.4.657...368.10 $x^{12} - 12 x^{8} + 24 x^{6} + 18 x^{4} - 216 x^{2} + 72$ $2^{37}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $58651.6509713$
12.4.657...368.16 $x^{12} - 6 x^{10} - 15 x^{8} + 96 x^{6} + 144 x^{4} - 576 x^{2} + 288$ $2^{37}\cdot 3^{14}$ $C_2\times A_4^2:C_4$ (as 12T198) trivial $163329.982884$
12.0.657...368.39 $x^{12} - 12 x^{8} + 240 x^{6} + 18 x^{4} - 432 x^{2} + 288$ $2^{37}\cdot 3^{14}$ $A_4^2:C_4$ (as 12T160) $[2]$ $42362.0562965$
12.0.657...368.42 $x^{12} + 12 x^{10} + 42 x^{8} + 84 x^{6} + 225 x^{4} + 432 x^{2} + 288$ $2^{37}\cdot 3^{14}$ $S_3^2:C_4$ (as 12T79) $[2, 6]$ $2300.25512656$
12.2.131...736.1 $x^{12} + 6 x^{10} + 51 x^{8} + 132 x^{6} + 441 x^{4} - 54 x^{2} - 441$ $-\,2^{38}\cdot 3^{14}$ $(C_2^2\times A_4^2):C_4$ (as 12T241) trivial $89363.76853$
12.2.131...736.11 $x^{12} + 6 x^{10} + 3 x^{8} - 24 x^{6} - 72 x^{4} - 72 x^{2} - 36$ $-\,2^{38}\cdot 3^{14}$ $(C_2^2\times A_4^2):C_4$ (as 12T241) trivial $51585.8914129$
12.2.131...736.13 $x^{12} - 6 x^{10} + 3 x^{8} + 24 x^{6} - 72 x^{4} + 72 x^{2} - 36$ $-\,2^{38}\cdot 3^{14}$ $(C_2^2\times A_4^2):C_4$ (as 12T241) trivial $95231.8040231$
12.2.131...736.25 $x^{12} - 6 x^{10} + 15 x^{8} - 12 x^{6} - 27 x^{4} + 54 x^{2} - 9$ $-\,2^{38}\cdot 3^{14}$ $(C_2^2\times A_4^2):C_4$ (as 12T241) trivial $63551.0263085$
12.8.262...472.2 $x^{12} - 18 x^{10} + 111 x^{8} - 312 x^{6} + 432 x^{4} - 288 x^{2} + 72$ $2^{39}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $337042.269235$
12.4.262...472.2 $x^{12} + 6 x^{10} - 21 x^{8} - 276 x^{6} - 846 x^{4} - 324 x^{2} + 18$ $2^{39}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) $[2]$ $67646.0496888$
12.8.262...472.3 $x^{12} - 42 x^{8} - 96 x^{6} + 864 x^{4} - 1152 x^{2} + 288$ $2^{39}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $259378.835226$
12.4.262...472.5 $x^{12} + 6 x^{10} + 3 x^{8} - 12 x^{6} + 18 x^{4} - 36 x^{2} + 18$ $2^{39}\cdot 3^{14}$ $S_4^2:C_4$ (as 12T237) trivial $144605.875396$
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