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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content
2.12.0.1 x12 + x7 + x6 + x5 + x3 + x + 1 $2$ $1$ $12$ $0$ $C_{12}$ (as 12T1) $[\ ]$ $[\ ]^{12}$
2.12.8.1 x12 + 11x9 + 3x8 - 9x6 - 90x5 + 3x4 - 27x3 + 135x2 + 27x + 55 $2$ $3$ $4$ $8$ $C_3 : C_4$ (as 12T5) $[\ ]$ $[\ ]_{3}^{4}$
2.12.8.2 x12 - 8x3 + 16 $2$ $3$ $4$ $8$ $C_3\times (C_3 : C_4)$ (as 12T19) $[\ ]$ $[\ ]_{3}^{12}$
2.12.12.1 x12 + 16x11 + 100x10 + 184x9 + 44x8 - 1472x7 - 2336x6 - 1600x5 + 18032x4 + 37504x3 + 66880x2 + 40064x + 13120 $2$ $2$ $6$ $12$ $C_2^4:C_3.D_4$ (as 12T134) $[2]$ $[2, 2, 2, 2, 2, 2]^{6}$
2.12.12.10 x12 + 8x11 + 32x10 + 120x9 + 356x8 + 16x7 - 1312x6 - 3936x5 - 17296x4 - 14272x3 + 103296x2 + 36352x + 38848 $2$ $2$ $6$ $12$ $C_2^2\wr C_2:C_3$ (as 12T58) $[2]$ $[2, 2, 2, 2]^{6}$
2.12.12.11 x12 + 28x10 + 40x9 + 356x8 + 896x7 + 2720x6 + 6656x5 + 12464x4 + 19456x3 + 26304x2 + 19840x + 5824 $2$ $2$ $6$ $12$ $A_4 \times C_2$ (as 12T7) $[2]$ $[2, 2]^{6}$
2.12.12.12 x12 + 84x10 - 88x9 + 1660x8 - 1568x7 + 13920x6 - 4928x5 + 47280x4 + 23936x3 + 63552x2 + 32896x + 51520 $2$ $2$ $6$ $12$ $C_4\times A_4$ (as 12T29) $[2]$ $[2, 2, 2]^{6}$
2.12.12.13 x12 - 6x11 + 60x10 - 100x9 + 876x8 - 304x7 + 5696x6 + 544x5 + 17712x4 - 1248x3 + 14144x2 - 5184x + 1600 $2$ $2$ $6$ $12$ $C_2^5.C_6$ (as 12T105) $[2]$ $[2, 2, 2, 2, 2]^{6}$
2.12.12.14 x12 - 6x11 + 36x10 - 164x9 + 660x8 - 2352x7 + 6720x6 - 15584x5 + 28656x4 - 41056x3 + 48320x2 - 37696x + 22720 $2$ $2$ $6$ $12$ $C_2^4:C_3.D_4$ (as 12T134) $[2]$ $[2, 2, 2, 2, 2, 2]^{6}$
2.12.12.15 x12 - 4x11 + 44x10 - 152x9 + 692x8 - 1952x7 + 6624x6 - 12224x5 + 33776x4 - 54976x3 + 73920x2 - 129664x + 96448 $2$ $2$ $6$ $12$ $C_2^4:C_3.D_4$ (as 12T134) $[2]$ $[2, 2, 2, 2, 2, 2]^{6}$
2.12.12.16 x12 - 6x11 + 16x10 - 12x9 - 68x8 + 16x7 + 832x6 - 4320x5 + 11632x4 - 6240x3 + 13568x2 + 9536x + 1600 $2$ $2$ $6$ $12$ $C_2^4:C_3.D_4$ (as 12T134) $[2]$ $[2, 2, 2, 2, 2, 2]^{6}$
2.12.12.17 x12 + 12x10 + 32x9 + 84x8 + 32x7 + 544x6 - 704x5 - 4176x4 - 5248x3 + 16064x2 + 21248x + 6592 $2$ $2$ $6$ $12$ $C_4\times A_4$ (as 12T29) $[2]$ $[2, 2]^{12}$
2.12.12.18 x12 - 10x11 + 72x10 - 332x9 + 1316x8 - 4160x7 + 12128x6 - 27904x5 + 53744x4 - 69600x3 + 71680x2 - 41536x + 38848 $2$ $2$ $6$ $12$ $D_4 \times C_3$ (as 12T14) $[2]$ $[2, 2]^{6}$
2.12.12.19 x12 + 6x11 + 40x10 + 188x9 + 732x8 + 2896x7 + 8224x6 + 22240x5 + 43760x4 + 56672x3 + 77824x2 - 19776x + 66112 $2$ $2$ $6$ $12$ $C_2^5.C_6$ (as 12T105) $[2]$ $[2, 2, 2, 2]^{12}$
2.12.12.2 x12 - 2x11 - 8x10 - 244x9 + 500x8 + 1696x7 + 6656x6 + 22336x5 + 35952x4 + 61344x3 + 75648x2 + 52288x + 36544 $2$ $2$ $6$ $12$ $C_2^5.C_6$ (as 12T105) $[2]$ $[2, 2, 2, 2, 2]^{6}$
2.12.12.20 x12 - 2x11 - 172x9 - 172x8 + 2112x7 + 7968x6 + 13568x5 + 22320x4 + 29216x3 + 22912x2 + 18624x + 11200 $2$ $2$ $6$ $12$ $C_2\times C_2^2\wr C_2:C_3$ (as 12T87) $[2]$ $[2, 2, 2, 2, 2]^{6}$
2.12.12.21 x12 + 16x11 + 88x10 + 24x9 - 1308x8 - 4288x7 - 736x6 + 26176x5 + 68592x4 + 77696x3 + 42752x2 + 13440x + 4544 $2$ $2$ $6$ $12$ $C_2^4:C_3.D_4$ (as 12T134) $[2]$ $[2, 2, 2, 2, 2, 2]^{6}$
2.12.12.22 x12 + 10x11 - 16x10 - 316x9 - 364x8 + 1040x7 + 7648x6 + 17632x5 + 25008x4 + 17056x3 + 6016x2 + 1344x + 4544 $2$ $2$ $6$ $12$ $C_2^4:C_3.D_4$ (as 12T134) $[2]$ $[2, 2, 2, 2, 2, 2]^{6}$
2.12.12.23 x12 + 56x10 - 152x9 - 764x8 + 2976x7 - 960x6 - 11008x5 + 20336x4 - 14976x3 + 80768x2 + 6016x + 38848 $2$ $2$ $6$ $12$ $C_2^2 \times A_4$ (as 12T25) $[2]$ $[2, 2, 2]^{6}$
2.12.12.24 x12 - 10x11 + 72x10 - 292x9 + 1028x8 - 2144x7 + 5280x6 - 5568x5 + 12400x4 - 12384x3 + 24832x2 - 14784x + 11200 $2$ $2$ $6$ $12$ $D_4 \times C_3$ (as 12T14) $[2]$ $[2, 2]^{6}$
2.12.12.25 x12 + 12x11 + 60x10 + 160x9 + 308x8 + 736x7 + 2272x6 + 5632x5 + 10608x4 + 15040x3 + 12224x2 + 3584x + 704 $2$ $2$ $6$ $12$ $C_{12}$ (as 12T1) $[2]$ $[2]^{6}$
2.12.12.26 x12 + 12x11 + 98x10 + 542x9 + 2359x8 + 7956x7 + 21831x6 + 47308x5 + 82476x4 + 109442x3 + 112071x2 + 76900x + 33205 $2$ $2$ $6$ $12$ $C_6\times C_2$ (as 12T2) $[2]$ $[2]^{6}$
2.12.12.27 x12 + 4x8 - 2x7 + 4x6 + 4x4 - 4x3 + 12x2 - 4x + 4 $2$ $6$ $2$ $12$ $A_4:C_4$ (as 12T30) $[4/3]$ $[4/3, 4/3]_{3}^{4}$
2.12.12.28 x12 + 6x11 + 21x10 + 50x9 + 90x8 + 130x7 + 159x6 + 132x5 + 10x4 - 100x3 - 53x2 + 22x + 19 $2$ $6$ $2$ $12$ $S_4$ (as 12T9) $[4/3]$ $[4/3, 4/3]_{3}^{2}$
2.12.12.29 x12 + 4x8 + 4x7 - 2x6 + 4x4 + 8x3 - 4x + 4 $2$ $6$ $2$ $12$ $A_4^2.C_4$ (as 12T159) $[4/3]$ $[4/3, 4/3, 4/3, 4/3]_{3}^{12}$
2.12.12.3 x12 - 4x11 + 52x10 - 128x9 + 532x8 - 1184x7 + 6080x6 - 2304x5 + 36144x4 - 10688x3 + 86208x2 - 38656x + 107968 $2$ $2$ $6$ $12$ $C_2^4:C_3.D_4$ (as 12T134) $[2]$ $[2, 2, 2, 2, 2, 2]^{6}$
2.12.12.30 x12 + 4x8 + 2x7 - 2x6 + 4x4 + 4x3 + 4x + 4 $2$ $6$ $2$ $12$ $A_4\wr C_2$ (as 12T126) $[4/3]$ $[4/3, 4/3, 4/3, 4/3]_{3}^{6}$
2.12.12.31 x12 + 2x10 + 2x9 + 6x8 + 12x7 + 32x6 + 48x5 + 76x4 + 48x3 + 40x2 + 8x + 8 $2$ $4$ $3$ $12$ 12T205 $[4/3, 4/3]$ $[4/3, 4/3, 4/3, 4/3, 4/3, 4/3]_{3}^{6}$
2.12.12.32 x12 - 4x10 - 4x9 + 26x8 + 40x7 - 4x6 - 40x5 + 28x4 + 72x3 + 24x2 - 16x + 8 $2$ $4$ $3$ $12$ $A_4\wr C_2$ (as 12T129) $[4/3, 4/3]$ $[4/3, 4/3, 4/3, 4/3]_{3}^{6}$
2.12.12.33 x12 + 2x10 + 6x9 + 6x8 + 8x7 + 28x6 + 24x5 + 20x4 + 24x3 + 32x2 + 24x + 8 $2$ $4$ $3$ $12$ $C_3\times S_4$ (as 12T45) $[4/3, 4/3]$ $[4/3, 4/3]_{3}^{6}$
2.12.12.34 x12 + 2x + 2 $2$ $12$ $1$ $12$ 12T254 $[10/9, 10/9]$ $[10/9, 10/9, 10/9, 10/9, 10/9, 10/9]_{9}^{6}$
2.12.12.4 x12 + 6x11 + 24x10 + 84x9 + 196x8 + 336x7 + 768x6 + 2144x5 + 4784x4 + 8032x3 + 9600x2 + 6976x + 2240 $2$ $2$ $6$ $12$ $C_2\times C_2^2\wr C_2:C_3$ (as 12T87) $[2]$ $[2, 2, 2, 2, 2]^{6}$
2.12.12.5 x12 + 4x11 + 24x10 - 8x9 + 140x8 - 1488x7 + 832x6 - 10208x5 + 20336x4 + 12160x3 + 113280x2 + 139520x + 45376 $2$ $2$ $6$ $12$ $D_4\times A_4$ (as 12T51) $[2]$ $[2, 2, 2, 2]^{6}$
2.12.12.6 x12 + 16x11 + 120x10 - 1052x8 - 1904x7 - 736x6 + 3104x5 + 15856x4 + 18368x3 + 28160x2 + 14208x + 11200 $2$ $2$ $6$ $12$ $C_2^5.C_6$ (as 12T105) $[2]$ $[2, 2, 2, 2]^{12}$
2.12.12.7 x12 + 2x11 + 8x10 + 108x9 + 452x8 + 1328x7 + 5952x6 + 25760x5 + 72688x4 + 129184x3 + 143232x2 + 92096x + 26560 $2$ $2$ $6$ $12$ $C_2^4:C_3.D_4$ (as 12T134) $[2]$ $[2, 2, 2, 2, 2, 2]^{6}$
2.12.12.8 x12 - 4x11 + 20x10 - 64x9 + 196x8 - 336x7 + 736x6 + 160x5 + 1712x4 + 5632x3 + 5440x2 + 6784x + 5824 $2$ $2$ $6$ $12$ $D_4\times A_4$ (as 12T51) $[2]$ $[2, 2, 2, 2]^{6}$
2.12.12.9 x12 + 2x11 + 52x10 + 116x9 + 964x8 + 2928x7 + 10272x6 + 24800x5 + 47088x4 + 67104x3 + 107584x2 + 64320x + 107968 $2$ $2$ $6$ $12$ $C_2^2\wr C_2:C_3$ (as 12T58) $[2]$ $[2, 2, 2, 2]^{6}$
2.12.14.1 x12 + 2x3 + 2 $2$ $12$ $1$ $14$ $S_4$ (as 12T8) $[4/3, 4/3]$ $[4/3, 4/3]_{3}^{2}$
2.12.14.2 x12 + 2x4 + 2x3 + 2 $2$ $12$ $1$ $14$ $A_4:C_4$ (as 12T27) $[4/3, 4/3]$ $[4/3, 4/3]_{3}^{4}$
2.12.14.3 x12 + 2x3 + 2x2 + 2 $2$ $12$ $1$ $14$ $A_4\wr C_2$ (as 12T128) $[4/3, 4/3]$ $[4/3, 4/3, 4/3, 4/3]_{3}^{6}$
2.12.16.1 x12 - 2x11 + 4x10 + 4x9 - 4x7 + 10x6 + 8x5 + 4x4 + 12x3 + 12x2 + 12 $2$ $6$ $2$ $16$ 12T208 $[2]$ $[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$
2.12.16.10 x12 - 2x11 + 8x10 - 2x9 + 8x8 + 4x7 + 2x6 + 8x5 - 4x4 + 4x3 + 4 $2$ $6$ $2$ $16$ $(C_2\times A_4^2).C_2$ (as 12T158) $[2]$ $[4/3, 4/3, 4/3, 4/3, 2]_{3}^{6}$
2.12.16.11 x12 + 4x11 + 4x10 + 2x9 + 8x8 + 8x7 + 6x6 + 8x5 + 4x4 + 20x3 + 4x2 + 28 $2$ $6$ $2$ $16$ $C_3\times (C_3 : C_4)$ (as 12T19) $[2]$ $[2]_{3}^{6}$
2.12.16.12 x12 - 2x11 + 4x10 + 2x9 + 8x8 - 4x7 + 10x6 + 4x5 + 4x4 + 12x3 + 12x2 + 12 $2$ $6$ $2$ $16$ $A_4^2.C_4$ (as 12T159) $[2]$ $[4/3, 4/3, 4/3, 4/3, 2]_{3}^{6}$
2.12.16.13 x12 + 10x11 + 47x10 + 144x9 + 330x8 + 578x7 + 785x6 + 830x5 + 530x4 - 64x3 - 189x2 - 30x + 25 $2$ $6$ $2$ $16$ $D_6$ (as 12T3) $[2]$ $[2]_{3}^{2}$
2.12.16.14 x12 - 2x11 + 4x10 - 2x9 + 12x8 - 4x7 + 10x6 - 4x5 + 4x4 + 12x2 + 12 $2$ $6$ $2$ $16$ 12T208 $[2]$ $[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$
2.12.16.15 x12 + 2x10 - 2x9 + 8x8 + 4x7 + 12x6 - 4x5 + 8x4 - 4x3 + 8x2 + 4 $2$ $6$ $2$ $16$ $\GL(2,\Z/4)$ (as 12T50) $[2]$ $[4/3, 4/3, 2, 2]_{3}^{2}$
2.12.16.16 x12 + 4x11 + 8x10 + 12x9 + 16x8 + 16x7 + 12x6 + 8x5 + 4x4 + 12 $2$ $6$ $2$ $16$ $A_4:C_4$ (as 12T30) $[2]$ $[4/3, 4/3, 2]_{3}^{2}$
2.12.16.17 x12 - 2x10 - 2x9 + 8x8 + 8x7 - 2x6 - 4x5 + 12x4 + 8x3 - 4x2 + 4 $2$ $6$ $2$ $16$ 12T208 $[2]$ $[4/3, 4/3, 4/3, 4/3, 2, 2]_{3}^{6}$
2.12.16.18 x12 + 4x10 + 4x9 + 8x8 + 8x7 + 12x6 + 8x5 + 4x4 + 12 $2$ $6$ $2$ $16$ $C_3 : C_4$ (as 12T5) $[2]$ $[2]_{3}^{2}$
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