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Label Polynomial Discriminant Galois group Class group
18.0.298880559887628015710208.1 x18 - 6x17 + 12x16 + 4x15 - 12x14 - 48x13 + 15x12 + 180x11 - 168x10 - 64x9 + 216x8 - 84x7 - 9x6 + 30x5 + 36x4 - 56x3 + 48x2 - 12x + 1 \( -\,2^{12}\cdot 3^{21}\cdot 17^{8} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$
18.2.435848050125000000000000.1 x18 - 4x15 + 15x12 + 15x6 + 16x3 + 1 \( 2^{12}\cdot 3^{20}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$
18.0.1307544150375000000000000.1 x18 - 6x15 + 5x12 + 10x9 + 145x6 + 4x3 + 1 \( -\,2^{12}\cdot 3^{21}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[6]$
18.2.1693656506029892089024512.1 x18 - 4x15 - 9x12 - 44x9 - 9x6 - 4x3 + 1 \( 2^{12}\cdot 3^{20}\cdot 17^{9} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$
18.0.2518170116818978404827136.2 x18 + 3x12 + 15x6 + 1 \( -\,2^{24}\cdot 3^{36} \) $C_2\times C_3:S_3$ (as 18T12) Trivial (GRH)
18.2.7554510350456935214481408.2 x18 - 12x15 + 21x12 - 70x9 + 51x6 - 42x3 + 1 \( 2^{24}\cdot 3^{37} \) $C_2\times C_3:S_3$ (as 18T12) Trivial (GRH)
18.0.14281868906496000000000000.2 x18 + 3x12 + 543x6 + 1 \( -\,2^{24}\cdot 3^{20}\cdot 5^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.2.42845606719488000000000000.1 x18 - 49x12 + 67x6 - 27 \( 2^{24}\cdot 3^{21}\cdot 5^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.0.67804051110532132041289728.2 x18 - 11x15 + 65x12 - 99x9 + 130x6 - 44x3 + 8 \( -\,2^{12}\cdot 3^{20}\cdot 7^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.2.203412153331596396123869184.1 x18 - 2x15 + 25x12 + 244x9 - 313x6 - 942x3 - 4913 \( 2^{12}\cdot 3^{21}\cdot 7^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.0.809695024340348725484322816.1 x18 - 29x12 + 999x6 + 729 \( -\,2^{24}\cdot 3^{20}\cdot 7^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.2.1200757082375992968000000000.2 x18 - 12x15 + 45x12 + 112x9 + 63x6 + 12x3 - 1 \( 2^{12}\cdot 3^{36}\cdot 5^{9} \) $C_2\times C_3:S_3$ (as 18T12) $[2]$ (GRH)
18.0.1289303099811316943271493632.4 x18 + 6x12 + 60x6 + 8 \( -\,2^{33}\cdot 3^{36} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.2.1289303099811316943271493632.4 x18 - 6x12 + 60x6 - 8 \( 2^{33}\cdot 3^{36} \) $C_2\times C_3:S_3$ (as 18T12) $[2]$ (GRH)
18.0.1785233613312000000000000000.3 x18 - 18x15 - 5x12 + 990x9 + 3145x6 + 2052x3 + 729 \( -\,2^{24}\cdot 3^{20}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[6]$ (GRH)
18.2.2429085073021046176452968448.1 x18 - 37x12 - 29x6 - 27 \( 2^{24}\cdot 3^{21}\cdot 7^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.0.3602271247127978904000000000.3 x18 - 15x15 + 39x12 + 475x9 + 834x6 - 300x3 + 1000 \( -\,2^{12}\cdot 3^{37}\cdot 5^{9} \) $C_2\times C_3:S_3$ (as 18T12) $[2, 2]$ (GRH)
18.0.3867909299433950829814480896.4 x18 + 90x12 + 108x6 + 216 \( -\,2^{33}\cdot 3^{37} \) $C_2\times C_3:S_3$ (as 18T12) $[2, 2]$ (GRH)
18.2.3867909299433950829814480896.1 x18 - 90x12 + 108x6 - 216 \( 2^{33}\cdot 3^{37} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.2.4580524758819553253173828125.2 x18 - 12x15 + 45x12 + 40x9 - 45x6 + 228x3 - 1 \( 3^{36}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[2]$ (GRH)
18.2.5355700839936000000000000000.1 x18 - 18x15 - 50x12 - 360x9 - 860x6 - 648x3 - 216 \( 2^{24}\cdot 3^{21}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[6]$ (GRH)
18.0.7312316880125952000000000000.1 x18 - 26x12 + 412x6 + 5832 \( -\,2^{33}\cdot 3^{20}\cdot 5^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 3]$ (GRH)
18.2.7312316880125952000000000000.1 x18 + 26x12 + 412x6 - 5832 \( 2^{33}\cdot 3^{20}\cdot 5^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[6]$ (GRH)
18.2.11351585665720125000000000000.1 x18 - 3x17 - 7x16 + 20x15 + 45x14 - 443x13 + 1134x12 - 1479x11 + 175x10 + 2090x9 - 2977x8 + 831x7 + 1899x6 - 2660x5 + 1110x4 - 640x3 + 280x2 - 480x + 20 \( 2^{12}\cdot 3^{8}\cdot 5^{15}\cdot 7^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.0.13741574276458659759521484375.2 x18 - 3x15 + 30x12 - 250x9 + 465x6 + 237x3 + 64 \( -\,3^{37}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[2, 2]$ (GRH)
18.0.21936950640377856000000000000.2 x18 + 98x12 + 268x6 + 216 \( -\,2^{33}\cdot 3^{21}\cdot 5^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[2, 6]$ (GRH)
18.2.21936950640377856000000000000.2 x18 - 98x12 + 268x6 - 216 \( 2^{33}\cdot 3^{21}\cdot 5^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 3]$ (GRH)
18.0.24808898255189732590303014912.1 x18 - 15x15 + 99x12 - 355x9 + 360x6 + 960x3 + 512 \( -\,2^{12}\cdot 3^{36}\cdot 7^{9} \) $C_2\times C_3:S_3$ (as 18T12) $[2]$ (GRH)
18.0.31148751066736023000000000000.1 x18 - 6x17 + 17x16 - 48x15 + 150x14 - 336x13 + 485x12 - 438x11 + 14x10 + 180x9 + 2597x8 - 7578x7 + 6185x6 + 1746x5 + 60x4 - 11598x3 + 14984x2 - 7584x + 1408 \( -\,2^{12}\cdot 3^{8}\cdot 5^{12}\cdot 7^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 3]$ (GRH)
18.0.34054756997160375000000000000.1 x18 - 6x17 + 22x16 - 51x15 + 50x14 + 54x13 - 179x12 + 108x11 + 206x10 - 705x9 + 982x8 - 792x7 + 634x6 - 372x5 - 240x4 + 684x3 - 144x2 - 432x + 216 \( -\,2^{12}\cdot 3^{9}\cdot 5^{15}\cdot 7^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[6]$ (GRH)
18.0.59658910745494721298677968896.1 x18 - 4x15 + 47x12 - 296x9 + 1215x6 - 1512x3 + 729 \( -\,2^{12}\cdot 3^{20}\cdot 11^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 6]$ (GRH)
18.2.74426694765569197770909044736.2 x18 - 12x15 + 93x12 + 2036x9 - 6321x6 + 8616x3 - 4913 \( 2^{12}\cdot 3^{37}\cdot 7^{9} \) $C_2\times C_3:S_3$ (as 18T12) $[2]$ (GRH)
18.2.93446253200208069000000000000.2 x18 - 3x17 - x16 + 14x15 - 3x14 + 91x13 + 170x12 + 117x11 + 203x10 + 416x9 + 407x8 - 75x7 + 1187x6 + 3232x5 + 372x4 - 388x3 - 460x2 + 180x - 20 \( 2^{12}\cdot 3^{9}\cdot 5^{12}\cdot 7^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 3]$ (GRH)
18.0.140704327411684407000000000000.1 x18 - 35x15 + 599x12 - 6435x9 + 33352x6 + 7360x3 + 512 \( -\,2^{12}\cdot 3^{20}\cdot 5^{12}\cdot 7^{9} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 6]$ (GRH)
18.2.178976732236484163896033906688.2 x18 - 37x15 + 245x12 + 3983x9 - 490x6 - 148x3 - 8 \( 2^{12}\cdot 3^{21}\cdot 11^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 6]$ (GRH)
18.0.183593462369306069451078107136.1 x18 - 3x16 - 18x14 + 177x12 + 1482x10 + 3849x8 + 2769x6 - 4752x4 - 5376x2 + 4096 \( -\,2^{24}\cdot 3^{20}\cdot 11^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 6]$ (GRH)
18.2.231627523606480125000000000000.1 x18 - 48x15 + 675x12 - 3780x9 + 6075x6 - 3888x3 + 729 \( 2^{12}\cdot 3^{32}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.2.231627523606480125000000000000.2 x18 - 48x15 + 135x12 + 1215x6 + 972x3 + 729 \( 2^{12}\cdot 3^{32}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[3]$ (GRH)
18.2.231627523606480125000000000000.3 x18 - 18x15 + 135x12 - 540x9 + 1035x6 - 1458x3 + 729 \( 2^{12}\cdot 3^{32}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[2, 6]$ (GRH)
18.2.277725393348739612841122725888.1 x18 - 16x15 + 235x12 - 1114x9 + 205x6 - 634x3 - 27 \( 2^{24}\cdot 3^{20}\cdot 7^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 3]$ (GRH)
18.0.371968759094317056000000000000.1 x18 + x16 - 30x14 + 53x12 + 302x10 - 351x8 - 3179x6 + 6484x4 - 672x2 + 36 \( -\,2^{24}\cdot 3^{8}\cdot 5^{12}\cdot 7^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[6]$ (GRH)
18.2.386092674417662012808000000000.2 x18 - 20x15 + 461x12 + 2592x9 + 3159x6 + 2916x3 - 729 \( 2^{12}\cdot 3^{20}\cdot 5^{9}\cdot 7^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[6]$ (GRH)
18.0.414563852462258547447973281792.2 x18 - 58x12 + 3996x6 + 5832 \( -\,2^{33}\cdot 3^{20}\cdot 7^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[6]$ (GRH)
18.2.414563852462258547447973281792.1 x18 + 58x12 + 3996x6 - 5832 \( 2^{33}\cdot 3^{20}\cdot 7^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 3]$ (GRH)
18.2.422112982235053221000000000000.1 x18 - 54x15 - 1237x12 - 6588x9 - 2849x6 + 594x3 - 27 \( 2^{12}\cdot 3^{21}\cdot 5^{12}\cdot 7^{9} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 6]$ (GRH)
18.2.550780387107918208353234321408.2 x18 + 35x12 + 907x6 - 27 \( 2^{24}\cdot 3^{21}\cdot 11^{12} \) $C_2\times C_3:S_3$ (as 18T12) $[3, 6]$ (GRH)
18.0.694882570819440375000000000000.1 x18 - 9x15 + 15x12 + 405x9 + 630x6 - 324x3 + 216 \( -\,2^{12}\cdot 3^{33}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[2, 2, 6]$ (GRH)
18.0.694882570819440375000000000000.2 x18 - 9x15 + 105x12 + 405x9 + 90x6 - 324x3 + 216 \( -\,2^{12}\cdot 3^{33}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[6]$ (GRH)
18.0.694882570819440375000000000000.5 x18 - 9x15 + 75x12 - 135x9 + 450x6 - 324x3 + 216 \( -\,2^{12}\cdot 3^{33}\cdot 5^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[6]$ (GRH)
18.0.712583513384965051151503760103.1 x18 - 12x15 + 81x12 + 680x9 + 891x6 + 228x3 + 1331 \( -\,3^{36}\cdot 7^{15} \) $C_2\times C_3:S_3$ (as 18T12) $[12]$ (GRH)
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