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Label Polynomial Discriminant Galois group Class group
31.31.606...801.1 x31 - x30 - 150x29 + 117x28 + 9434x27 - 4958x26 - 328880x25 + 78328x24 + 7098810x23 + 507925x22 - 100297691x21 - 39217806x20 + 950942678x19 + 677567200x18 - 6056859921x17 - 6293114670x16 + 25303767350x15 + 35315191500x14 - 65145555320x13 - 122001770825x12 + 87706314807x11 + 253609179978x10 - 19776440614x9 - 299693882286x8 - 98200795275x7 + 175359843704x6 + 113820457794x5 - 30260338943x4 - 38729335872x3 - 5811762482x2 + 1056847214x - 26458109 \( 311^{30} \) $C_{31}$ (as 31T1) n/a
31.31.141...449.1 x31 - x30 - 180x29 + 381x28 + 13354x27 - 40454x26 - 531040x25 + 2069355x24 + 12295300x23 - 60883682x22 - 164683595x21 + 1114070344x20 + 1058778882x19 - 13103530537x18 + 1853849258x17 + 99224120479x16 - 91885359548x15 - 467511308511x14 + 762650059488x13 + 1229830733203x12 - 3225889300699x11 - 1095874556276x10 + 7495923118841x9 - 2504773526476x8 - 8920808783994x7 + 7437366186489x6 + 3836259163454x5 - 6642200925120x4 + 1200673450587x3 + 1711910811444x2 - 967097412303x + 151576217389 \( 373^{30} \) $C_{31}$ (as 31T1) trivial (GRH)
31.31.107...849.1 x31 - x30 - 330x29 + 852x28 + 43784x27 - 173944x26 - 2923572x25 + 15562316x24 + 100635650x23 - 707709554x22 - 1616621784x21 + 17266725972x20 + 7046247776x19 - 243865756432x18 + 142454592564x17 + 2084163747748x16 - 2521472241195x15 - 10836712986085x14 + 18499228115810x13 + 32698257976552x12 - 74538290301632x11 - 47884603550112x10 + 168256221920320x9 + 4878741111552x8 - 195294436805376x7 + 62882730299136x6 + 92885896276480x5 - 43440624908288x4 - 15171034030080x3 + 6823763935232x2 + 786648006656x + 5192548352 \( 683^{30} \) $C_{31}$ (as 31T1) trivial (GRH)
31.31.303...801.1 x31 - 465x29 - 341x28 + 91078x27 + 119908x26 - 9914451x25 - 18008892x24 + 666449563x23 + 1538774528x22 - 28934386579x21 - 83032233092x20 + 817351924162x19 + 2943382779538x18 - 14471455469735x17 - 68751097280499x16 + 137645143880654x15 + 1028543867187214x14 - 144266178422457x13 - 9110738641752719x12 - 11199776062831713x11 + 37846129267859005x10 + 105950708850677777x9 + 9682358886535270x8 - 290542929220278846x7 - 437492517497239584x6 - 201727405103545942x5 + 73256081844015542x4 + 87563225965427030x3 + 7669633084320922x2 - 7522164033404415x - 310695313260929 \( 31^{60} \) $C_{31}$ (as 31T1) n/a
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