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Degree Signature Ramified prime count Ramified Unramified primes
Galois group Field is Intermediate field Class group structure Class number
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CM field Relative class number Regulator $p$-adic completions Monogenic
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Results (44 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
8.0.433...696.1 $x^{8} + 2096$ $2^{16}\cdot 131^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[5]$ $1853315.29516$
8.0.433...696.2 $x^{8} + 131$ $2^{16}\cdot 131^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[5]$ $1853315.29516$
8.0.173...784.1 $x^{8} + 2358 x^{4} - 39300 x^{2} + 1471916$ $2^{18}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[5]$ $3421889.68259$
8.0.173...784.2 $x^{8} + 2358 x^{4} + 39300 x^{2} + 1471916$ $2^{18}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[5]$ $5600149.56116$
8.0.694...136.1 $x^{8} + 4716 x^{4} - 39300 x^{2} + 81875$ $2^{20}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[5]$ $34276664.9218$
8.0.694...136.2 $x^{8} + 4716 x^{4} + 39300 x^{2} + 81875$ $2^{20}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[5]$ $20944256.0004$
8.0.277...544.1 $x^{8} + 8384$ $2^{22}\cdot 131^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[5]$ $54870749.0497$
8.0.277...544.2 $x^{8} + 524$ $2^{22}\cdot 131^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[5]$ $54870749.0497$
8.0.177...816.1 $x^{8} + 262 x^{4} + 10611$ $2^{28}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[70]$ $12079806.2397$
8.4.177...816.1 $x^{8} - 786 x^{4} - 5240 x^{2} + 10611$ $2^{28}\cdot 131^{7}$ $Z_8 : Z_8^\times$ (as 8T15) trivial $2789378971.92$
8.8.177...816.1 $x^{8} - 1048 x^{6} + 75718 x^{4} - 1598200 x^{2} + 6631875$ $2^{28}\cdot 131^{7}$ $QD_{16}$ (as 8T8) trivial $7682052183.26$
8.0.177...816.2 $x^{8} + 1048 x^{4} + 169776$ $2^{28}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[70]$ $11639934.1923$
8.4.177...816.2 $x^{8} - 262 x^{4} + 10611$ $2^{28}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) trivial $2767228809.69$
8.0.177...816.3 $x^{8} + 2096 x^{4} + 679104$ $2^{28}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[70]$ $12058586.9407$
8.4.177...816.3 $x^{8} - 786 x^{4} + 5240 x^{2} + 10611$ $2^{28}\cdot 131^{7}$ $Z_8 : Z_8^\times$ (as 8T15) trivial $2789378971.92$
8.0.177...816.4 $x^{8} + 1048 x^{6} + 75718 x^{4} + 1598200 x^{2} + 6631875$ $2^{28}\cdot 131^{7}$ $QD_{16}$ (as 8T8) $[11826]$ $72889.5328164$
8.4.177...816.4 $x^{8} - 1048 x^{4} + 169776$ $2^{28}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) trivial $2871802133.05$
8.0.177...816.5 $x^{8} + 524 x^{4} + 42444$ $2^{28}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) $[70]$ $9113339.03726$
8.4.177...816.5 $x^{8} - 2096 x^{4} + 679104$ $2^{28}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) trivial $2166566745.12$
8.4.177...816.6 $x^{8} - 524 x^{4} + 42444$ $2^{28}\cdot 131^{7}$ $(C_4^2 : C_2):C_2$ (as 8T26) trivial $2866757546.49$
8.2.355...632.1 $x^{8} - 37728 x^{4} - 50304 x^{2} - 16768$ $-\,2^{29}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $2677556526.16$
8.6.355...632.1 $x^{8} - 37728 x^{4} + 50304 x^{2} - 16768$ $-\,2^{29}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $5558432429.13$
8.2.355...632.2 $x^{8} - 22008 x^{4} - 693776 x^{2} - 4989528$ $-\,2^{29}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $2401347430.43$
8.6.355...632.2 $x^{8} - 22008 x^{4} + 693776 x^{2} - 4989528$ $-\,2^{29}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $6478030149.88$
8.6.355...632.3 $x^{8} - 524 x^{6} + 30916 x^{4} - 407672 x^{2} - 2266038$ $-\,2^{29}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $5238095916.38$
8.2.355...632.3 $x^{8} + 524 x^{6} + 30916 x^{4} + 407672 x^{2} - 2266038$ $-\,2^{29}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $2389235510.03$
8.2.355...632.4 $x^{8} - 9432 x^{4} - 6288 x^{2} - 1048$ $-\,2^{29}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[15]$ $184059777.629$
8.6.355...632.4 $x^{8} - 9432 x^{4} + 6288 x^{2} - 1048$ $-\,2^{29}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $4953199974.76$
8.4.710...264.1 $x^{8} - 4716 x^{4} - 6288 x^{2} + 5559116$ $2^{30}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $4542628993.03$
8.0.710...264.1 $x^{8} - 4716 x^{4} + 6288 x^{2} + 5559116$ $2^{30}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $1094116557.25$
8.0.710...264.2 $x^{8} - 18864 x^{4} + 50304 x^{2} + 88945856$ $2^{30}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[30]$ $75211428.1291$
8.4.710...264.2 $x^{8} - 18864 x^{4} - 50304 x^{2} + 88945856$ $2^{30}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $4048002759.86$
8.4.710...264.3 $x^{8} + 20436 x^{4} - 693776 x^{2} + 570636$ $2^{30}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $4134637608.1$
8.0.710...264.3 $x^{8} + 20436 x^{4} + 693776 x^{2} + 570636$ $2^{30}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $942959345.538$
8.0.710...264.4 $x^{8} + 524 x^{6} + 63666 x^{4} + 1857580 x^{2} + 21913811$ $2^{30}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $947739555.984$
8.4.710...264.4 $x^{8} - 524 x^{6} + 63666 x^{4} - 1857580 x^{2} + 21913811$ $2^{30}\cdot 131^{7}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $5113367053.92$
8.2.142...528.1 $x^{8} - 16768$ $-\,2^{31}\cdot 131^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[3]$ $1267421566.57$
8.2.142...528.2 $x^{8} - 262$ $-\,2^{31}\cdot 131^{7}$ $Z_8 : Z_8^\times$ (as 8T15) trivial $4548504585.04$
8.2.142...528.3 $x^{8} - 10480 x^{4} - 6875928$ $-\,2^{31}\cdot 131^{7}$ $QD_{16}$ (as 8T8) trivial $3255933387.41$
8.2.142...528.4 $x^{8} + 10480 x^{4} - 6875928$ $-\,2^{31}\cdot 131^{7}$ $QD_{16}$ (as 8T8) trivial $4300951453.2$
8.2.142...528.5 $x^{8} - 5240 x^{4} - 1718982$ $-\,2^{31}\cdot 131^{7}$ $QD_{16}$ (as 8T8) trivial $5223750825.75$
8.2.142...528.6 $x^{8} + 5240 x^{4} - 1718982$ $-\,2^{31}\cdot 131^{7}$ $QD_{16}$ (as 8T8) $[11]$ $406809627.381$
8.2.142...528.7 $x^{8} - 4192$ $-\,2^{31}\cdot 131^{7}$ $Z_8 : Z_8^\times$ (as 8T15) trivial $4548504585.04$
8.2.142...528.8 $x^{8} - 1048$ $-\,2^{31}\cdot 131^{7}$ $Z_8 : Z_8^\times$ (as 8T15) $[3]$ $1267421566.57$
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