↑

Learn more

Refine search

Degree Signature Ramified prime count Ramified Unramified primes
Galois group Field is Intermediate field Class group structure Class number
Discriminant Root discriminant Galois root discriminant Narrow class group Narrow class number
CM field Relative class number Regulator $p$-adic completions Monogenic
Index Ines. \(p\) Minimal sibling
Sort order Select

Results (1-50 of at least 1000)

Next   To download results, determine the number of results.
Label Polynomial Discriminant Galois group Class group Regulator
6.0.2725888.4 $x^{6} + 6 x^{4} + 20 x^{2} + 22$ $-\,2^{11}\cdot 11^{3}$ $D_{6}$ (as 6T3) $[2]$ $3.57140454954$
6.0.2988032.1 $x^{6} - 2 x^{5} + 5 x^{4} - 4 x^{3} + 7 x^{2} - 2 x + 1$ $-\,2^{11}\cdot 1459$ $S_6$ (as 6T16) $[2]$ $6.29708737863$
6.0.4478976.2 $x^{6} + 6 x^{4} + 12 x^{2} + 6$ $-\,2^{11}\cdot 3^{7}$ $D_{6}$ (as 6T3) $[2]$ $9.15522080603$
6.2.4614144.1 $x^{6} - 2 x^{5} + x^{4} - 4 x^{3} + x^{2} - 2 x - 1$ $2^{11}\cdot 3\cdot 751$ $S_6$ (as 6T16) $[2]$ $11.4562346194$
6.2.5171200.1 $x^{6} + 2 x^{4} - 4 x^{3} - 4 x^{2} + 8 x - 4$ $2^{11}\cdot 5^{2}\cdot 101$ $S_6$ (as 6T16) $[2]$ $12.4173045417$
6.2.5318656.1 $x^{6} - 2 x^{4} - 4 x^{3} - 4$ $2^{11}\cdot 7^{2}\cdot 53$ $S_6$ (as 6T16) $[2]$ $13.5957058849$
6.2.5597184.1 $x^{6} - 2 x^{5} + 5 x^{4} - 4 x^{3} + 5 x^{2} + 22 x - 1$ $2^{11}\cdot 3\cdot 911$ $S_6$ (as 6T16) $[2]$ $12.6107683379$
6.2.5613568.1 $x^{6} - 4 x^{4} - 4 x^{3} + 2 x^{2} + 12 x + 10$ $2^{11}\cdot 2741$ $S_6$ (as 6T16) $[2]$ $10.7357396714$
6.0.5806080.1 $x^{6} - 2 x^{5} + 5 x^{4} - 8 x^{3} + 17 x^{2} - 14 x + 7$ $-\,2^{11}\cdot 3^{4}\cdot 5\cdot 7$ $C_3^2:D_4$ (as 6T13) $[2]$ $15.6470698297$
6.2.5908480.1 $x^{6} - 4 x^{3} - 8 x^{2} - 8 x - 6$ $2^{11}\cdot 5\cdot 577$ $S_6$ (as 6T16) $[2]$ $14.9827470194$
6.2.6547456.1 $x^{6} - 2 x^{5} + 3 x^{4} - 8 x^{3} - 3 x^{2} + 2 x + 1$ $2^{11}\cdot 23\cdot 139$ $S_6$ (as 6T16) $[2]$ $17.1382067074$
6.0.6690816.1 $x^{6} - 6 x^{4} + 54$ $-\,2^{11}\cdot 3^{3}\cdot 11^{2}$ $D_{6}$ (as 6T3) $[2]$ $7.43613207986$
6.2.7186432.2 $x^{6} - 2 x^{4} + 12 x^{2} - 58$ $2^{11}\cdot 11^{2}\cdot 29$ $S_4\times C_2$ (as 6T11) $[2]$ $10.7413979851$
6.2.7825408.1 $x^{6} - 2 x^{5} - 3 x^{4} + 8 x^{3} + 7 x^{2} - 6 x - 1$ $2^{11}\cdot 3821$ $S_6$ (as 6T16) $[2]$ $12.8317635371$
6.0.8017920.1 $x^{6} - 2 x^{5} + 3 x^{4} + 5 x^{2} + 2 x + 1$ $-\,2^{11}\cdot 3^{3}\cdot 5\cdot 29$ $C_3^2:D_4$ (as 6T13) $[2]$ $9.0480011195$
6.2.8562688.2 $x^{6} - 4 x^{3} - 8 x^{2} - 4$ $2^{11}\cdot 37\cdot 113$ $S_6$ (as 6T16) $[2]$ $18.8443641608$
6.0.8804352.1 $x^{6} - 2 x^{5} + 9 x^{4} - 12 x^{3} + 25 x^{2} - 18 x + 23$ $-\,2^{11}\cdot 3\cdot 1433$ $S_6$ (as 6T16) $[2]$ $18.2520407072$
6.2.8890368.1 $x^{6} - 2 x^{5} - 3 x^{4} + 8 x^{3} - 9 x^{2} + 10 x - 9$ $2^{11}\cdot 3\cdot 1447$ $S_6$ (as 6T16) $[2]$ $21.1828694097$
6.2.8923136.1 $x^{6} - 2 x^{5} + 5 x^{4} - 4 x^{3} - x^{2} + 6 x + 1$ $2^{11}\cdot 4357$ $S_6$ (as 6T16) $[2]$ $19.1560031631$
6.2.9037824.1 $x^{6} - 2 x^{5} + 3 x^{4} - 17 x^{2} + 18 x - 7$ $2^{11}\cdot 3\cdot 1471$ $S_6$ (as 6T16) $[2]$ $22.6802534872$
6.2.9316352.1 $x^{6} - 4 x^{4} - 4 x^{3} - 4 x^{2} - 8 x + 4$ $2^{11}\cdot 4549$ $S_6$ (as 6T16) $[2]$ $24.4019181756$
6.2.9611264.2 $x^{6} - 8 x^{4} + 24 x^{2} - 26$ $2^{11}\cdot 13\cdot 19^{2}$ $S_4\times C_2$ (as 6T11) $[2]$ $19.8439736308$
6.2.9955328.2 $x^{6} - 2 x^{5} + 7 x^{4} - 8 x^{3} + 11 x^{2} + 2 x - 1$ $2^{11}\cdot 4861$ $S_6$ (as 6T16) $[2]$ $17.6633770588$
6.2.10496000.1 $x^{6} - 2 x^{4} - 4 x^{3} + 16 x^{2} - 16 x + 4$ $2^{11}\cdot 5^{3}\cdot 41$ $C_3^2:D_4$ (as 6T13) $[2]$ $16.3773192683$
6.0.10655744.1 $x^{6} + 4 x^{4} + 28 x^{2} + 86$ $-\,2^{11}\cdot 11^{2}\cdot 43$ $S_4\times C_2$ (as 6T11) $[2]$ $10.4735325583$
6.0.11327488.1 $x^{6} + 2 x^{4} - 4 x^{3} + 12 x^{2} - 8 x + 4$ $-\,2^{11}\cdot 5531$ $S_6$ (as 6T16) $[2]$ $11.2949801591$
6.0.12261376.1 $x^{6} - 2 x^{5} + 5 x^{4} - 8 x^{3} + 11 x^{2} - 6 x + 9$ $-\,2^{11}\cdot 5987$ $S_6$ (as 6T16) $[2]$ $15.0775668479$
6.2.12544000.1 $x^{6} - 8 x^{4} + 16 x^{2} - 10$ $2^{11}\cdot 5^{3}\cdot 7^{2}$ $D_{6}$ (as 6T3) $[2]$ $17.1747103132$
6.2.13133824.3 $x^{6} - 6 x^{4} + 8 x^{2} - 106$ $2^{11}\cdot 11^{2}\cdot 53$ $S_4\times C_2$ (as 6T11) $[2]$ $11.7412320439$
6.2.14018560.3 $x^{6} - 2 x^{4} - 12 x^{2} - 10$ $2^{11}\cdot 5\cdot 37^{2}$ $S_4\times C_2$ (as 6T11) $[2]$ $15.709397656$
6.0.14047232.4 $x^{6} + 2 x^{4} + 38$ $-\,2^{11}\cdot 19^{3}$ $S_4\times C_2$ (as 6T11) $[2]$ $8.22891157463$
6.0.14047232.5 $x^{6} - 4 x^{4} + 4 x^{2} + 38$ $-\,2^{11}\cdot 19^{3}$ $D_{6}$ (as 6T3) $[6]$ $6.70253374953$
6.2.15116288.1 $x^{6} + 8 x^{4} - 8 x^{2} - 122$ $2^{11}\cdot 11^{2}\cdot 61$ $S_4\times C_2$ (as 6T11) $[2]$ $18.8888308805$
6.0.15980544.1 $x^{6} - 2 x^{4} + 4 x^{2} + 6$ $-\,2^{11}\cdot 3^{3}\cdot 17^{2}$ $D_{6}$ (as 6T3) $[2]$ $27.5884549852$
6.2.16181248.1 $x^{6} - 2 x^{5} + 5 x^{4} - 9 x^{2} + 2 x - 1$ $2^{11}\cdot 7901$ $S_6$ (as 6T16) $[2]$ $15.5747076293$
6.0.16422912.2 $x^{6} + 6 x^{2} - 12 x + 6$ $-\,2^{11}\cdot 3^{6}\cdot 11$ $C_3^2:D_4$ (as 6T13) $[2]$ $16.2877777312$
6.2.16640000.2 $x^{6} - 2 x^{5} + x^{4} + 4 x^{3} + x^{2} - 10 x - 1$ $2^{11}\cdot 5^{4}\cdot 13$ $C_3^2:D_4$ (as 6T13) $[2]$ $27.7900944508$
6.2.16754688.1 $x^{6} - 2 x^{5} + 11 x^{4} - 12 x^{3} + 19 x^{2} - 10 x - 1$ $2^{11}\cdot 3^{4}\cdot 101$ $S_6$ (as 6T16) $[2]$ $35.9712047852$
6.2.16984064.1 $x^{6} - 2 x^{5} - x^{4} - 8 x^{3} - 5 x^{2} - 6 x - 1$ $2^{11}\cdot 8293$ $S_6$ (as 6T16) $[2]$ $16.6763798309$
6.0.17307648.1 $x^{6} - 2 x^{5} + x^{4} + 8 x^{3} - 5 x^{2} - 6 x + 7$ $-\,2^{11}\cdot 3^{3}\cdot 313$ $C_3^2:D_4$ (as 6T13) $[2]$ $10.8322282367$
6.4.17520640.1 $x^{6} - 2 x^{5} + x^{4} - 12 x^{3} + 17 x^{2} + 6 x - 1$ $-\,2^{11}\cdot 5\cdot 29\cdot 59$ $S_6$ (as 6T16) $[2]$ $29.1450019916$
6.0.17553408.1 $x^{6} - 2 x^{2} - 4 x + 6$ $-\,2^{11}\cdot 3\cdot 2857$ $S_6$ (as 6T16) $[2]$ $24.3069168056$
6.2.17639424.1 $x^{6} - 2 x^{5} + 7 x^{4} - 16 x^{3} + 19 x^{2} - 14 x + 1$ $2^{11}\cdot 3^{3}\cdot 11\cdot 29$ $S_6$ (as 6T16) $[2]$ $25.1898055584$
6.2.17803264.1 $x^{6} - 6 x^{4} + 8 x^{2} - 8 x + 6$ $2^{11}\cdot 8693$ $S_6$ (as 6T16) $[2]$ $26.8047700207$
6.2.18081792.1 $x^{6} - 2 x^{5} + 9 x^{4} - 8 x^{3} + 19 x^{2} - 6 x - 9$ $2^{11}\cdot 3^{4}\cdot 109$ $S_6$ (as 6T16) $[2]$ $37.7813641149$
6.2.18081792.3 $x^{6} - 2 x^{5} + 5 x^{4} + x^{2} + 2 x - 1$ $2^{11}\cdot 3^{4}\cdot 109$ $S_6$ (as 6T16) $[2]$ $27.4713728576$
6.0.18651136.1 $x^{6} - 2 x^{5} + 7 x^{4} - 4 x^{3} + 15 x^{2} - 2 x + 7$ $-\,2^{11}\cdot 7\cdot 1301$ $S_6$ (as 6T16) $[2]$ $12.9514720488$
6.2.18802688.1 $x^{6} - 4 x^{4} - 8 x^{3} + 4 x^{2} + 32 x + 22$ $2^{11}\cdot 9181$ $S_6$ (as 6T16) $[2]$ $17.6278664931$
6.2.19081216.3 $x^{6} - 12 x^{4} + 44 x^{2} - 154$ $2^{11}\cdot 7\cdot 11^{3}$ $S_4\times C_2$ (as 6T11) $[2]$ $17.0339830104$
6.0.19961856.1 $x^{6} + 6 x^{4} + 36 x^{2} + 54$ $-\,2^{11}\cdot 3^{3}\cdot 19^{2}$ $D_{6}$ (as 6T3) $[2]$ $11.1240392363$
Next   To download results, determine the number of results.