Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Results (14 matches)
Download displayed columns for results| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 10.0.825...656.1 | $x^{10} - 5 x^{9} + 4180 x^{8} - 15682 x^{7} + 5962002 x^{6} - 14030366 x^{5} + 3310401386 x^{4} - 2470245810 x^{3} + 557983275513 x^{2} + 1171541584631 x + 14528697011030$ | $-\,2^{12}\cdot 103^{5}\cdot 223\cdot 239^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 4, 14697144]$ |
| 10.0.743...576.1 | $x^{10} - 4 x^{9} + 4997 x^{8} - 9960 x^{7} + 8898419 x^{6} + 2412970 x^{5} + 6677943372 x^{4} + 16839687466 x^{3} + 1919516719874 x^{2} + 6632174559220 x + 138574544764117$ | $-\,2^{10}\cdot 3^{5}\cdot 7\cdot 11^{4}\cdot 73\cdot 3313^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 2, 8808236]$ |
| 10.0.161...239.1 | $x^{10} - x^{9} + 5287 x^{8} - 2758 x^{7} + 10162533 x^{6} - 600397 x^{5} + 8668027250 x^{4} + 3322233073 x^{3} + 3200059710156 x^{2} + 2795774963504 x + 379292449108135$ | $-\,3^{4}\cdot 31\cdot 229849^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[126496194]$ |
| 10.0.165...408.1 | $x^{10} - x^{9} + 3512 x^{8} + 4394 x^{7} + 4299453 x^{6} + 10399823 x^{5} + 2241203252 x^{4} + 6389130552 x^{3} + 491247773243 x^{2} + 1114140263383 x + 33653210739604$ | $-\,2^{12}\cdot 3^{9}\cdot 17\cdot 16453^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 22671938]$ |
| 10.0.182...000.1 | $x^{10} - x^{9} + 5228 x^{8} + 5138 x^{7} + 8891988 x^{6} + 31432355 x^{5} + 5288810947 x^{4} + 33823504834 x^{3} + 671167046424 x^{2} + 2281958755424 x + 23464704823376$ | $-\,2^{3}\cdot 5^{7}\cdot 17^{5}\cdot 43^{5}\cdot 107^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 2, 2, 2, 2036580]$ |
| 10.0.221...000.1 | $x^{10} - 5 x^{9} + 5700 x^{8} - 4184 x^{7} + 8796088 x^{6} + 36286324 x^{5} + 2431612636 x^{4} + 9205274300 x^{3} + 213902664415 x^{2} + 310290712865 x + 4012885706300$ | $-\,2^{12}\cdot 5^{4}\cdot 11^{5}\cdot 5573^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 51432626]$ |
| 10.0.484...888.1 | $x^{10} + 6318 x^{8} - 5406 x^{7} + 13905305 x^{6} - 29416558 x^{5} + 13080139985 x^{4} - 43800746782 x^{3} + 4690866826603 x^{2} - 20485010377988 x + 185866203990566$ | $-\,2^{15}\cdot 7\cdot 11^{4}\cdot 17053^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 4, 59754864]$ |
| 10.0.818...992.1 | $x^{10} - 5 x^{9} + 4448 x^{8} - 11138 x^{7} + 5981380 x^{6} - 12065086 x^{5} + 2979655475 x^{4} - 5638588525 x^{3} + 611130772720 x^{2} - 718318933248 x + 43494896774112$ | $-\,2^{4}\cdot 3^{7}\cdot 7\cdot 13^{5}\cdot 9791^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 2, 17959338]$ |
| 10.0.105...416.1 | $x^{10} - 2 x^{9} + 7623 x^{8} - 1528 x^{7} + 19098590 x^{6} + 28974228 x^{5} + 19862224580 x^{4} + 59948580104 x^{3} + 7788406648188 x^{2} + 33120582532960 x + 332340894808288$ | $-\,2^{17}\cdot 3^{8}\cdot 11^{5}\cdot 23\cdot 31^{5}\cdot 41^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 2, 2, 26949776]$ |
| 10.0.115...575.1 | $x^{10} - x^{9} + 6084 x^{8} - 10335 x^{7} + 11201378 x^{6} - 7241194 x^{5} + 8677991584 x^{4} + 2574619086 x^{3} + 2885637791694 x^{2} + 1370116763023 x + 319977398107869$ | $-\,5^{2}\cdot 7^{5}\cdot 122489^{5}$ | $C_2 \wr S_5$ (as 10T39) | $[2, 2, 91515950]$ |
| 10.0.287...875.1 | $x^{10} - 6765 x^{7} + 696795 x^{6} + 83279856 x^{5} + 3706058675 x^{4} + 94284129720 x^{3} + 1257274742625 x^{2} + 10961015191335 x + 85798288501893$ | $-\,5^{16}\cdot 11^{9}\cdot 41^{8}$ | $C_{10}$ (as 10T1) | $[5, 5, 6779905]$ |
| 10.0.634...875.1 | $x^{10} + 4510 x^{8} - 266090 x^{7} + 21057190 x^{6} - 599153951 x^{5} + 14466896125 x^{4} - 87476668070 x^{3} + 397271646145 x^{2} - 630321392910 x + 772639242001$ | $-\,3^{5}\cdot 5^{16}\cdot 11^{8}\cdot 41^{8}$ | $C_{10}$ (as 10T1) | $[4, 4, 20, 739420]$ |
| 10.0.317...375.1 | $x^{10} + 4510 x^{8} - 133045 x^{7} + 2751100 x^{6} - 480905359 x^{5} + 706818475 x^{4} - 163060479670 x^{3} + 12256011666415 x^{2} + 140389724566575 x + 9142215828856099$ | $-\,3^{5}\cdot 5^{17}\cdot 11^{8}\cdot 41^{8}$ | $C_{10}$ (as 10T1) | $[2, 2, 2, 110, 413710]$ |
| 10.2.636...000.1 | $x^{10} - 5 x^{9} - 9690 x^{8} + 38790 x^{7} + 37577805 x^{6} - 112686681 x^{5} - 72901398000 x^{4} + 149531844600 x^{3} + 70745098715400 x^{2} - 67385222095700 x - 27481198710005660$ | $2^{8}\cdot 3^{9}\cdot 5^{18}\cdot 13^{9}\cdot 199^{5}$ | $F_{5}\times C_2$ (as 10T5) | $[2, 2, 4, 4, 2283960]$ |