| Label |
Dimension |
Base field |
Base char. |
Simple |
Geom. simple |
Primitive |
Ordinary |
Almost ordinary |
Supersingular |
Princ. polarizable |
Jacobian |
L-polynomial |
Newton slopes |
Newton elevation |
$p$-rank |
$p$-corank |
Angle rank |
Angle corank |
$\mathbb{F}_q$ points on curve |
$\mathbb{F}_{q^k}$ points on curve |
$\mathbb{F}_q$ points on variety |
$\mathbb{F}_{q^k}$ points on variety |
Jacobians |
Hyperelliptic Jacobians |
Num. twists |
Max. twist degree |
End. degree |
Number fields |
Galois groups |
Isogeny factors |
| 4.5.aq_em_atc_cao |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{4}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-10$ |
$[-10, 2, 110, 682, 3430, 16562, 80350, 394842, 1958870, 9767522]$ |
$16$ |
$[16, 160000, 221533456, 167772160000, 105119989862416, 63272170368160000, 38326711929781551376, 23535616807151861760000, 14594788452214325009080336, 9096716659728898824100000000]$ |
$None$ |
$0$ |
$124$ |
$24$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.5.ae 4 |
| 4.5.ap_ea_aqr_btm |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{3}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-9$ |
$[-9, 9, 132, 717, 3411, 16254, 79287, 392637, 1956516, 9770049]$ |
$24$ |
$[24, 216000, 261482112, 176947200000, 104496229772664, 62043429606912000, 37808915041276457592, 23403120802607923200000, 14577211045093695158980224, 9099070455307393302687000000]$ |
$None$ |
$0$ |
$88$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.5.ae 3 $\times$ 1.5.ad |
| 4.5.ao_dn_any_blk |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-8$ |
$[-8, 12, 118, 608, 3092, 15810, 79316, 393600, 1955998, 9761292]$ |
$28$ |
$[28, 221200, 230463856, 148816281600, 94313975316988, 60307689652537600, 37824215428924710268, 23460952075775882035200, 14573350564538393946716272, 9090913800345378830015530000]$ |
$None$ |
$0$ |
$96$ |
$24$ |
$6$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.5.ae 2 $\times$ 2.5.ag_r |
| 4.5.ao_do_aog_bmk |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{3}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-8$ |
$[-8, 14, 136, 682, 3272, 16094, 79736, 394842, 1959832, 9766574]$ |
$32$ |
$[32, 256000, 268745504, 167772160000, 99932932273952, 61405122717952000, 38027626991359982624, 23535616807151861760000, 14601971742634905262179872, 9095833637090033463712000000]$ |
$None$ |
$0$ |
$124$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.5.ae 3 $\times$ 1.5.ac |
| 4.5.ao_dp_aoo_bnk |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 5 x^{2} )^{2}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-8$ |
$[-8, 16, 154, 752, 3392, 15946, 78224, 390432, 1954162, 9772576]$ |
$36$ |
$[36, 291600, 308634624, 186624000000, 103876170945156, 60838550898278400, 37298113629404912964, 23271370696986624000000, 14559654807532466321826816, 9101424859935705708138090000]$ |
$None$ |
$0$ |
$96$ |
$24$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.5.ae 2 $\times$ 1.5.ad 2 |
| 4.5.an_db_aln_bei |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-7$ |
$[-7, 15, 113, 591, 3178, 16263, 79933, 393087, 1955453, 9772410]$ |
$36$ |
$[36, 248400, 224644212, 144731750400, 97001204486976, 62083954900328400, 38123717990186149812, 23430229459787612160000, 14569261124430772495455876, 9101269404942073078210560000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.4901.1 |
$C_2$, $D_{4}$ |
1.5.ae 2 $\times$ 2.5.af_n |
| 4.5.an_dc_alv_bfi |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{3}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-7$ |
$[-7, 17, 128, 637, 3253, 16382, 80353, 394077, 1954928, 9763097]$ |
$40$ |
$[40, 280000, 254218720, 155975680000, 99309172184200, 62554075118080000, 38328173256842243080, 23489648805575393280000, 14565353388973236279643360, 9092594955955713993175000000]$ |
$None$ |
$0$ |
$88$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.5.ae 3 $\times$ 1.5.ab |
| 4.5.an_dd_ame_bgm |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-7$ |
$[-7, 19, 140, 643, 3073, 15502, 78253, 391395, 1953644, 9763819]$ |
$42$ |
$[42, 298620, 272022912, 156954672000, 93754335863202, 59136518882488320, 37313207307614283906, 23328876403474294464000, 14555798976392853728830848, 9093266094421158595971587100]$ |
$None$ |
$0$ |
$48$ |
$24$ |
$6$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2$, $C_2$, $C_2^2$ |
1.5.ae $\times$ 1.5.ad $\times$ 2.5.ag_r |
| 4.5.an_dd_amd_bgi |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-7$ |
$[-7, 19, 143, 679, 3278, 16219, 79863, 393359, 1952873, 9754074]$ |
$44$ |
$[44, 312400, 285043484, 166666649600, 100060969290304, 61906285437739600, 38089735991599372124, 23446514423076677222400, 14550041109224787799036844, 9084194718280899304552960000]$ |
$None$ |
$0$ |
$112$ |
$120$ |
$10$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{5})\) |
$C_2$, $C_4$ |
1.5.ae 2 $\times$ 2.5.af_p |
| 4.5.an_de_aml_bhi |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-7$ |
$[-7, 21, 158, 717, 3253, 15786, 78673, 392637, 1957478, 9769101]$ |
$48$ |
$[48, 345600, 317207808, 176947200000, 99339951101808, 60212639880806400, 37513870763864295408, 23403120802607923200000, 14584385684232990885973248, 9098187204184464865659840000]$ |
$None$ |
$0$ |
$88$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$, $C_2$ |
1.5.ae 2 $\times$ 1.5.ad $\times$ 1.5.ac |
| 4.5.an_df_ams_bie |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )^{3}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-7$ |
$[-7, 23, 176, 787, 3373, 15638, 77161, 388227, 1951808, 9775103]$ |
$54$ |
$[54, 393660, 364290048, 196830000000, 103259791417374, 59657070843002880, 36794213184728145438, 23140362291178680000000, 14542119714034827758444544, 9103779873771429029456166300]$ |
$None$ |
$0$ |
$40$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.5.ae $\times$ 1.5.ad 3 |
| 4.5.am_co_aiu_wg |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-6$ |
$[-6, 14, 90, 562, 3234, 16094, 78450, 391002, 1956474, 9766574]$ |
$40$ |
$[40, 232000, 185901160, 137789440000, 98724762356200, 61408246839784000, 37406785762368758440, 23305441008408330240000, 14576888205733196794245160, 9095832593830975111969000000]$ |
$None$ |
$0$ |
$96$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(i, \sqrt{6})\) |
$C_2$, $C_2^2$ |
1.5.ae 2 $\times$ 2.5.ae_i |
| 4.5.am_cp_ajc_xg |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 4 x + 9 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-6$ |
$[-6, 16, 102, 592, 3314, 16426, 79402, 392672, 1960014, 9778176]$ |
$44$ |
$[44, 259600, 206947136, 144877568000, 101344979199244, 62729484748902400, 37865824253945399756, 23405215805135290368000, 14603329963432731221966144, 9106643109419934768670090000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.1025.1 |
$C_2$, $D_{4}$ |
1.5.ae 2 $\times$ 2.5.ae_j |
| 4.5.am_cq_ajk_yg |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{3}$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$1$ |
$3$ |
$-6$ |
$[-6, 18, 114, 618, 3354, 16578, 79794, 392538, 1957434, 9773298]$ |
$48$ |
$[48, 288000, 228796848, 150994944000, 102624949503408, 63336001057056000, 38055879314533355568, 23397172002403909632000, 14584065785848469246657328, 9102096763908314775156000000]$ |
$None$ |
$0$ |
$44$ |
$12$ |
$2$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) |
$C_2$, $C_2$ |
1.5.ae 3 $\times$ 1.5.a |
| 4.5.am_cr_ajt_zk |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 8 x + 32 x^{2} - 85 x^{3} + 160 x^{4} - 200 x^{5} + 125 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$4$ |
$0$ |
$-6$ |
$[-6, 20, 123, 608, 3194, 16055, 78618, 389568, 1951044, 9771300]$ |
$50$ |
$[50, 305500, 241563050, 148057520000, 97494032110250, 61265218325369500, 37488695779133845450, 23220052872659847360000, 14536417880726821090275200, 9100235005249189095028637500]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 6.0.4426955.1 |
$C_2$, $A_4\times C_2$ |
1.5.ae $\times$ 3.5.ai_bg_adh |
| 4.5.am_cr_ajs_zg |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 4 x + 11 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-6$ |
$[-6, 20, 126, 640, 3354, 16562, 79794, 391680, 1953126, 9766100]$ |
$52$ |
$[52, 317200, 251539600, 156234956800, 102588049661812, 63272170368160000, 38056342149202802932, 23345947240459252531200, 14551929298156324491648400, 9095389395817645702197130000]$ |
$None$ |
$0$ |
$124$ |
$60$ |
$6$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2^2$ |
1.5.ae 2 $\times$ 2.5.ae_l |
| 4.5.am_cs_ake_bax |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )^{2}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-6$ |
$[-6, 22, 126, 534, 2754, 15058, 78282, 392358, 1953126, 9755062]$ |
$49$ |
$[49, 305809, 239754256, 132002149041, 84618786129409, 57482103270113536, 37328307093883814449, 23386524211874297677329, 14551944166392407808553744, 9085114642646574814495668049]$ |
$None$ |
$0$ |
$24$ |
$24$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2^2$ |
2.5.ag_r 2 |
| 4.5.am_cs_akb_bak |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-6$ |
$[-6, 22, 135, 626, 3159, 15955, 78870, 390882, 1953099, 9774937]$ |
$54$ |
$[54, 335340, 265153824, 152646768000, 96425619575904, 60878289193562880, 37608663565748948454, 23298326743389451200000, 14551714461451081885255584, 9103624378553472574290739200]$ |
$None$ |
$0$ |
$16$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), 4.0.4901.1 |
$C_2$, $C_2$, $D_{4}$ |
1.5.ae $\times$ 1.5.ad $\times$ 2.5.af_n |
| 4.5.am_cs_aka_bag |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 4 x + 12 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-6$ |
$[-6, 22, 138, 658, 3314, 16390, 79570, 391130, 1950618, 9763542]$ |
$56$ |
$[56, 347200, 275264696, 160700825600, 101269959432376, 62587649617729600, 37947228001422018104, 23313090284952433459200, 14533235451611243981663672, 9093008912788201114938280000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.10496.2 |
$C_2$, $D_{4}$ |
1.5.ae 2 $\times$ 2.5.ae_m |
| 4.5.am_ct_akk_bbo |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-6$ |
$[-6, 24, 144, 608, 2934, 15342, 78702, 393600, 1956960, 9760344]$ |
$56$ |
$[56, 353920, 279579104, 148816281600, 89660131438136, 58528118482462720, 37529051753962714232, 23460952075775882035200, 14580523303619111741790944, 9090031340992850449276969600]$ |
$None$ |
$0$ |
$96$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2$, $C_2$, $C_2^2$ |
1.5.ae $\times$ 1.5.ac $\times$ 2.5.ag_r |
| 4.5.am_ct_akj_bbk |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 8 x + 34 x^{2} - 93 x^{3} + 170 x^{4} - 200 x^{5} + 125 x^{6} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-6$ |
$[-6, 24, 147, 640, 3084, 15711, 79052, 393232, 1957476, 9772784]$ |
$58$ |
$[58, 365980, 289808194, 156569171840, 94128265961138, 59931647673780220, 37696051384494647986, 23438944479771914595840, 14584359406912159084235392, 9101614396243900551995791900]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 6.0.1178891.1 |
$C_2$, $A_4\times C_2$ |
1.5.ae $\times$ 3.5.ai_bi_adp |
| 4.5.am_ct_aki_bbg |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-6$ |
$[-6, 24, 150, 672, 3234, 16074, 79290, 391872, 1952574, 9765624]$ |
$60$ |
$[60, 378000, 300061440, 164505600000, 98719892274300, 61339279712256000, 37810356625693780860, 23357411582290329600000, 14547811432321238032362240, 9094947685034230503272250000]$ |
$None$ |
$0$ |
$64$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$, $C_2$ |
1.5.ae 2 $\times$ 1.5.ad $\times$ 1.5.ab |
| 4.5.am_cu_akq_bcf |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )^{2}( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-6$ |
$[-6, 26, 162, 678, 3054, 15194, 77190, 389190, 1951290, 9766346]$ |
$63$ |
$[63, 403137, 321076224, 165538130625, 93198017193183, 57988092160180224, 36809102946159389727, 23197544263794809120625, 14538268526711324681567232, 9095618997158239136593946097]$ |
$None$ |
$0$ |
$36$ |
$24$ |
$6$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.5.ad 2 $\times$ 2.5.ag_r |
| 4.5.am_cu_akq_bcg |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 2 x + 5 x^{2} )^{2}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-6$ |
$[-6, 26, 162, 682, 3114, 15626, 79122, 394842, 1960794, 9765626]$ |
$64$ |
$[64, 409600, 326019136, 167772160000, 95001825684544, 59593168277094400, 37730875981310733376, 23535616807151861760000, 14609158568540870270638144, 9094950700166598177187840000]$ |
$None$ |
$0$ |
$124$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.5.ae 2 $\times$ 1.5.ac 2 |
| 4.5.am_cu_akp_bcc |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-6$ |
$[-6, 26, 165, 714, 3259, 15911, 78800, 391154, 1950519, 9756601]$ |
$66$ |
$[66, 421740, 336444768, 175781232000, 99467228373216, 60704070058494720, 37575140666632160658, 23314520028921029568000, 14532517594099089483772896, 9086545273779316874774707200]$ |
$None$ |
$0$ |
$56$ |
$60$ |
$10$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), \(\Q(\zeta_{5})\) |
$C_2$, $C_2$, $C_4$ |
1.5.ae $\times$ 1.5.ad $\times$ 2.5.af_p |
| 4.5.am_cv_akw_bcy |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )^{2}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-6$ |
$[-6, 28, 180, 752, 3234, 15478, 77610, 390432, 1955124, 9771628]$ |
$72$ |
$[72, 466560, 374409216, 186624000000, 98750488556232, 59043314970132480, 37007055423354550536, 23271370696986624000000, 14566820805809751070328832, 9100541380269593437220188800]$ |
$None$ |
$0$ |
$96$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$, $C_2$ |
1.5.ae $\times$ 1.5.ad 2 $\times$ 1.5.ac |
| 4.5.am_cw_alc_bdr |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )^{4}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-6$ |
$[-6, 30, 198, 822, 3354, 15330, 76098, 386022, 1949454, 9777630]$ |
$81$ |
$[81, 531441, 429981696, 207594140625, 102647069357121, 58498535041007616, 36297120474637323921, 23010091409714094140625, 14524605739135674912669696, 9106135496972197033178986641]$ |
$None$ |
$0$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
1.5.ad 4 |
| 4.5.al_cc_agj_pe |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 4 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-5$ |
$[-5, 13, 82, 605, 3335, 15946, 78731, 393885, 1957834, 9763573]$ |
$48$ |
$[48, 230400, 173606976, 148163788800, 101953185785328, 60838550898278400, 37541881767426974832, 23478119514722480947200, 14587053626073722920017984, 9093036552015063765432960000]$ |
$None$ |
$0$ |
$96$ |
$24$ |
$3$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{-11})\) |
$C_2$, $C_2^2$ |
1.5.ae 2 $\times$ 2.5.ad_e |
| 4.5.al_cd_agr_qe |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-5$ |
$[-5, 15, 91, 623, 3410, 16215, 79151, 394623, 1960615, 9766650]$ |
$52$ |
$[52, 254800, 188267716, 152635392000, 104445396370432, 61894084760981200, 37743422774763944836, 23522449559682318336000, 14607820454067422008883092, 9095901361683172330577920000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.37845.1 |
$C_2$, $D_{4}$ |
1.5.ae 2 $\times$ 2.5.ad_f |
| 4.5.al_ce_aha_ri |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 23 x^{2} - 55 x^{3} + 115 x^{4} - 175 x^{5} + 125 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$4$ |
$0$ |
$-5$ |
$[-5, 17, 97, 609, 3325, 15929, 77856, 390641, 1953637, 9755557]$ |
$54$ |
$[54, 270540, 195495606, 148498323840, 101585855236734, 60772837352036940, 37124083642174038144, 23284050299033598973440, 14555721144181616923404438, 9085575765610606761485642700]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 6.0.12305095.1 |
$C_2$, $S_4\times C_2$ |
1.5.ae $\times$ 3.5.ah_x_acd |
| 4.5.al_ce_agz_re |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 + x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{3}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-5$ |
$[-5, 17, 100, 637, 3455, 16382, 79235, 394077, 1959940, 9763097]$ |
$56$ |
$[56, 280000, 203374976, 155975680000, 105940726822616, 62554075118080000, 37783585372224468056, 23489648805575393280000, 14602778182723702213671296, 9092594955955713993175000000]$ |
$None$ |
$0$ |
$88$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.5.ae 3 $\times$ 1.5.b |
| 4.5.al_cf_ahi_si |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 24 x^{2} - 59 x^{3} + 120 x^{4} - 175 x^{5} + 125 x^{6} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-5$ |
$[-5, 19, 106, 619, 3345, 16066, 78073, 390755, 1956022, 9765519]$ |
$58$ |
$[58, 296380, 211105384, 150921438080, 102289949299058, 61311750441672640, 37227732300849261922, 23290811307029403164160, 14573500322886707436902248, 9094849235129799353382307900]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 6.0.29215664.1 |
$C_2$, $S_4\times C_2$ |
1.5.ae $\times$ 3.5.ah_y_ach |
| 4.5.al_cf_ahh_se |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 7 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-5$ |
$[-5, 19, 109, 647, 3470, 16459, 79109, 392847, 1957915, 9760474]$ |
$60$ |
$[60, 306000, 219018060, 158238720000, 106436408884800, 62860964749362000, 37723253866119092940, 23415883237073387520000, 14587645433752853450921340, 9090152629464840455232000000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.48069.2 |
$C_2$, $D_{4}$ |
1.5.ae 2 $\times$ 2.5.ad_h |
| 4.5.al_cg_ahr_tm |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 8 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-5$ |
$[-5, 21, 112, 597, 3215, 15786, 77387, 388797, 1954120, 9769101]$ |
$60$ |
$[60, 313200, 219424320, 145324800000, 98138950212300, 60215703332428800, 36901417148640103980, 23174240800525516800000, 14559332356987392903013440, 9098186160655460922487830000]$ |
$None$ |
$0$ |
$48$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), \(\Q(i, \sqrt{6})\) |
$C_2$, $C_2$, $C_2^2$ |
1.5.ae $\times$ 1.5.ad $\times$ 2.5.ae_i |
| 4.5.al_cg_ahq_ti |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 25 x^{2} - 63 x^{3} + 125 x^{4} - 175 x^{5} + 125 x^{6} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-5$ |
$[-5, 21, 115, 625, 3335, 16125, 78192, 390529, 1957075, 9773621]$ |
$62$ |
$[62, 323020, 227332238, 152331063680, 102004742170342, 61542658281520780, 37284327213404217344, 23277220076463368394240, 14581361287667006692266974, 9102397551739387088407677100]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 6.0.40529831.1 |
$C_2$, $A_4\times C_2$ |
1.5.ae $\times$ 3.5.ah_z_acl |
| 4.5.al_cg_ahp_te |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 8 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-5$ |
$[-5, 21, 118, 653, 3455, 16458, 78899, 391485, 1955998, 9762381]$ |
$64$ |
$[64, 332800, 235286272, 159488409600, 105937056318784, 62857951053414400, 37622750928200078656, 23334330333320655667200, 14573326513210221066708736, 9091927125274661971438720000]$ |
$None$ |
$0$ |
$64$ |
$24$ |
$6$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{17})\) |
$C_2$, $C_2^2$ |
1.5.ae 2 $\times$ 2.5.ad_i |
| 4.5.al_ch_ahz_um |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 26 x^{2} - 68 x^{3} + 130 x^{4} - 175 x^{5} + 125 x^{6} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-5$ |
$[-5, 23, 121, 599, 3180, 15839, 77849, 389679, 1956595, 9779718]$ |
$64$ |
$[64, 340480, 236305216, 145954242560, 97099396455424, 60419585726456320, 37120951071118044992, 23226689054721740636160, 14577807273559580351296576, 9108081009512793909929574400]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 6.0.2419571.1 |
$C_2$, $S_4\times C_2$ |
1.5.ae $\times$ 3.5.ah_ba_acq |
| 4.5.al_ch_ahy_ui |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 9 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-5$ |
$[-5, 23, 124, 627, 3295, 16118, 78339, 390467, 1957660, 9780703]$ |
$66$ |
$[66, 350460, 244265472, 152800560000, 100743619235226, 61511282901319680, 37354253994140819802, 23273453905497005760000, 14585742269241438927684096, 9108999473489266863893406300]$ |
$None$ |
$0$ |
$16$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), 4.0.1025.1 |
$C_2$, $C_2$, $D_{4}$ |
1.5.ae $\times$ 1.5.ad $\times$ 2.5.ae_j |
| 4.5.al_ch_ahx_ue |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 9 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-5$ |
$[-5, 23, 127, 655, 3410, 16391, 78731, 390495, 1954999, 9768698]$ |
$68$ |
$[68, 360400, 252268916, 159798476800, 104455895241728, 62590163252952400, 37542139214220476372, 23275134774468653875200, 14565881008837190764198724, 9097810705223061110824960000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.30589.1 |
$C_2$, $D_{4}$ |
1.5.ae 2 $\times$ 2.5.ad_j |
| 4.5.al_ci_aik_vz |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-5$ |
$[-5, 25, 121, 517, 2840, 15511, 78899, 391845, 1952581, 9766180]$ |
$63$ |
$[63, 343413, 233700012, 128379112029, 87029776331568, 59175145450918224, 37623882916287319491, 23355899060757619121325, 14547860733152098732413852, 9095463641330437680639848448]$ |
$None$ |
$0$ |
$12$ |
$24$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{-3})\), 4.0.4901.1 |
$C_2^2$, $D_{4}$ |
2.5.ag_r $\times$ 2.5.af_n |
| 4.5.al_ci_aii_vq |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 27 x^{2} - 73 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-5$ |
$[-5, 25, 127, 569, 3005, 15613, 78164, 390177, 1953541, 9769465]$ |
$66$ |
$[66, 358380, 245992626, 139189057920, 91763628038346, 59543280160366860, 37270822609601606784, 23256270099354103764480, 14555004246562122843625026, 9098524113569455041140805900]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 6.0.3194271.1 |
$C_2$, $S_4\times C_2$ |
1.5.ae $\times$ 3.5.ah_bb_acv |
| 4.5.al_ci_aih_vm |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 27 x^{2} - 72 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-5$ |
$[-5, 25, 130, 597, 3115, 15838, 78451, 390973, 1957486, 9782145]$ |
$68$ |
$[68, 368560, 253973744, 145725675520, 95113205467828, 60413486247562240, 37408435140425549492, 23303788858944706314240, 14584444447485317147745776, 9110344141423473374156090800]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 6.0.31554496.1 |
$C_2$, $S_4\times C_2$ |
1.5.ae $\times$ 3.5.ah_bb_acu |
| 4.5.al_ci_aig_vi |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 27 x^{2} - 71 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-5$ |
$[-5, 25, 133, 625, 3225, 16057, 78640, 391025, 1957993, 9784125]$ |
$70$ |
$[70, 378700, 261994390, 152413116800, 98529792816350, 61266667616927500, 37498238315499418240, 23306761596246922483200, 14588230530131581136310070, 9112190427730262575095767500]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 6.0.39563351.1 |
$C_2$, $S_4\times C_2$ |
1.5.ae $\times$ 3.5.ah_bb_act |
| 4.5.al_ci_aif_ve |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$2$ |
$2$ |
$-5$ |
$[-5, 25, 136, 653, 3335, 16270, 78731, 390333, 1955080, 9775825]$ |
$72$ |
$[72, 388800, 270055296, 159252480000, 102015994462632, 62106020708659200, 37541741395932545256, 23265455386121994240000, 14566501292698654967751552, 9104451951600678800860920000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$2$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-5}) \) |
$C_2$, $C_2$, $C_2$ |
1.5.ae 2 $\times$ 1.5.ad $\times$ 1.5.a |
| 4.5.al_cj_aiq_wq |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - x + 5 x^{2} )( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-5$ |
$[-5, 27, 136, 563, 2915, 15630, 79319, 392835, 1952056, 9756867]$ |
$70$ |
$[70, 387100, 264466720, 138352636800, 89100491984350, 59623239202508800, 37825657596717684190, 23415129903752882265600, 14543958737660858033842720, 9086794725835950470555477500]$ |
$None$ |
$0$ |
$48$ |
$24$ |
$6$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2$, $C_2$, $C_2^2$ |
1.5.ae $\times$ 1.5.ab $\times$ 2.5.ag_r |
| 4.5.al_cj_aip_wm |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-5$ |
$[-5, 27, 139, 591, 3020, 15795, 79319, 393087, 1956415, 9771462]$ |
$72$ |
$[72, 397440, 272519208, 144731750400, 92214761542272, 60251969345892480, 37826217127905395688, 23430229459787612160000, 14576431850763169422818952, 9100385940366051423171379200]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \), 4.0.4901.1 |
$C_2$, $C_2$, $D_{4}$ |
1.5.ae $\times$ 1.5.ac $\times$ 2.5.af_n |
| 4.5.al_cj_aio_wh |
$4$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 11 x + 61 x^{2} - 222 x^{3} + 579 x^{4} - 1110 x^{5} + 1525 x^{6} - 1375 x^{7} + 625 x^{8}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-5$ |
$[-5, 27, 142, 615, 3070, 15594, 77744, 388423, 1949155, 9766042]$ |
$73$ |
$[73, 402157, 276998281, 149496636709, 93676590558953, 59478260049940333, 37071479785304297357, 23152245270339841315317, 14522353952086465698392557, 9095333989766520554012236597]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
8.0.2071948309.1 |
$C_2 \wr S_4$ |
simple |
| 4.5.al_cj_aio_wi |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 28 x^{2} - 75 x^{3} + 140 x^{4} - 175 x^{5} + 125 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$4$ |
$0$ |
$-5$ |
$[-5, 27, 142, 619, 3125, 15954, 79221, 392611, 1957642, 9778007]$ |
$74$ |
$[74, 407740, 280608296, 151261754240, 95397532510834, 60862715950229440, 37778120833792126274, 23401661133629045399040, 14585586808425220946415848, 9106486304538120500625312700]$ |
$None$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), 6.0.16537520.2 |
$C_2$, $S_4\times C_2$ |
1.5.ae $\times$ 3.5.ah_bc_acx |
| 4.5.al_cj_ain_wd |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 8 x + 32 x^{2} - 85 x^{3} + 160 x^{4} - 200 x^{5} + 125 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$4$ |
$0$ |
$-5$ |
$[-5, 27, 145, 643, 3175, 15747, 77555, 387363, 1948690, 9773827]$ |
$75$ |
$[75, 412425, 285123600, 156154415625, 96915522862875, 60075452420942400, 36982220554645153275, 23089333365449331215625, 14518910772898452925516800, 9102589711207377594106379625]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), 6.0.4426955.1 |
$C_2$, $A_4\times C_2$ |
1.5.ad $\times$ 3.5.ai_bg_adh |
| 4.5.al_cj_ain_we |
$4$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 11 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-5$ |
$[-5, 27, 145, 647, 3230, 16107, 79025, 391407, 1955755, 9776922]$ |
$76$ |
$[76, 418000, 288734716, 157943808000, 98651495818816, 61458772341538000, 37682909808445408156, 23329649713854578688000, 14571525193312758813944236, 9105474366436704604480000000]$ |
$None$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), 4.0.6525.1 |
$C_2$, $D_{4}$ |
1.5.ae 2 $\times$ 2.5.ad_l |
