| 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 |
| 4.2.ai_bg_adc_fg |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$6$ |
$0$ |
$4$ |
$0$ |
$4$ |
$-5$ |
$[-5, 5, 25, 49, 65, 65, 65, 129, 385, 1025]$ |
$1$ |
$[1, 625, 28561, 390625, 2825761, 17850625, 163047361, 2562890625, 53527912321, 1103812890625]$ |
$0$ |
$0$ |
$65$ |
$40$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.2.ac 4 |
| 4.2.ah_z_acg_ds |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-4$ |
$[-4, 6, 17, 26, 46, 87, 136, 210, 449, 1086]$ |
$1$ |
$[1, 475, 12844, 106875, 1615441, 24403600, 281569219, 3540661875, 60469436404, 1170185074375]$ |
$0$ |
$0$ |
$44$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ac 2 $\times$ 2.2.ad_f |
| 4.2.ah_ba_ack_ea |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$1$ |
$3$ |
$-4$ |
$[-4, 8, 26, 40, 46, 56, 94, 192, 422, 968]$ |
$2$ |
$[2, 1000, 30758, 250000, 1516262, 15379000, 204891374, 3280500000, 57645444038, 1042430125000]$ |
$0$ |
$0$ |
$50$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac 3 $\times$ 1.2.ab |
| 4.2.ag_s_abk_ce |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$6$ |
$0$ |
$4$ |
$0$ |
$4$ |
$-3$ |
$[-3, 5, 9, 25, 57, 65, 81, 225, 513, 1025]$ |
$1$ |
$[1, 325, 4225, 105625, 2220601, 17850625, 184499281, 3773030625, 68720001025, 1100585370625]$ |
$0$ |
$0$ |
$65$ |
$120$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2^2$ |
1.2.ac 2 $\times$ 2.2.ac_c |
| 4.2.ag_t_abq_cr |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-3$ |
$[-3, 7, 9, 3, 27, 109, 207, 291, 513, 1147]$ |
$1$ |
$[1, 361, 5776, 29241, 923521, 33362176, 486246601, 4891463721, 68311140496, 1240548212401]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2^2$ |
2.2.ad_f 2 |
| 4.2.ag_t_abp_co |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$1$ |
$3$ |
$-3$ |
$[-3, 7, 12, 15, 32, 52, 74, 199, 543, 1092]$ |
$1$ |
$[1, 355, 5473, 51475, 1050461, 13600405, 176381248, 3424992075, 72845887231, 1176542581525]$ |
$0$ |
$0$ |
$42$ |
$168$ |
$28$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{7})\) |
$C_2$, $C_6$ |
1.2.ac $\times$ 3.2.ae_j_ap |
| 4.2.ag_t_abo_cm |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-3$ |
$[-3, 7, 15, 31, 67, 91, 95, 191, 483, 987]$ |
$2$ |
$[2, 700, 10478, 140000, 2961922, 25671100, 204891374, 3311280000, 64822262258, 1062589517500]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.1088.2 |
$C_2$, $D_{4}$ |
1.2.ac 2 $\times$ 2.2.ac_d |
| 4.2.ag_u_abt_cw |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$2$ |
$2$ |
$-3$ |
$[-3, 9, 18, 17, 27, 78, 165, 273, 486, 1029]$ |
$2$ |
$[2, 760, 13832, 68400, 866822, 21024640, 353830346, 4532047200, 65120931512, 1105111367800]$ |
$0$ |
$0$ |
$24$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2$, $C_2^2$ |
1.2.ac $\times$ 1.2.ab $\times$ 2.2.ad_f |
| 4.2.ag_u_abs_cu |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$6$ |
$0$ |
$4$ |
$0$ |
$4$ |
$-3$ |
$[-3, 9, 21, 33, 57, 81, 81, 129, 417, 1089]$ |
$3$ |
$[3, 1125, 19773, 140625, 2274393, 22244625, 186133713, 2562890625, 57089020833, 1172733890625]$ |
$0$ |
$0$ |
$65$ |
$40$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.2.ac 3 $\times$ 1.2.a |
| 4.2.ag_v_abw_dc |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 2 x^{2} )^{2}$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-3$ |
$[-3, 11, 27, 31, 27, 47, 123, 255, 459, 911]$ |
$4$ |
$[4, 1600, 33124, 160000, 813604, 13249600, 257474116, 4199040000, 62079708964, 984460840000]$ |
$0$ |
$0$ |
$66$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac 2 $\times$ 1.2.ab 2 |
| 4.2.af_k_aj_g |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$1$ |
$3$ |
$-2$ |
$[-2, 0, 7, 36, 43, 87, 152, 220, 538, 1015]$ |
$1$ |
$[1, 145, 3913, 203725, 1429301, 24397555, 323551544, 3698219925, 72057648481, 1089091629475]$ |
$0$ |
$0$ |
$42$ |
$168$ |
$28$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{7})\) |
$C_2$, $C_6$ |
1.2.ac $\times$ 3.2.ad_c_b |
| 4.2.af_l_ao_q |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-2$ |
$[-2, 2, 7, 34, 38, 47, 110, 162, 439, 1082]$ |
$1$ |
$[1, 175, 2704, 161875, 1262431, 13249600, 231157207, 2950171875, 59705945104, 1165381616875]$ |
$0$ |
$0$ |
$66$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2$, $C_2^2$ |
1.2.ac 2 $\times$ 2.2.ab_ab |
| 4.2.af_m_au_bd |
$4$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
|
$1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-2$ |
$[-2, 4, 4, 20, 33, 46, 159, 324, 508, 1019]$ |
$1$ |
$[1, 211, 1861, 88831, 1046771, 12172801, 344358281, 5598573775, 68193052891, 1095729526441]$ |
$0$ |
$0$ |
$6$ |
$20$ |
$10$ |
8.0.13140625.1 |
$C_2^2:C_4$ |
simple |
| 4.2.af_m_as_y |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x - 2 x^{3} + 4 x^{4} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$2$ |
$2$ |
$-2$ |
$[-2, 4, 10, 40, 58, 64, 138, 224, 442, 1104]$ |
$2$ |
$[2, 400, 4394, 260000, 2356762, 16697200, 285336074, 3748680000, 59774890682, 1190164810000]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.2312.1 |
$C_2$, $D_{4}$ |
1.2.ac 2 $\times$ 2.2.ab_a |
| 4.2.af_n_aba_bq |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-2$ |
$[-2, 6, 1, 2, 38, 87, 152, 306, 577, 1086]$ |
$1$ |
$[1, 247, 1900, 28899, 1269481, 24403600, 318614899, 5212483731, 77631642100, 1166763483847]$ |
$0$ |
$0$ |
$44$ |
$24$ |
$12$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{12})\) |
$C_2^2$, $C_2^2$ |
2.2.ad_f $\times$ 2.2.ac_c |
| 4.2.af_n_az_bn |
$4$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
|
|
$1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-2$ |
$[-2, 6, 4, 10, 33, 54, 124, 274, 418, 781]$ |
$1$ |
$[1, 241, 1891, 43621, 929296, 14127661, 256112011, 4581295525, 57170567071, 863591055616]$ |
$0$ |
$0$ |
$18$ |
$60$ |
$10$ |
\(\Q(\zeta_{15})\) |
$C_4\times C_2$ |
simple |
| 4.2.af_n_ax_bi |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-2$ |
$[-2, 6, 10, 30, 48, 42, 110, 286, 532, 1126]$ |
$2$ |
$[2, 460, 3926, 156400, 1756522, 11738740, 233066794, 4785840000, 71094273302, 1214020180300]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.679024.1 |
$C_2$, $S_4\times C_2$ |
1.2.ac $\times$ 3.2.ad_f_ah |
| 4.2.af_n_aw_bg |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-2$ |
$[-2, 6, 13, 42, 68, 63, 110, 210, 373, 966]$ |
$3$ |
$[3, 675, 6084, 286875, 3030843, 16426800, 234400533, 3555241875, 52197817932, 1039958004375]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.2873.1 |
$C_2$, $D_{4}$ |
1.2.ac 2 $\times$ 2.2.ab_b |
| 4.2.af_o_abd_bv |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-2$ |
$[-2, 8, 7, 8, 48, 113, 166, 272, 547, 1048]$ |
$2$ |
$[2, 532, 4712, 38304, 1693282, 35094976, 353830346, 4574570112, 73228442792, 1126482943012]$ |
$0$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.1088.2 |
$C_2^2$, $D_{4}$ |
2.2.ad_f $\times$ 2.2.ac_d |
| 4.2.af_o_abc_bs |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$1$ |
$3$ |
$-2$ |
$[-2, 8, 10, 16, 38, 56, 110, 288, 550, 968]$ |
$2$ |
$[2, 520, 4550, 67600, 1191542, 15379000, 231848654, 4829479200, 74006154950, 1039382086600]$ |
$0$ |
$0$ |
$50$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2$, $C_2^2$ |
1.2.ac $\times$ 1.2.ab $\times$ 2.2.ac_c |
| 4.2.af_o_abb_bq |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-2$ |
$[-2, 8, 13, 28, 53, 59, 110, 300, 562, 983]$ |
$3$ |
$[3, 765, 6669, 141525, 1923843, 15305355, 230848152, 5045224725, 75677417829, 1057199824575]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.465831.1 |
$C_2$, $A_4\times C_2$ |
1.2.ac $\times$ 3.2.ad_g_aj |
| 4.2.af_o_aba_bo |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$1$ |
$3$ |
$-2$ |
$[-2, 8, 16, 40, 68, 56, 68, 192, 412, 968]$ |
$4$ |
$[4, 1000, 8788, 250000, 3032524, 15379000, 167376052, 3280500000, 56532597628, 1042430125000]$ |
$0$ |
$0$ |
$50$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac 3 $\times$ 1.2.b |
| 4.2.af_p_abg_bz |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-2$ |
$[-2, 10, 13, 6, 13, 43, 103, 262, 580, 1035]$ |
$2$ |
$[2, 568, 5894, 32944, 563662, 11717272, 221647232, 4383989856, 78449417018, 1111115335528]$ |
$0$ |
$0$ |
$32$ |
$84$ |
$14$ |
\(\Q(\sqrt{-7}) \), \(\Q(\zeta_{7})\) |
$C_2$, $C_6$ |
1.2.ab $\times$ 3.2.ae_j_ap |
| 4.2.af_p_abg_ca |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-2$ |
$[-2, 10, 13, 10, 38, 103, 152, 210, 481, 1150]$ |
$3$ |
$[3, 855, 8892, 38475, 1300233, 30410640, 321437427, 3540661875, 64492351092, 1243250288775]$ |
$0$ |
$0$ |
$44$ |
$24$ |
$24$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2$, $C_2^2$ |
1.2.ac $\times$ 1.2.a $\times$ 2.2.ad_f |
| 4.2.af_p_abf_by |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-2$ |
$[-2, 10, 16, 22, 48, 82, 124, 254, 520, 930]$ |
$4$ |
$[4, 1120, 11284, 89600, 1589324, 22116640, 257474116, 4238438400, 69808590124, 1003499173600]$ |
$0$ |
$0$ |
$12$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), 4.0.1088.2 |
$C_2$, $C_2$, $D_{4}$ |
1.2.ac $\times$ 1.2.ab $\times$ 2.2.ac_d |
| 4.2.af_p_abe_bw |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-2$ |
$[-2, 10, 19, 34, 58, 55, 54, 194, 523, 1050]$ |
$5$ |
$[5, 1375, 13520, 171875, 2311375, 14872000, 147545795, 3355171875, 69982075280, 1128239921875]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.1025.1 |
$C_2$, $D_{4}$ |
1.2.ac 2 $\times$ 2.2.ab_d |
| 4.2.af_q_abj_cf |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-2$ |
$[-2, 12, 19, 8, 8, 69, 194, 336, 523, 972]$ |
$4$ |
$[4, 1216, 14896, 43776, 465124, 18113536, 444636364, 5801020416, 70130233936, 1043656394176]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ab 2 $\times$ 2.2.ad_f |
| 4.2.af_q_abi_ce |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$1$ |
$3$ |
$-2$ |
$[-2, 12, 22, 24, 38, 72, 110, 192, 454, 1032]$ |
$6$ |
$[6, 1800, 21294, 90000, 1220406, 19164600, 233902542, 3280500000, 61480483974, 1107518445000]$ |
$0$ |
$0$ |
$50$ |
$24$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$, $C_2$ |
1.2.ac 2 $\times$ 1.2.ab $\times$ 1.2.a |
| 4.2.af_r_abl_ck |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )^{3}$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$1$ |
$3$ |
$-2$ |
$[-2, 14, 28, 22, 8, 38, 152, 318, 496, 854]$ |
$8$ |
$[8, 2560, 35672, 102400, 436568, 11415040, 323551544, 5374771200, 66855071192, 929715212800]$ |
$0$ |
$0$ |
$42$ |
$56$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac $\times$ 1.2.ab 3 |
| 4.2.ae_e_h_av |
$4$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
|
|
$1 - 4 x + 4 x^{2} + 7 x^{3} - 21 x^{4} + 14 x^{5} + 16 x^{6} - 32 x^{7} + 16 x^{8}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-1$ |
$[-1, -3, 14, 13, 39, 54, 146, 301, 608, 1147]$ |
$1$ |
$[1, 31, 7471, 55831, 1343281, 14127661, 308739901, 5138741071, 82847868931, 1240548212401]$ |
$0$ |
$0$ |
$18$ |
$120$ |
$30$ |
\(\Q(\zeta_{15})\) |
$C_4\times C_2$ |
simple |
| 4.2.ae_e_i_ay |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x^{2} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$6$ |
$0$ |
$4$ |
$0$ |
$4$ |
$-1$ |
$[-1, -3, 17, 17, 49, 33, 97, 129, 449, 897]$ |
$1$ |
$[1, 25, 8281, 50625, 1615441, 10144225, 205951201, 2562890625, 60413215681, 970274250625]$ |
$0$ |
$0$ |
$65$ |
$40$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{2}) \) |
$C_2$, $C_2$ |
1.2.ac 2 $\times$ 2.2.a_ae |
| 4.2.ae_f_c_al |
$4$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
|
$1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-1$ |
$[-1, -1, 11, 19, 19, 65, 97, 291, 479, 959]$ |
$1$ |
$[1, 61, 5044, 76921, 660661, 15999568, 207872197, 4902098409, 64314697252, 1032534524341]$ |
$0$ |
$0$ |
$8$ |
$24$ |
$12$ |
8.0.22581504.2 |
$D_4\times C_2$ |
simple |
| 4.2.ae_f_e_aq |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x^{2} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-1$ |
$[-1, -1, 17, 31, 49, 83, 97, 255, 449, 1139]$ |
$2$ |
$[2, 100, 12506, 160000, 1818842, 23136100, 208109162, 4199040000, 60418999706, 1229991902500]$ |
$0$ |
$0$ |
$66$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(i, \sqrt{7})\) |
$C_2$, $C_2^2$ |
1.2.ac 2 $\times$ 2.2.a_ad |
| 4.2.ae_g_ae_c |
$4$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
|
|
? |
|
$1 - 4 x + 6 x^{2} - 4 x^{3} + 2 x^{4} - 8 x^{5} + 24 x^{6} - 32 x^{7} + 16 x^{8}$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4},\frac{1}{4},\frac{3}{4},\frac{3}{4},\frac{3}{4},\frac{3}{4}]$ |
$4$ |
$0$ |
$4$ |
$2$ |
$2$ |
$-1$ |
$[-1, 1, 5, 17, 9, 73, 153, 273, 545, 881]$ |
$1$ |
$[1, 97, 2689, 67609, 457601, 19040809, 323696297, 4570976881, 73309284673, 955259018737]$ |
$0$ |
$0$ |
$6$ |
$16$ |
$8$ |
8.0.18939904.2 |
$D_4\times C_2$ |
simple |
| 4.2.ae_g_ab_ag |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-1$ |
$[-1, 1, 14, 33, 29, 70, 83, 241, 554, 1101]$ |
$2$ |
$[2, 160, 8216, 174400, 957022, 18403840, 187036922, 4046428800, 74587173128, 1183262000800]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.1539727.2 |
$C_2$, $D_{6}$ |
1.2.ac $\times$ 3.2.ac_a_d |
| 4.2.ae_g_a_ai |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x^{2} + 4 x^{4} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$6$ |
$0$ |
$4$ |
$0$ |
$4$ |
$-1$ |
$[-1, 1, 17, 41, 49, 97, 97, 225, 449, 961]$ |
$3$ |
$[3, 225, 13689, 275625, 1669233, 27720225, 207585633, 3773030625, 60887043009, 1035967730625]$ |
$0$ |
$0$ |
$65$ |
$120$ |
$24$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.2.ac 2 $\times$ 2.2.a_ac |
| 4.2.ae_h_ak_p |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-1$ |
$[-1, 3, -1, 11, 19, 69, 181, 243, 503, 1143]$ |
$1$ |
$[1, 133, 1216, 44289, 721711, 18113536, 399189253, 4075695225, 67448639296, 1235455923373]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2^2$, $C_2^2$ |
2.2.ad_f $\times$ 2.2.ab_ab |
| 4.2.ae_h_ah_h |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-1$ |
$[-1, 3, 8, 27, 24, 78, 181, 283, 575, 958]$ |
$2$ |
$[2, 232, 4214, 130384, 766942, 21019432, 406586896, 4733721504, 77600544518, 1028527509592]$ |
$0$ |
$0$ |
$32$ |
$84$ |
$7$ |
\(\Q(\sqrt{-7}) \), \(\Q(\zeta_{7})\) |
$C_2$, $C_6$ |
1.2.ab $\times$ 3.2.ad_c_b |
| 4.2.ae_h_ag_e |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-1$ |
$[-1, 3, 11, 31, 19, 51, 111, 223, 587, 1043]$ |
$2$ |
$[2, 220, 5018, 149600, 686422, 13799500, 237933026, 3753763200, 79235379158, 1121647869100]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.2580992.1 |
$C_2$, $D_{6}$ |
1.2.ac $\times$ 3.2.ac_b_a |
| 4.2.ae_h_af_c |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + x^{2} + x^{3} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-1$ |
$[-1, 3, 14, 39, 34, 72, 118, 231, 599, 1068]$ |
$3$ |
$[3, 315, 8541, 247275, 1097283, 18832905, 245655672, 3865650075, 81042243633, 1146962487825]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.2369943.1 |
$C_2$, $S_4\times C_2$ |
1.2.ac $\times$ 3.2.ac_b_b |
| 4.2.ae_h_ae_a |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x^{2} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-1$ |
$[-1, 3, 17, 47, 49, 87, 97, 159, 449, 903]$ |
$4$ |
$[4, 400, 12844, 360000, 1620484, 24403600, 212425084, 2916000000, 60469436404, 976341610000]$ |
$0$ |
$0$ |
$44$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ac 2 $\times$ 2.2.a_ab |
| 4.2.ae_i_aq_bc |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$6$ |
$0$ |
$4$ |
$0$ |
$4$ |
$-1$ |
$[-1, 5, -7, 1, 49, 65, 97, 321, 641, 1025]$ |
$1$ |
$[1, 169, 625, 28561, 1745041, 17850625, 208773601, 5554571841, 88223850625, 1097367287809]$ |
$0$ |
$0$ |
$65$ |
$120$ |
$12$ |
\(\Q(\zeta_{12})\) |
$C_2^2$ |
2.2.ac_c 2 |
| 4.2.ae_i_an_u |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-1$ |
$[-1, 5, 2, 17, 39, 86, 209, 305, 506, 1165]$ |
$2$ |
$[2, 304, 1976, 71136, 1347322, 22826752, 492751646, 5178843072, 67526525768, 1261729327984]$ |
$0$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.2312.1 |
$C_2^2$, $D_{4}$ |
2.2.ad_f $\times$ 2.2.ab_a |
| 4.2.ae_i_am_r |
$4$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
|
$1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$2$ |
$2$ |
$-1$ |
$[-1, 5, 5, 21, 29, 65, 181, 253, 437, 1025]$ |
$2$ |
$[2, 292, 2402, 85264, 930082, 17183908, 403078034, 4278206464, 59240758994, 1097334925732]$ |
$0$ |
$0$ |
$8$ |
$24$ |
$4$ |
8.0.18939904.2 |
$D_4\times C_2$ |
simple |
| 4.2.ae_i_al_o |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$1$ |
$3$ |
$-1$ |
$[-1, 5, 8, 25, 19, 38, 139, 225, 476, 1025]$ |
$2$ |
$[2, 280, 2912, 103600, 677402, 11415040, 290480738, 3776220000, 64298710112, 1100575029400]$ |
$0$ |
$0$ |
$42$ |
$168$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2$, $C_2$, $C_2^2$ |
1.2.ac $\times$ 1.2.ab $\times$ 2.2.ab_ab |
| 4.2.ae_i_ak_m |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 2 x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},\frac{1}{2},\frac{2}{3},\frac{2}{3},\frac{2}{3}]$ |
$5$ |
$0$ |
$4$ |
$3$ |
$1$ |
$-1$ |
$[-1, 5, 11, 33, 29, 53, 153, 257, 569, 1105]$ |
$3$ |
$[3, 405, 5031, 180225, 963213, 14262885, 323900601, 4244839425, 76636533753, 1190459027025]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.1142512.1 |
$C_2$, $S_4\times C_2$ |
1.2.ac $\times$ 3.2.ac_c_ac |
| 4.2.ae_i_aj_k |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-1$ |
$[-1, 5, 14, 41, 39, 62, 139, 225, 554, 1065]$ |
$4$ |
$[4, 520, 7696, 275600, 1295764, 16007680, 288538268, 3775168800, 74530703728, 1146297622600]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.2464727.1 |
$C_2$, $S_4\times C_2$ |
1.2.ac $\times$ 3.2.ac_c_ab |
| 4.2.ae_i_ai_i |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$6$ |
$0$ |
$4$ |
$0$ |
$4$ |
$-1$ |
$[-1, 5, 17, 49, 49, 65, 97, 129, 449, 1025]$ |
$5$ |
$[5, 625, 10985, 390625, 1723025, 17850625, 209220065, 2562890625, 60650129345, 1103812890625]$ |
$0$ |
$0$ |
$65$ |
$40$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.2.ac 3 $\times$ 1.2.c |
| 4.2.ae_j_as_be |
$4$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-1$ |
$[-1, 7, -1, 7, 59, 91, 111, 287, 611, 987]$ |
$2$ |
$[2, 364, 1550, 37856, 2327602, 25671100, 231848654, 4874792832, 83219870450, 1059482533564]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$12$ |
\(\Q(\zeta_{12})\), 4.0.1088.2 |
$C_2^2$, $D_{4}$ |
2.2.ac_c $\times$ 2.2.ac_d |
| 4.2.ae_j_ar_bb |
$4$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 4 x + 9 x^{2} - 17 x^{3} + 27 x^{4} - 34 x^{5} + 36 x^{6} - 32 x^{7} + 16 x^{8}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-1$ |
$[-1, 7, 2, 11, 44, 70, 125, 235, 425, 1002]$ |
$2$ |
$[2, 352, 1682, 42944, 1475342, 18057952, 267337072, 3936504704, 57996253142, 1075252855072]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
8.0.316180889.1 |
$C_2 \wr S_4$ |
simple |
