| 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 |
| 5.2.ak_by_age_nw_awu |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{5}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$9$ |
$0$ |
$5$ |
$0$ |
$5$ |
$-7$ |
$[-7, 5, 29, 57, 73, 65, 49, 97, 353, 1025]$ |
$1$ |
$[1, 3125, 371293, 9765625, 115856201, 1160290625, 18424351793, 576650390625, 25746925826401, 1131408212890625]$ |
$0$ |
$0$ |
$131$ |
$40$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.2.ac 5 |
| 5.2.aj_bp_aes_kc_aqi |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$1$ |
$4$ |
$-6$ |
$[-6, 6, 21, 34, 54, 87, 120, 178, 417, 1086]$ |
$1$ |
$[1, 2375, 166972, 2671875, 66233081, 1586234000, 31817321747, 796648921875, 29085798910324, 1199439701234375]$ |
$0$ |
$0$ |
$100$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ac 3 $\times$ 2.2.ad_f |
| 5.2.aj_bq_aey_ku_aro |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$6$ |
$1$ |
$4$ |
$1$ |
$4$ |
$-6$ |
$[-6, 8, 30, 48, 54, 56, 78, 160, 390, 968]$ |
$2$ |
$[2, 5000, 399854, 6250000, 62166742, 999635000, 23152725262, 738112500000, 27727458582278, 1068490878125000]$ |
$0$ |
$0$ |
$130$ |
$40$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac 4 $\times$ 1.2.ab |
| 5.2.ai_bg_adg_gi_ajw |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$9$ |
$0$ |
$5$ |
$0$ |
$5$ |
$-5$ |
$[-5, 5, 13, 33, 65, 65, 65, 193, 481, 1025]$ |
$1$ |
$[1, 1625, 54925, 2640625, 91044641, 1160290625, 20848418753, 848931890625, 33054320493025, 1128100004890625]$ |
$0$ |
$0$ |
$131$ |
$120$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2^2$ |
1.2.ac 3 $\times$ 2.2.ac_c |
| 5.2.ai_bh_ado_hj_alu |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$1$ |
$4$ |
$-5$ |
$[-5, 7, 13, 11, 35, 109, 191, 259, 481, 1147]$ |
$1$ |
$[1, 1805, 75088, 731025, 37864361, 2168541440, 54945865913, 1100579337225, 32857658578576, 1271561917711025]$ |
$0$ |
$0$ |
$54$ |
$120$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ac $\times$ 2.2.ad_f 2 |
| 5.2.ai_bh_adn_he_alk |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$1$ |
$4$ |
$-5$ |
$[-5, 7, 16, 23, 40, 52, 58, 167, 511, 1092]$ |
$1$ |
$[1, 1775, 71149, 1286875, 43068901, 884026325, 19931081024, 770623216875, 35038871758111, 1205956146063125]$ |
$0$ |
$0$ |
$154$ |
$168$ |
$28$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{7})\) |
$C_2$, $C_6$ |
1.2.ac 2 $\times$ 3.2.ae_j_ap |
| 5.2.ai_bh_adm_ha_alc |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$2$ |
$3$ |
$-5$ |
$[-5, 7, 19, 39, 75, 91, 79, 159, 451, 987]$ |
$2$ |
$[2, 3500, 136214, 3500000, 121438802, 1668621500, 23152725262, 745038000000, 31179508146098, 1089154255437500]$ |
$0$ |
$0$ |
$50$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.1088.2 |
$C_2$, $D_{4}$ |
1.2.ac 3 $\times$ 2.2.ac_d |
| 5.2.ai_bi_adt_hw_amq |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$2$ |
$3$ |
$-5$ |
$[-5, 9, 22, 25, 35, 78, 149, 241, 454, 1029]$ |
$2$ |
$[2, 3800, 179816, 1710000, 35539702, 1366601600, 39982829098, 1019710620000, 31323168057272, 1132739151995000]$ |
$0$ |
$0$ |
$88$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2$, $C_2^2$ |
1.2.ac 2 $\times$ 1.2.ab $\times$ 2.2.ad_f |
| 5.2.ai_bi_ads_hs_ami |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$9$ |
$0$ |
$5$ |
$0$ |
$5$ |
$-5$ |
$[-5, 9, 25, 41, 65, 81, 65, 97, 385, 1089]$ |
$3$ |
$[3, 5625, 257049, 3515625, 93250113, 1445900625, 21033109569, 576650390625, 27459819020673, 1202052237890625]$ |
$0$ |
$0$ |
$131$ |
$40$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.2.ac 4 $\times$ 1.2.a |
| 5.2.ai_bj_ady_ik_ano |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{3}$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$1$ |
$4$ |
$-5$ |
$[-5, 11, 31, 39, 35, 47, 107, 223, 427, 911]$ |
$4$ |
$[4, 8000, 430612, 4000000, 33357764, 861224000, 29094575108, 944784000000, 29860340011684, 1009072361000000]$ |
$0$ |
$0$ |
$150$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac 3 $\times$ 1.2.ab 2 |
| 5.2.ah_w_abn_bs_abw |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$1$ |
$4$ |
$-4$ |
$[-4, 0, 11, 44, 51, 87, 136, 188, 506, 1015]$ |
$1$ |
$[1, 725, 50869, 5093125, 58601341, 1585841075, 36561324472, 832099483125, 34659728919361, 1116318920211875]$ |
$0$ |
$0$ |
$154$ |
$168$ |
$28$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{7})\) |
$C_2$, $C_6$ |
1.2.ac 2 $\times$ 3.2.ad_c_b |
| 5.2.ah_x_abu_co_adk |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$1$ |
$4$ |
$-4$ |
$[-4, 2, 11, 42, 46, 47, 94, 130, 407, 1082]$ |
$1$ |
$[1, 875, 35152, 4046875, 51759671, 861224000, 26120764391, 663788671875, 28718559595024, 1194516157296875]$ |
$0$ |
$0$ |
$150$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2$, $C_2^2$ |
1.2.ac 3 $\times$ 2.2.ab_ab |
| 5.2.ah_y_acc_dp_afi |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$2$ |
$3$ |
$-4$ |
$[-4, 4, 8, 28, 41, 46, 143, 292, 476, 1019]$ |
$1$ |
$[1, 1055, 24193, 2220775, 42917611, 791232065, 38912485753, 1259679099375, 32800858440571, 1123122764602025]$ |
$0$ |
$0$ |
$18$ |
$40$ |
$20$ |
\(\Q(\sqrt{-1}) \), 8.0.13140625.1 |
$C_2$, $C_2^2:C_4$ |
1.2.ac $\times$ 4.2.af_m_au_bd |
| 5.2.ah_y_aca_dg_aeq |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x - 2 x^{3} + 4 x^{4} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$6$ |
$1$ |
$4$ |
$2$ |
$3$ |
$-4$ |
$[-4, 4, 14, 48, 66, 64, 122, 192, 410, 1104]$ |
$2$ |
$[2, 2000, 57122, 6500000, 96627242, 1085318000, 32242976362, 843453000000, 28751722418042, 1219918930250000]$ |
$0$ |
$0$ |
$50$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.2312.1 |
$C_2$, $D_{4}$ |
1.2.ac 3 $\times$ 2.2.ab_a |
| 5.2.ah_z_ack_eq_ahg |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$1$ |
$4$ |
$-4$ |
$[-4, 6, 5, 10, 46, 87, 136, 274, 545, 1086]$ |
$1$ |
$[1, 1235, 24700, 722475, 52048721, 1586234000, 36003483587, 1172808839475, 37340819850100, 1195932570943175]$ |
$0$ |
$0$ |
$100$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{12})\) |
$C_2$, $C_2^2$, $C_2^2$ |
1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ac_c |
| 5.2.ah_z_acj_el_agw |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$1$ |
$4$ |
$-4$ |
$[-4, 6, 8, 18, 41, 54, 108, 242, 386, 781]$ |
$1$ |
$[1, 1205, 24583, 1090525, 38101136, 918297965, 28940657243, 1030791493125, 27499042761151, 885180832006400]$ |
$0$ |
$0$ |
$54$ |
$120$ |
$20$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{15})\) |
$C_2$, $C_4\times C_2$ |
1.2.ac $\times$ 4.2.af_n_az_bn |
| 5.2.ah_z_ach_ec_age |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$3$ |
$2$ |
$-4$ |
$[-4, 6, 14, 38, 56, 42, 94, 254, 500, 1126]$ |
$2$ |
$[2, 2300, 51038, 3910000, 72017402, 763018100, 26336547722, 1076814000000, 34196345458262, 1244370684807500]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.679024.1 |
$C_2$, $S_4\times C_2$ |
1.2.ac 2 $\times$ 3.2.ad_f_ah |
| 5.2.ah_z_acg_dy_afw |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$2$ |
$3$ |
$-4$ |
$[-4, 6, 17, 50, 76, 63, 94, 178, 341, 966]$ |
$3$ |
$[3, 3375, 79092, 7171875, 124264563, 1067742000, 26487260229, 799929421875, 25107150425292, 1065956954484375]$ |
$0$ |
$0$ |
$50$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.2873.1 |
$C_2$, $D_{4}$ |
1.2.ac 3 $\times$ 2.2.ab_b |
| 5.2.ah_ba_acq_fg_aih |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,1,1,1,1,1]$ |
$0$ |
$5$ |
$0$ |
$2$ |
$3$ |
$-4$ |
$[-4, 8, 8, 0, 21, 74, 129, 248, 575, 1153]$ |
$1$ |
$[1, 1349, 31996, 352089, 24621781, 1208552912, 34419317696, 1064624536593, 39582728628364, 1278470195863379]$ |
$0$ |
$0$ |
$56$ |
$84$ |
$42$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{7})\) |
$C_2^2$, $C_6$ |
2.2.ad_f $\times$ 3.2.ae_j_ap |
| 5.2.ah_ba_acp_fd_aic |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$3$ |
$2$ |
$-4$ |
$[-4, 8, 11, 16, 56, 113, 150, 240, 515, 1048]$ |
$2$ |
$[2, 2660, 61256, 957600, 69424562, 2281173440, 39982829098, 1029278275200, 35222880982952, 1154645016587300]$ |
$0$ |
$0$ |
$24$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.1088.2 |
$C_2$, $C_2^2$, $D_{4}$ |
1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ac_d |
| 5.2.ah_ba_aco_ey_ahs |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$6$ |
$1$ |
$4$ |
$1$ |
$4$ |
$-4$ |
$[-4, 8, 14, 24, 46, 56, 94, 256, 518, 968]$ |
$2$ |
$[2, 2600, 59150, 1690000, 48853222, 999635000, 26198897902, 1086632820000, 35596960530950, 1065366638765000]$ |
$0$ |
$0$ |
$130$ |
$120$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2$, $C_2^2$ |
1.2.ac 2 $\times$ 1.2.ab $\times$ 2.2.ac_c |
| 5.2.ah_ba_acn_eu_ahk |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$3$ |
$2$ |
$-4$ |
$[-4, 8, 17, 36, 61, 59, 94, 268, 530, 983]$ |
$3$ |
$[3, 3825, 86697, 3538125, 78877563, 994848075, 26085841176, 1135175563125, 36400837975749, 1083629820189375]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.465831.1 |
$C_2$, $A_4\times C_2$ |
1.2.ac 2 $\times$ 3.2.ad_g_aj |
| 5.2.ah_ba_acm_eq_ahc |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$6$ |
$1$ |
$4$ |
$1$ |
$4$ |
$-4$ |
$[-4, 8, 20, 48, 76, 56, 52, 160, 380, 968]$ |
$4$ |
$[4, 5000, 114244, 6250000, 124333484, 999635000, 18913493876, 738112500000, 27192179459068, 1068490878125000]$ |
$0$ |
$0$ |
$130$ |
$40$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac 4 $\times$ 1.2.b |
| 5.2.ah_bb_acv_ft_ajd |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ |
$[0,0,0,0,0,1,1,1,1,1]$ |
$0$ |
$5$ |
$0$ |
$2$ |
$3$ |
$-4$ |
$[-4, 10, 14, 2, 16, 100, 220, 322, 518, 1090]$ |
$2$ |
$[2, 2888, 80864, 467856, 20317462, 1868281856, 69047017342, 1408741551648, 35385170776928, 1200850669604168]$ |
$0$ |
$0$ |
$36$ |
$30$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ab $\times$ 2.2.ad_f 2 |
| 5.2.ah_bb_acu_fp_aiw |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$1$ |
$4$ |
$-4$ |
$[-4, 10, 17, 14, 21, 43, 87, 230, 548, 1035]$ |
$2$ |
$[2, 2840, 76622, 823600, 23110142, 761622680, 25046137216, 986397717600, 37734169585658, 1138893218916200]$ |
$0$ |
$0$ |
$96$ |
$280$ |
$28$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\zeta_{7})\) |
$C_2$, $C_2$, $C_6$ |
1.2.ac $\times$ 1.2.ab $\times$ 3.2.ae_j_ap |
| 5.2.ah_bb_acu_fq_aiy |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$1$ |
$4$ |
$-4$ |
$[-4, 10, 17, 18, 46, 103, 136, 178, 449, 1150]$ |
$3$ |
$[3, 4275, 115596, 961875, 53309553, 1976691600, 36322429251, 796648921875, 31020820875252, 1274331545994375]$ |
$0$ |
$0$ |
$100$ |
$24$ |
$24$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2$, $C_2^2$ |
1.2.ac 2 $\times$ 1.2.a $\times$ 2.2.ad_f |
| 5.2.ah_bb_act_fm_aiq |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$3$ |
$2$ |
$-4$ |
$[-4, 10, 20, 30, 56, 82, 108, 222, 488, 930]$ |
$4$ |
$[4, 5600, 146692, 2240000, 65162284, 1437581600, 29094575108, 953648640000, 33577931849644, 1028586652940000]$ |
$0$ |
$0$ |
$44$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), 4.0.1088.2 |
$C_2$, $C_2$, $D_{4}$ |
1.2.ac 2 $\times$ 1.2.ab $\times$ 2.2.ac_d |
| 5.2.ah_bb_acs_fi_aii |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$2$ |
$3$ |
$-4$ |
$[-4, 10, 23, 42, 66, 55, 38, 162, 491, 1050]$ |
$5$ |
$[5, 6875, 175760, 4296875, 94766375, 966680000, 16672674835, 754913671875, 33661378209680, 1156445919921875]$ |
$0$ |
$0$ |
$50$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.1025.1 |
$C_2$, $D_{4}$ |
1.2.ac 3 $\times$ 2.2.ab_d |
| 5.2.ah_bc_acz_gd_aju |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$2$ |
$3$ |
$-4$ |
$[-4, 12, 23, 16, 16, 69, 178, 304, 491, 972]$ |
$4$ |
$[4, 6080, 193648, 1094400, 19070084, 1177379840, 50243909132, 1305229593600, 33732642523216, 1069747804030400]$ |
$0$ |
$0$ |
$72$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2$, $C_2^2$ |
1.2.ac $\times$ 1.2.ab 2 $\times$ 2.2.ad_f |
| 5.2.ah_bc_acy_ga_ajo |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{3}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$6$ |
$1$ |
$4$ |
$1$ |
$4$ |
$-4$ |
$[-4, 12, 26, 32, 46, 72, 94, 160, 422, 1032]$ |
$6$ |
$[6, 9000, 276822, 2250000, 50036646, 1245699000, 26430987246, 738112500000, 29572112791494, 1135206406125000]$ |
$0$ |
$0$ |
$130$ |
$40$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$, $C_2$ |
1.2.ac 3 $\times$ 1.2.ab $\times$ 1.2.a |
| 5.2.ah_bd_add_go_akm |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - x + 2 x^{2} )^{3}$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$1$ |
$4$ |
$-4$ |
$[-4, 14, 32, 30, 16, 38, 136, 286, 464, 854]$ |
$8$ |
$[8, 12800, 463736, 2560000, 17899288, 741977600, 36561324472, 1209323520000, 32157289243352, 952958093120000]$ |
$0$ |
$0$ |
$154$ |
$168$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac 2 $\times$ 1.2.ab 3 |
| 5.2.ag_o_aj_abb_cs |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 4 x^{2} + 7 x^{3} - 21 x^{4} + 14 x^{5} + 16 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$1$ |
$4$ |
$-3$ |
$[-3, -3, 18, 21, 47, 54, 130, 269, 576, 1147]$ |
$1$ |
$[1, 155, 97123, 1395775, 55074521, 918297965, 34887608813, 1156216740975, 39849824955811, 1271561917711025]$ |
$0$ |
$0$ |
$54$ |
$120$ |
$60$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{15})\) |
$C_2$, $C_4\times C_2$ |
1.2.ac $\times$ 4.2.ae_e_h_av |
| 5.2.ag_o_ai_abg_dc |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} )^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$9$ |
$0$ |
$5$ |
$0$ |
$5$ |
$-3$ |
$[-3, -3, 21, 25, 57, 33, 81, 97, 417, 897]$ |
$1$ |
$[1, 125, 107653, 1265625, 66233081, 659374625, 23272485713, 576650390625, 29058756742561, 994531106890625]$ |
$0$ |
$0$ |
$131$ |
$40$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{2}) \) |
$C_2$, $C_2$ |
1.2.ac 3 $\times$ 2.2.a_ae |
| 5.2.ag_p_aq_af_be |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$2$ |
$3$ |
$-3$ |
$[-3, -1, 15, 27, 27, 65, 81, 259, 447, 959]$ |
$1$ |
$[1, 305, 65572, 1923025, 27087101, 1039971920, 23489558261, 1102972142025, 30935369378212, 1058347887449525]$ |
$0$ |
$0$ |
$24$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), 8.0.22581504.2 |
$C_2$, $D_4\times C_2$ |
1.2.ac $\times$ 4.2.ae_f_c_al |
| 5.2.ag_p_ao_ao_bw |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 3 x^{2} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$1$ |
$4$ |
$-3$ |
$[-3, -1, 21, 39, 57, 83, 81, 223, 417, 1139]$ |
$2$ |
$[2, 500, 162578, 4000000, 74572522, 1503846500, 23516335306, 944784000000, 29061538858586, 1260741700062500]$ |
$0$ |
$0$ |
$150$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(i, \sqrt{7})\) |
$C_2$, $C_2^2$ |
1.2.ac 3 $\times$ 2.2.a_ad |
| 5.2.ag_q_aba_bh_abr |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,1,1,1,1,1]$ |
$0$ |
$5$ |
$0$ |
$2$ |
$3$ |
$-3$ |
$[-3, 1, 3, 21, 32, 109, 207, 269, 570, 1076]$ |
$1$ |
$[1, 551, 22876, 1393479, 33501421, 2168004272, 63138363688, 1149554681487, 39154418373364, 1183443090553781]$ |
$0$ |
$0$ |
$56$ |
$84$ |
$42$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{7})\) |
$C_2^2$, $C_6$ |
2.2.ad_f $\times$ 3.2.ad_c_b |
| 5.2.ag_q_ay_w_au |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
? |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 6 x^{2} - 4 x^{3} + 2 x^{4} - 8 x^{5} + 24 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[\frac{1}{4},\frac{1}{4},\frac{1}{4},\frac{1}{4},\frac{1}{2},\frac{1}{2},\frac{3}{4},\frac{3}{4},\frac{3}{4},\frac{3}{4}]$ |
$6$ |
$0$ |
$5$ |
$2$ |
$3$ |
$-3$ |
$[-3, 1, 9, 25, 17, 73, 137, 241, 513, 881]$ |
$1$ |
$[1, 485, 34957, 1690225, 18761641, 1237652585, 36577681561, 1028469798225, 35261765927713, 979140494205425]$ |
$0$ |
$0$ |
$18$ |
$16$ |
$8$ |
\(\Q(\sqrt{-1}) \), 8.0.18939904.2 |
$C_2$, $D_4\times C_2$ |
1.2.ac $\times$ 4.2.ae_g_ae_c |
| 5.2.ag_q_av_i_i |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$3$ |
$2$ |
$-3$ |
$[-3, 1, 18, 41, 37, 70, 67, 209, 522, 1101]$ |
$2$ |
$[2, 800, 106808, 4360000, 39237902, 1196249600, 21135172186, 910446480000, 35876430274568, 1212843550820000]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.1539727.2 |
$C_2$, $D_{6}$ |
1.2.ac 2 $\times$ 3.2.ac_a_d |
| 5.2.ag_q_au_e_q |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}( 1 - 2 x^{2} + 4 x^{4} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$9$ |
$0$ |
$5$ |
$0$ |
$5$ |
$-3$ |
$[-3, 1, 21, 49, 57, 97, 81, 193, 417, 961]$ |
$3$ |
$[3, 1125, 177957, 6890625, 68438553, 1801814625, 23457176529, 848931890625, 29286667687329, 1061866923890625]$ |
$0$ |
$0$ |
$131$ |
$120$ |
$24$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.2.ac 3 $\times$ 2.2.a_ac |
| 5.2.ag_r_abg_bx_acs |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$2$ |
$3$ |
$-3$ |
$[-3, 3, 3, 19, 27, 69, 165, 211, 471, 1143]$ |
$1$ |
$[1, 665, 15808, 1107225, 29590151, 1177379840, 45108385589, 917031425625, 32442795501376, 1266342321457325]$ |
$0$ |
$0$ |
$72$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2$, $C_2^2$, $C_2^2$ |
1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ab_ab |
| 5.2.ag_r_abd_bj_abq |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$1$ |
$4$ |
$-3$ |
$[-3, 3, 12, 35, 32, 78, 165, 251, 543, 958]$ |
$2$ |
$[2, 1160, 54782, 3259600, 31444622, 1366263080, 45944319248, 1065087338400, 37325861913158, 1054240697331800]$ |
$0$ |
$0$ |
$96$ |
$280$ |
$28$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\zeta_{7})\) |
$C_2$, $C_2$, $C_6$ |
1.2.ac $\times$ 1.2.ab $\times$ 3.2.ad_c_b |
| 5.2.ag_r_abc_be_abg |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$2$ |
$3$ |
$-3$ |
$[-3, 3, 15, 39, 27, 51, 95, 191, 555, 1043]$ |
$2$ |
$[2, 1100, 65234, 3740000, 28143302, 896967500, 26886431938, 844596720000, 38112217374998, 1149689065827500]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.2580992.1 |
$C_2$, $D_{6}$ |
1.2.ac 2 $\times$ 3.2.ac_b_a |
| 5.2.ag_r_abb_ba_ay |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + x^{2} + x^{3} + 2 x^{4} - 8 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$3$ |
$2$ |
$-3$ |
$[-3, 3, 18, 47, 42, 72, 102, 199, 567, 1068]$ |
$3$ |
$[3, 1575, 111033, 6181875, 44988603, 1224138825, 27759090936, 869771266875, 38981319187473, 1175636550020625]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.2369943.1 |
$C_2$, $S_4\times C_2$ |
1.2.ac 2 $\times$ 3.2.ac_b_b |
| 5.2.ag_r_aba_w_aq |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}( 1 - x^{2} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$4$ |
$2$ |
$3$ |
$1$ |
$4$ |
$-3$ |
$[-3, 3, 21, 55, 57, 87, 81, 127, 417, 903]$ |
$4$ |
$[4, 2000, 166972, 9000000, 66439844, 1586234000, 24004034492, 656100000000, 29085798910324, 1000750150250000]$ |
$0$ |
$0$ |
$100$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ac 3 $\times$ 2.2.a_ab |
| 5.2.ag_s_abo_cy_aeq |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$9$ |
$0$ |
$5$ |
$0$ |
$5$ |
$-3$ |
$[-3, 5, -3, 9, 57, 65, 81, 289, 609, 1025]$ |
$1$ |
$[1, 845, 8125, 714025, 71546681, 1160290625, 23591416913, 1249778664225, 42435672150625, 1124801470004225]$ |
$0$ |
$0$ |
$131$ |
$120$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2^2$ |
1.2.ac $\times$ 2.2.ac_c 2 |
| 5.2.ag_s_abl_ck_ado |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - x - 2 x^{3} + 4 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$3$ |
$2$ |
$-3$ |
$[-3, 5, 6, 25, 47, 86, 193, 273, 474, 1165]$ |
$2$ |
$[2, 1520, 25688, 1778400, 55240202, 1483738880, 55680935998, 1165239691200, 32480258894408, 1293272561183600]$ |
$0$ |
$0$ |
$24$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.2312.1 |
$C_2$, $C_2^2$, $D_{4}$ |
1.2.ac $\times$ 2.2.ad_f $\times$ 2.2.ab_a |
| 5.2.ag_s_abk_cf_ade |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,\frac{1}{2},\frac{1}{2},1,1,1,1]$ |
$1$ |
$4$ |
$1$ |
$2$ |
$3$ |
$-3$ |
$[-3, 5, 9, 29, 37, 65, 165, 221, 405, 1025]$ |
$2$ |
$[2, 1460, 31226, 2131600, 38133362, 1116954020, 45547817842, 962596454400, 28494805076114, 1124768298875300]$ |
$0$ |
$0$ |
$24$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 8.0.18939904.2 |
$C_2$, $D_4\times C_2$ |
1.2.ac $\times$ 4.2.ae_i_am_r |
| 5.2.ag_s_abj_ca_acu |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$1$ |
$4$ |
$-3$ |
$[-3, 5, 12, 33, 27, 38, 123, 193, 444, 1025]$ |
$2$ |
$[2, 1400, 37856, 2590000, 27773482, 741977600, 32824323394, 849649500000, 30927679563872, 1128089405135000]$ |
$0$ |
$0$ |
$154$ |
$168$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2$, $C_2$, $C_2^2$ |
1.2.ac 2 $\times$ 1.2.ab $\times$ 2.2.ab_ab |
| 5.2.ag_s_abi_bw_acm |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 2 x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{2}{3},\frac{2}{3},\frac{2}{3}]$ |
$7$ |
$0$ |
$5$ |
$3$ |
$2$ |
$-3$ |
$[-3, 5, 15, 41, 37, 53, 137, 225, 537, 1105]$ |
$3$ |
$[3, 2025, 65403, 4505625, 39491733, 927087525, 36600767913, 955088870625, 36862172735193, 1220220502700625]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.1142512.1 |
$C_2$, $S_4\times C_2$ |
1.2.ac 2 $\times$ 3.2.ac_c_ac |
| 5.2.ag_s_abh_bs_ace |
$5$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1,1]$ |
$2$ |
$3$ |
$2$ |
$3$ |
$2$ |
$-3$ |
$[-3, 5, 18, 49, 47, 62, 123, 193, 522, 1065]$ |
$4$ |
$[4, 2600, 100048, 6890000, 53126324, 1040499200, 32604824284, 849412980000, 35849268493168, 1174955063165000]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), 6.0.2464727.1 |
$C_2$, $S_4\times C_2$ |
1.2.ac 2 $\times$ 3.2.ac_c_ab |
