| 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 |
| 6.2.aj_bq_aff_ms_ayp_bmn |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{3}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$1$ |
$5$ |
$-6$ |
$[-6, 8, 9, -4, 24, 131, 246, 308, 513, 1208]$ |
$1$ |
$[1, 6859, 438976, 5000211, 887503681, 192699928576, 10722223798651, 342104081183019, 17854072924596544, 1381721358424021399]$ |
$0$ |
$0$ |
$54$ |
$60$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2^2$ |
2.2.ad_f 3 |
| 6.2.ai_bg_adj_hb_amh_sn |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-5$ |
$[-5, 5, 4, 13, 30, 68, 198, 341, 508, 1080]$ |
$1$ |
$[1, 4009, 141436, 15190101, 1005946931, 70310098576, 7593444454331, 391558651249725, 17823209075803324, 1220422450820459359]$ |
$0$ |
$0$ |
$24$ |
$60$ |
$30$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 8.0.13140625.1 |
$C_2^2$, $C_2^2:C_4$ |
2.2.ad_f $\times$ 4.2.af_m_au_bd |
| 6.2.ai_bh_adr_if_apa_xb |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$1$ |
$5$ |
$-5$ |
$[-5, 7, 4, 3, 30, 76, 163, 291, 418, 842]$ |
$1$ |
$[1, 4579, 143716, 7459191, 893053456, 81601369936, 5647525954561, 320411227722975, 14942328091944844, 961866854154045184]$ |
$0$ |
$0$ |
$54$ |
$120$ |
$30$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{15})\) |
$C_2^2$, $C_4\times C_2$ |
2.2.ad_f $\times$ 4.2.af_n_az_bn |
| 6.2.ai_bi_ady_jd_are_bar |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )^{2}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$1$ |
$5$ |
$-5$ |
$[-5, 9, 7, -3, 15, 39, 51, 205, 637, 1159]$ |
$1$ |
$[1, 5041, 177241, 4239481, 656435641, 43780122169, 2436396322816, 231714977062969, 22936118388456001, 1317551406202509241]$ |
$0$ |
$0$ |
$132$ |
$210$ |
$7$ |
\(\Q(\zeta_{7})\) |
$C_6$ |
3.2.ae_j_ap 2 |
| 6.2.ai_bi_ady_je_arg_bat |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-5$ |
$[-5, 9, 7, 1, 45, 135, 205, 289, 547, 1109]$ |
$2$ |
$[2, 10108, 358112, 6549984, 1627244002, 202708581376, 7802312959646, 319940859063168, 19139278721888288, 1254675575443822588]$ |
$0$ |
$0$ |
$36$ |
$30$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.1088.2 |
$C_2^2$, $D_{4}$ |
2.2.ad_f 2 $\times$ 2.2.ac_d |
| 6.2.ai_bj_aee_jw_ast_bdf |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$2$ |
$4$ |
$-5$ |
$[-5, 11, 13, -1, 10, 65, 142, 279, 580, 1096]$ |
$2$ |
$[2, 10792, 447944, 5633424, 541679182, 67678963072, 4887543112832, 306611866538784, 20503853429492552, 1237559149595750872]$ |
$0$ |
$0$ |
$128$ |
$420$ |
$42$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{7})\) |
$C_2$, $C_2^2$, $C_6$ |
1.2.ab $\times$ 2.2.ad_f $\times$ 3.2.ae_j_ap |
| 6.2.ai_bk_aek_kq_aum_bgb |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$2$ |
$4$ |
$-5$ |
$[-5, 13, 19, 1, 5, 91, 233, 353, 523, 1033]$ |
$4$ |
$[4, 23104, 1132096, 7485696, 446984164, 104623783936, 9804676462564, 405717566874624, 18329518462448704, 1162423448176834624]$ |
$0$ |
$0$ |
$108$ |
$60$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ab 2 $\times$ 2.2.ad_f 2 |
| 6.2.ah_v_abf_g_cu_agb |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 4 x^{2} + 7 x^{3} - 21 x^{4} + 14 x^{5} + 16 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$1$ |
$5$ |
$-4$ |
$[-4, -2, 14, 6, 36, 76, 185, 318, 608, 1208]$ |
$1$ |
$[1, 589, 567796, 9547101, 1290893041, 81601369936, 6808023556951, 359398411764669, 21653450415281884, 1381721358424021399]$ |
$0$ |
$0$ |
$54$ |
$120$ |
$30$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{15})\) |
$C_2^2$, $C_4\times C_2$ |
2.2.ad_f $\times$ 4.2.ae_e_h_av |
| 6.2.ah_w_abn_bk_b_abn |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-4$ |
$[-4, 0, 11, 12, 16, 87, 136, 308, 479, 1020]$ |
$1$ |
$[1, 1159, 383344, 13153491, 634895221, 92413504768, 4583789816047, 342847860627051, 16809546532571728, 1150035920676481459]$ |
$0$ |
$0$ |
$32$ |
$24$ |
$12$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 8.0.22581504.2 |
$C_2^2$, $D_4\times C_2$ |
2.2.ad_f $\times$ 4.2.ae_f_c_al |
| 6.2.ah_x_abx_dd_aep_gn |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$1$ |
$5$ |
$-4$ |
$[-4, 2, 2, 18, 26, 74, 129, 226, 632, 1082]$ |
$1$ |
$[1, 2059, 126721, 16778791, 893173681, 78536480239, 4469294786048, 250199978957671, 22687935025254751, 1219619442959938399]$ |
$0$ |
$0$ |
$132$ |
$210$ |
$14$ |
\(\Q(\zeta_{7})\), \(\Q(\zeta_{7})\) |
$C_6$, $C_6$ |
3.2.ae_j_ap $\times$ 3.2.ad_c_b |
| 6.2.ah_y_acf_ee_agr_jr |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$2$ |
$4$ |
$-4$ |
$[-4, 4, -1, 4, 16, 91, 220, 260, 503, 1204]$ |
$1$ |
$[1, 2527, 92416, 7573419, 693564271, 104623783936, 8802522217903, 285050048341275, 17628646160959744, 1376049571996924027]$ |
$0$ |
$0$ |
$108$ |
$60$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2^2$, $C_2^2$ |
2.2.ad_f 2 $\times$ 2.2.ab_ab |
| 6.2.ah_y_acc_dn_aey_gt |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$2$ |
$4$ |
$-4$ |
$[-4, 4, 8, 20, 21, 100, 220, 300, 575, 1019]$ |
$2$ |
$[2, 4408, 320264, 22295664, 737031262, 121408239232, 8965647643696, 331071748268256, 20281988717402552, 1145572911656060008]$ |
$0$ |
$0$ |
$128$ |
$420$ |
$42$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(\zeta_{7})\) |
$C_2$, $C_2^2$, $C_6$ |
1.2.ab $\times$ 2.2.ad_f $\times$ 3.2.ad_c_b |
| 6.2.ah_z_acl_ez_ais_nf |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$4$ |
$2$ |
$-4$ |
$[-4, 6, 2, 18, 51, 72, 157, 322, 542, 981]$ |
$2$ |
$[2, 5908, 115382, 19898144, 1844410502, 73961938876, 5525572976926, 366191513475200, 19106193172894598, 1108207694288110108]$ |
$0$ |
$0$ |
$12$ |
$20$ |
$10$ |
4.0.1088.2, 8.0.13140625.1 |
$D_{4}$, $C_2^2:C_4$ |
2.2.ac_d $\times$ 4.2.af_m_au_bd |
| 6.2.ah_z_ack_er_ahr_lh |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 17 x^{4} - 24 x^{5} + 32 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-4$ |
$[-4, 6, 5, 14, 26, 87, 220, 270, 437, 1086]$ |
$2$ |
$[2, 5548, 182552, 14580144, 893808802, 99254252608, 8888273727734, 299213481885696, 15483401733707816, 1222210542945375868]$ |
$0$ |
$0$ |
$32$ |
$24$ |
$12$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 8.0.18939904.2 |
$C_2^2$, $D_4\times C_2$ |
2.2.ad_f $\times$ 4.2.ae_i_am_r |
| 6.2.ah_ba_acs_fv_akk_pv |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 17 x^{3} + 27 x^{4} - 34 x^{5} + 36 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$5$ |
$1$ |
$-4$ |
$[-4, 8, 2, 4, 41, 92, 164, 252, 425, 1063]$ |
$2$ |
$[2, 6688, 127832, 7343424, 1417803662, 104302730752, 5895049774672, 275315202493056, 15158132706205688, 1197615554726338528]$ |
$0$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 8.0.316180889.1 |
$C_2^2$, $C_2 \wr S_4$ |
2.2.ad_f $\times$ 4.2.ae_j_ar_bb |
| 6.2.ah_ba_acs_fw_akp_qf |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-4$ |
$[-4, 8, 2, 8, 51, 80, 122, 272, 452, 743]$ |
$2$ |
$[2, 6748, 117242, 9771104, 1637419552, 85839668236, 4109573328506, 299653377699200, 16017935140818638, 873425630557355008]$ |
$0$ |
$0$ |
$36$ |
$60$ |
$10$ |
4.0.1088.2, \(\Q(\zeta_{15})\) |
$D_{4}$, $C_4\times C_2$ |
2.2.ac_d $\times$ 4.2.af_n_az_bn |
| 6.2.ah_ba_acr_fq_aka_ph |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$4$ |
$2$ |
$-4$ |
$[-4, 8, 5, 12, 31, 29, 87, 292, 626, 1193]$ |
$2$ |
$[2, 6532, 127142, 12881104, 1097654882, 37787365252, 3219407314048, 323782006364800, 22384608536993642, 1359520701443053372]$ |
$0$ |
$0$ |
$28$ |
$42$ |
$7$ |
\(\Q(\zeta_{7})\), 6.0.679024.1 |
$C_6$, $S_4\times C_2$ |
3.2.ae_j_ap $\times$ 3.2.ad_f_ah |
| 6.2.ah_ba_acr_fq_ajx_oz |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-4$ |
$[-4, 8, 5, 12, 46, 107, 220, 308, 437, 1088]$ |
$3$ |
$[3, 9747, 207936, 13421619, 1665108363, 129712140288, 8926028854557, 343512822734667, 15411813029583552, 1227952926400492647]$ |
$0$ |
$0$ |
$36$ |
$30$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.2873.1 |
$C_2^2$, $D_{4}$ |
2.2.ad_f 2 $\times$ 2.2.ab_b |
| 6.2.ah_bb_acy_gp_amd_sr |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )^{2}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-4$ |
$[-4, 10, 5, 6, 66, 139, 164, 270, 581, 1010]$ |
$4$ |
$[4, 14896, 292144, 8580096, 2983562884, 213237074176, 5677561731916, 299213481885696, 20516998644576976, 1139311330767020656]$ |
$0$ |
$0$ |
$32$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.1088.2 |
$C_2^2$, $D_{4}$ |
2.2.ad_f $\times$ 2.2.ac_d 2 |
| 6.2.ah_bb_acx_gi_alk_rl |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 4 x + 10 x^{2} - 19 x^{3} + 29 x^{4} - 38 x^{5} + 40 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$5$ |
$1$ |
$-4$ |
$[-4, 10, 8, 6, 26, 64, 157, 302, 494, 1100]$ |
$3$ |
$[3, 10773, 230508, 9404829, 899239413, 69531355152, 5422793011653, 337240775323053, 17350635614151636, 1241166523032153963]$ |
$0$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 8.0.371495353.1 |
$C_2^2$, $C_2 \wr S_4$ |
2.2.ad_f $\times$ 4.2.ae_k_at_bd |
| 6.2.ah_bb_acx_gj_alp_rv |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$4$ |
$2$ |
$-4$ |
$[-4, 10, 8, 10, 36, 46, 87, 306, 656, 1050]$ |
$3$ |
$[3, 10863, 215973, 11655999, 1202214183, 49268408679, 3188760681984, 341330463204327, 23827648761479259, 1183905399922186923]$ |
$0$ |
$0$ |
$28$ |
$42$ |
$7$ |
\(\Q(\zeta_{7})\), 6.0.465831.1 |
$C_6$, $A_4\times C_2$ |
3.2.ae_j_ap $\times$ 3.2.ad_g_aj |
| 6.2.ah_bb_acw_gd_akx_qp |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$5$ |
$1$ |
$-4$ |
$[-4, 10, 11, 14, 26, 55, 178, 366, 569, 1130]$ |
$4$ |
$[4, 13984, 321328, 17116416, 905765564, 58414859776, 6458305612196, 428437585612800, 20010828543250384, 1276980370720414624]$ |
$0$ |
$0$ |
$16$ |
$12$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), 6.0.679024.1 |
$C_2$, $C_2^2$, $S_4\times C_2$ |
1.2.ab $\times$ 2.2.ad_f $\times$ 3.2.ad_f_ah |
| 6.2.ah_bb_acv_fx_akg_pl |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )^{2}( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-4$ |
$[-4, 10, 14, 18, 11, 28, 185, 386, 518, 905]$ |
$4$ |
$[4, 13504, 364756, 22740736, 506637164, 38173903936, 6943640378084, 464368103193600, 18297832723924684, 1026724863783851584]$ |
$0$ |
$0$ |
$36$ |
$60$ |
$10$ |
\(\Q(\sqrt{-7}) \), 8.0.13140625.1 |
$C_2$, $C_2^2:C_4$ |
1.2.ab 2 $\times$ 4.2.af_m_au_bd |
| 6.2.ah_bc_add_hc_ane_uj |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-4$ |
$[-4, 12, 11, 4, 31, 69, 101, 260, 614, 997]$ |
$4$ |
$[4, 15904, 365428, 7379456, 993172444, 71194144672, 3556551484672, 286748008501248, 21979800761269204, 1123768716968992864]$ |
$0$ |
$0$ |
$64$ |
$84$ |
$14$ |
\(\Q(\sqrt{-7}) \), 4.0.1088.2, \(\Q(\zeta_{7})\) |
$C_2$, $D_{4}$, $C_6$ |
1.2.ab $\times$ 2.2.ac_d $\times$ 3.2.ae_j_ap |
| 6.2.ah_bc_add_hc_and_uh |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-4$ |
$[-4, 12, 11, 4, 36, 99, 164, 292, 587, 1172]$ |
$5$ |
$[5, 19855, 462080, 8041275, 1269841375, 117434859520, 5618579474555, 324181758109275, 20662753777230080, 1332193711592123875]$ |
$0$ |
$0$ |
$36$ |
$30$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.1025.1 |
$C_2^2$, $D_{4}$ |
2.2.ad_f 2 $\times$ 2.2.ab_d |
| 6.2.ah_bc_adc_gw_amn_tf |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )^{2}( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$2$ |
$4$ |
$-4$ |
$[-4, 12, 14, 8, 11, 36, 150, 336, 428, 667]$ |
$4$ |
$[4, 15424, 370636, 11166976, 449779264, 44304344896, 5164242589804, 379990976025600, 15340235238759004, 809205545297526784]$ |
$0$ |
$0$ |
$108$ |
$120$ |
$10$ |
\(\Q(\sqrt{-7}) \), \(\Q(\zeta_{15})\) |
$C_2$, $C_4\times C_2$ |
1.2.ab 2 $\times$ 4.2.af_n_az_bn |
| 6.2.ah_bc_adc_gx_amq_tl |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$5$ |
$1$ |
$-4$ |
$[-4, 12, 14, 12, 31, 72, 178, 380, 599, 987]$ |
$6$ |
$[6, 23256, 545832, 15488496, 992046066, 76163213952, 6396826806768, 451658204213472, 21300841297570968, 1112027168755739016]$ |
$0$ |
$0$ |
$16$ |
$12$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), 6.0.465831.1 |
$C_2$, $C_2^2$, $A_4\times C_2$ |
1.2.ab $\times$ 2.2.ad_f $\times$ 3.2.ad_g_aj |
| 6.2.ah_bd_adi_hr_aoj_wh |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$4$ |
$2$ |
$-4$ |
$[-4, 14, 17, 6, 26, 95, 192, 334, 557, 934]$ |
$8$ |
$[8, 34048, 923552, 9805824, 819548488, 110057844736, 7134635096744, 379433143369728, 19648948683720608, 1055541553192876288]$ |
$0$ |
$0$ |
$48$ |
$12$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\), 4.0.1088.2 |
$C_2$, $C_2^2$, $D_{4}$ |
1.2.ab 2 $\times$ 2.2.ad_f $\times$ 2.2.ac_d |
| 6.2.ah_be_adn_ig_apq_yh |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )^{3}( 1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$1$ |
$5$ |
$-4$ |
$[-4, 16, 23, 4, -9, 25, 129, 324, 590, 921]$ |
$8$ |
$[8, 36352, 1155224, 8433664, 272812408, 36745364992, 4469294786048, 363625654616064, 21049861371937832, 1041141736157788672]$ |
$0$ |
$0$ |
$132$ |
$210$ |
$14$ |
\(\Q(\sqrt{-7}) \), \(\Q(\zeta_{7})\) |
$C_2$, $C_6$ |
1.2.ab 3 $\times$ 3.2.ae_j_ap |
| 6.2.ah_bf_ads_ix_arb_bar |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )^{4}( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$2$ |
$4$ |
$-4$ |
$[-4, 18, 29, 6, -14, 51, 220, 398, 533, 858]$ |
$16$ |
$[16, 77824, 2919616, 11206656, 225120016, 56804048896, 8965647643696, 481159837384704, 18817624890643264, 977931089096372224]$ |
$0$ |
$0$ |
$128$ |
$84$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ab 4 $\times$ 2.2.ad_f |
| 6.2.ag_n_ak_g_abs_eb |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )^{2}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$1$ |
$5$ |
$-3$ |
$[-3, -5, -3, 39, 37, 109, 207, 247, 627, 1005]$ |
$1$ |
$[1, 841, 90601, 66406201, 1215289321, 140885370409, 8198418170944, 270159617060089, 22442437163616001, 1128966641182639561]$ |
$0$ |
$0$ |
$132$ |
$210$ |
$7$ |
\(\Q(\zeta_{7})\) |
$C_6$ |
3.2.ad_c_b 2 |
| 6.2.ag_p_av_y_abn_cn |
$6$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
|
$1 - 6 x + 15 x^{2} - 21 x^{3} + 24 x^{4} - 39 x^{5} + 65 x^{6} - 78 x^{7} + 96 x^{8} - 168 x^{9} + 240 x^{10} - 192 x^{11} + 64 x^{12}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-3$ |
$[-3, -1, 0, 23, 27, 50, 81, 263, 513, 929]$ |
$1$ |
$[1, 1009, 75421, 24527781, 854410681, 53498151667, 3083197893931, 291443042814741, 18059531552684191, 1047995943549703399]$ |
$0$ |
$0$ |
$10$ |
$36$ |
$18$ |
12.0.15035401757601.1 |
$C_2^2 \times A_4$ |
simple |
| 6.2.ag_p_at_g_bb_acj |
$6$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
|
|
$1 - 6 x + 15 x^{2} - 19 x^{3} + 6 x^{4} + 27 x^{5} - 61 x^{6} + 54 x^{7} + 24 x^{8} - 152 x^{9} + 240 x^{10} - 192 x^{11} + 64 x^{12}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-3$ |
$[-3, -1, 6, -1, 27, 74, 123, 311, 537, 1049]$ |
$1$ |
$[1, 577, 195301, 6045229, 891243181, 79220139931, 4189948510987, 345796535402469, 18850357195339609, 1179133611232275847]$ |
$0$ |
$0$ |
$12$ |
$36$ |
$9$ |
12.0.15342238784889.1 |
$C_2^2 \times A_4$ |
simple |
| 6.2.ag_p_ar_ad_bt_adj |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 4 x + 4 x^{2} + 7 x^{3} - 21 x^{4} + 14 x^{5} + 16 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-3$ |
$[-3, -1, 12, 11, 57, 80, 144, 299, 642, 1109]$ |
$2$ |
$[2, 868, 463202, 12506144, 2366861122, 85839668236, 4954040451446, 336114775971968, 23212150221349718, 1254675575443822588]$ |
$0$ |
$0$ |
$36$ |
$120$ |
$30$ |
4.0.1088.2, \(\Q(\zeta_{15})\) |
$D_{4}$, $C_4\times C_2$ |
2.2.ac_d $\times$ 4.2.ae_e_h_av |
| 6.2.ag_q_abd_bz_adp_fr |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 5 x + 12 x^{2} - 20 x^{3} + 29 x^{4} - 40 x^{5} + 48 x^{6} - 40 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-3$ |
$[-3, 1, -6, 21, 22, 28, 172, 293, 498, 1076]$ |
$1$ |
$[1, 1477, 29776, 23007229, 786125021, 38173903936, 6233917960943, 326256886738125, 17598172001263024, 1215412775425571107]$ |
$0$ |
$0$ |
$36$ |
$60$ |
$30$ |
\(\Q(\sqrt{-3}, \sqrt{-7})\), 8.0.13140625.1 |
$C_2^2$, $C_2^2:C_4$ |
2.2.ab_ab $\times$ 4.2.af_m_au_bd |
| 6.2.ag_q_abb_bh_abb_v |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + x^{4} + 8 x^{6} - 24 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$3$ |
$3$ |
$-3$ |
$[-3, 1, 0, -3, 12, 112, 144, 261, 540, 1136]$ |
$1$ |
$[1, 1045, 123196, 4749525, 586172521, 139553964880, 4923102312871, 284392100695725, 18974294544470404, 1284441377695609375]$ |
$0$ |
$0$ |
$40$ |
$60$ |
$30$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 8.0.26265625.1 |
$C_2^2$, $C_2^2:C_4$ |
2.2.ad_f $\times$ 4.2.ad_c_a_b |
| 6.2.ag_q_abb_bq_acx_er |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )( 1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$4$ |
$2$ |
$-3$ |
$[-3, 1, 0, 33, 42, 64, 165, 313, 621, 1116]$ |
$2$ |
$[2, 2668, 90902, 50980144, 1493514962, 67786166812, 5905640304944, 349611631523200, 22142392860541142, 1258469212495857508]$ |
$0$ |
$0$ |
$28$ |
$42$ |
$7$ |
\(\Q(\zeta_{7})\), 6.0.679024.1 |
$C_6$, $S_4\times C_2$ |
3.2.ad_c_b $\times$ 3.2.ad_f_ah |
| 6.2.ag_q_az_bb_aba_bf |
$6$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 6 x + 16 x^{2} - 25 x^{3} + 27 x^{4} - 26 x^{5} + 31 x^{6} - 52 x^{7} + 108 x^{8} - 200 x^{9} + 256 x^{10} - 192 x^{11} + 64 x^{12}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$6$ |
$0$ |
$-3$ |
$[-3, 1, 6, 21, 37, 88, 102, 317, 609, 961]$ |
$2$ |
$[2, 2008, 228302, 24051824, 1188918982, 96499602568, 3558563044906, 359729903064800, 21727689341902658, 1084812722799624328]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
12.0.2071049029467449.1 |
12T293 |
simple |
| 6.2.ag_q_ay_q_s_acd |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x^{2} + 4 x^{4} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )^{2}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$2$ |
$4$ |
$-3$ |
$[-3, 1, 9, 1, 27, 127, 207, 353, 513, 1261]$ |
$2$ |
$[2, 1444, 427424, 7485696, 999249722, 182691275776, 7924847103098, 405717566874624, 17839181095968416, 1452339565414948324]$ |
$0$ |
$0$ |
$108$ |
$60$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), \(\Q(i, \sqrt{7})\) |
$C_2^2$, $C_2^2$ |
2.2.ad_f 2 $\times$ 2.2.a_ad |
| 6.2.ag_q_ay_t_b_at |
$6$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 6 x + 16 x^{2} - 24 x^{3} + 19 x^{4} + x^{5} - 19 x^{6} + 2 x^{7} + 76 x^{8} - 192 x^{9} + 256 x^{10} - 192 x^{11} + 64 x^{12}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$6$ |
$0$ |
$-3$ |
$[-3, 1, 9, 13, 32, 91, 109, 317, 576, 1106]$ |
$2$ |
$[2, 1648, 336422, 14729824, 1091161462, 103399974544, 3817303330402, 355341125249728, 20293895102697434, 1248613730245717168]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
12.0.838729789620313.1 |
12T293 |
simple |
| 6.2.ag_q_ay_u_ae_aj |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )( 1 - 4 x + 5 x^{2} + 2 x^{3} - 11 x^{4} + 4 x^{5} + 20 x^{6} - 32 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$4$ |
$2$ |
$-3$ |
$[-3, 1, 9, 17, 37, 91, 95, 289, 513, 921]$ |
$2$ |
$[2, 1708, 312728, 17230304, 1164084682, 97213375168, 3335517273062, 320636452735872, 18019563246670856, 1044293027504195308]$ |
$0$ |
$0$ |
$16$ |
$24$ |
$12$ |
4.0.1088.2, 8.0.22581504.2 |
$D_{4}$, $D_4\times C_2$ |
2.2.ac_d $\times$ 4.2.ae_f_c_al |
| 6.2.ag_q_ax_m_x_ach |
$6$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 6 x + 16 x^{2} - 23 x^{3} + 12 x^{4} + 23 x^{5} - 59 x^{6} + 46 x^{7} + 48 x^{8} - 184 x^{9} + 256 x^{10} - 192 x^{11} + 64 x^{12}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$6$ |
$0$ |
$-3$ |
$[-3, 1, 12, 9, 32, 88, 123, 281, 471, 1036]$ |
$2$ |
$[2, 1348, 438866, 10444304, 1045219642, 96133597300, 4251737340496, 306396191004800, 16594108349445314, 1164425409878104828]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
12.0.2531230810905488.1 |
12T293 |
simple |
| 6.2.ag_q_aw_e_by_aef |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + 5 x^{3} - 13 x^{4} + 10 x^{5} + 8 x^{6} - 24 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$5$ |
$1$ |
$-3$ |
$[-3, 1, 15, 1, 27, 79, 179, 257, 411, 981]$ |
$2$ |
$[2, 988, 587936, 6331104, 869745362, 88293876736, 6524401235494, 283396650585984, 14741996255756768, 1105517895137005948]$ |
$0$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 8.0.903363136.2 |
$C_2^2$, $C_2^2 \wr C_2$ |
2.2.ad_f $\times$ 4.2.ad_c_f_an |
| 6.2.ag_q_av_ab_cl_afb |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 2 x^{2} + 6 x^{3} - 15 x^{4} + 12 x^{5} + 8 x^{6} - 24 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$4$ |
$2$ |
$-3$ |
$[-3, 1, 18, 5, 42, 88, 228, 293, 540, 976]$ |
$3$ |
$[3, 1197, 987012, 8542989, 1387129503, 99242082576, 9456192359463, 322940575154925, 18910172246120532, 1096939859534540847]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 8.0.98188281.1 |
$C_2^2$, $S_4\times C_2$ |
2.2.ad_f $\times$ 4.2.ad_c_g_ap |
| 6.2.ag_r_abj_cn_aeg_gj |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 50 x^{5} + 52 x^{6} - 40 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$2$ |
$4$ |
$-3$ |
$[-3, 3, -6, 11, 22, 36, 137, 243, 408, 838]$ |
$1$ |
$[1, 1687, 30256, 11297839, 697901296, 44304344896, 4636395735133, 266974996719375, 14753665220610544, 957918515847768832]$ |
$0$ |
$0$ |
$108$ |
$120$ |
$30$ |
\(\Q(\sqrt{-3}, \sqrt{-7})\), \(\Q(\zeta_{15})\) |
$C_2^2$, $C_4\times C_2$ |
2.2.ab_ab $\times$ 4.2.af_n_az_bn |
| 6.2.ag_r_abh_cf_adt_ft |
$6$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 6 x + 17 x^{2} - 33 x^{3} + 57 x^{4} - 97 x^{5} + 149 x^{6} - 194 x^{7} + 228 x^{8} - 264 x^{9} + 272 x^{10} - 192 x^{11} + 64 x^{12}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$6$ |
$0$ |
$-3$ |
$[-3, 3, 0, 27, 37, 48, 144, 283, 540, 953]$ |
$2$ |
$[2, 3148, 76394, 32890304, 1187093902, 52787184484, 4994237174222, 309237400993536, 19009213053145418, 1076100211428509908]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
12.0.1651760367141776.1 |
12T293 |
simple |
| 6.2.ag_r_abg_bu_acb_cl |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )( 1 - 3 x + 3 x^{2} - 2 x^{3} + 3 x^{4} - 4 x^{5} + 12 x^{6} - 24 x^{7} + 16 x^{8} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$5$ |
$1$ |
$-3$ |
$[-3, 3, 3, 7, 22, 129, 186, 263, 570, 1108]$ |
$2$ |
$[2, 2584, 209912, 8976816, 792596282, 183335461504, 6921259565488, 288735498423648, 20158421049664376, 1250009090619626824]$ |
$0$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\), 8.0.1794086993.1 |
$C_2^2$, $C_2 \wr S_4$ |
2.2.ad_f $\times$ 4.2.ad_d_ac_d |
| 6.2.ag_r_abg_bx_acs_dv |
$6$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 6 x + 17 x^{2} - 32 x^{3} + 49 x^{4} - 70 x^{5} + 99 x^{6} - 140 x^{7} + 196 x^{8} - 256 x^{9} + 272 x^{10} - 192 x^{11} + 64 x^{12}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$6$ |
$0$ |
$-3$ |
$[-3, 3, 3, 19, 27, 75, 123, 267, 615, 903]$ |
$2$ |
$[2, 2788, 145202, 19817104, 838866382, 82786339492, 4262096717006, 292847016554752, 21889630136449202, 1023758047300395268]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
12.0.8793276534489088.1 |
12T260 |
simple |
| 6.2.ag_r_abg_ca_adg_ex |
$6$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6} )( 1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6} )$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$4$ |
$2$ |
$-3$ |
$[-3, 3, 3, 31, 47, 81, 165, 327, 651, 973]$ |
$3$ |
$[3, 4437, 154413, 46131489, 1635782703, 88381832049, 5849422508352, 368560011932793, 23569818473605509, 1095907178705123997]$ |
$0$ |
$0$ |
$28$ |
$42$ |
$7$ |
\(\Q(\zeta_{7})\), 6.0.465831.1 |
$C_6$, $A_4\times C_2$ |
3.2.ad_c_b $\times$ 3.2.ad_g_aj |
| 6.2.ag_r_abf_bp_abr_bx |
$6$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 6 x + 17 x^{2} - 31 x^{3} + 41 x^{4} - 43 x^{5} + 49 x^{6} - 86 x^{7} + 164 x^{8} - 248 x^{9} + 272 x^{10} - 192 x^{11} + 64 x^{12}$ |
$[0,0,0,0,0,0,1,1,1,1,1,1]$ |
$0$ |
$6$ |
$0$ |
$6$ |
$0$ |
$-3$ |
$[-3, 3, 6, 11, 17, 96, 130, 251, 546, 993]$ |
$2$ |
$[2, 2428, 236942, 11576704, 638343922, 114196092436, 4544325255038, 275952735577600, 19247885806999022, 1114587422961178468]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
12.0.915890837972368.1 |
12T293 |
simple |
