| 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 |
| 4.3.am_co_aii_rr |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$6$ |
$0$ |
$4$ |
$0$ |
$4$ |
$-8$ |
$[-8, -2, 28, 118, 352, 946, 2512, 6886, 19684, 58078]$ |
$1$ |
$[1, 2401, 614656, 68574961, 5393580481, 377801998336, 26505620986321, 1947408269043601, 150125140011540736, 11959584699384036001]$ |
$0$ |
$0$ |
$51$ |
$60$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.3.ad 4 |
| 4.3.al_cf_agy_oo |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{3}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$1$ |
$3$ |
$-7$ |
$[-7, 3, 38, 123, 323, 846, 2345, 6771, 19874, 58803]$ |
$2$ |
$[2, 4116, 834176, 72342816, 4816407662, 329612967936, 24554788591118, 1913695797127296, 151574224374586496, 12107028012374894676]$ |
$0$ |
$0$ |
$42$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.3.ad 3 $\times$ 1.3.ac |
| 4.3.ak_bv_afi_kw |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-6$ |
$[-6, 4, 24, 72, 254, 838, 2402, 6656, 19392, 58564]$ |
$2$ |
$[2, 3332, 490784, 38291344, 3619319362, 327058457600, 25217176717378, 1880566937174016, 147899391592223264, 12058613378200922372]$ |
$0$ |
$0$ |
$72$ |
$24$ |
$12$ |
\(\Q(\sqrt{-3}) \), \(\Q(\zeta_{8})\) |
$C_2$, $C_2^2$ |
1.3.ad 2 $\times$ 2.3.ae_i |
| 4.3.ak_bw_afo_ll |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{3}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$1$ |
$3$ |
$-6$ |
$[-6, 6, 36, 102, 294, 882, 2514, 6918, 19548, 57846]$ |
$3$ |
$[3, 5145, 790272, 56517825, 4239234843, 346961018880, 26528984248539, 1956789130794225, 149087900677992192, 11912402839226961225]$ |
$0$ |
$0$ |
$42$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.3.ad 3 $\times$ 1.3.ab |
| 4.3.ak_bx_afu_ma |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - 2 x + 3 x^{2} )^{2}$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-6$ |
$[-6, 8, 48, 128, 294, 746, 2178, 6656, 20064, 59528]$ |
$4$ |
$[4, 7056, 1132096, 76317696, 4300998724, 287570497536, 22747538835844, 1880566937174016, 153037296038433856, 12256289074986008976]$ |
$0$ |
$0$ |
$72$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.3.ad 2 $\times$ 1.3.ac 2 |
| 4.3.aj_bm_ady_ht |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-5$ |
$[-5, 5, 19, 77, 310, 899, 2347, 6725, 20143, 59360]$ |
$3$ |
$[3, 3969, 430416, 40916421, 4586243568, 355330789632, 24599121127689, 1899813952225917, 153645866448077808, 12221700189956054784]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-26 -6 \sqrt{13}})\) |
$C_2$, $C_4$ |
1.3.ad 2 $\times$ 2.3.ad_f |
| 4.3.aj_bn_aee_ii |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$6$ |
$0$ |
$4$ |
$0$ |
$4$ |
$-5$ |
$[-5, 7, 28, 91, 325, 946, 2431, 6643, 19684, 58807]$ |
$4$ |
$[4, 5488, 614656, 48228544, 4856212684, 377801998336, 25559408866492, 1876172350124800, 150125140011540736, 12107841492722430448]$ |
$0$ |
$0$ |
$51$ |
$60$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.3.ad 3 $\times$ 1.3.a |
| 4.3.aj_bo_ael_ja |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$1$ |
$3$ |
$-5$ |
$[-5, 9, 34, 77, 225, 738, 2235, 6541, 19582, 59289]$ |
$4$ |
$[4, 5712, 666064, 40395264, 3232012124, 285341817600, 23361174728924, 1848011586011136, 149326991897167504, 12207277562723099472]$ |
$0$ |
$0$ |
$42$ |
$24$ |
$24$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \), \(\Q(\zeta_{8})\) |
$C_2$, $C_2$, $C_2^2$ |
1.3.ad $\times$ 1.3.ac $\times$ 2.3.ae_i |
| 4.3.aj_bo_aek_ix |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - 3 x + 7 x^{2} - 9 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-5$ |
$[-5, 9, 37, 101, 310, 903, 2389, 6485, 19171, 58464]$ |
$5$ |
$[5, 7105, 827120, 54033525, 4553342000, 357302606080, 25077434754755, 1831615948705725, 146237929245768080, 12037965374815072000]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-9 +2 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.3.ad 2 $\times$ 2.3.ad_h |
| 4.3.aj_bp_aeq_jm |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} )( 1 - x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-5$ |
$[-5, 11, 46, 107, 265, 782, 2347, 6803, 19738, 58571]$ |
$6$ |
$[6, 8820, 1072512, 59623200, 3785589786, 302705786880, 24576432300762, 1922914262505600, 150526973078358912, 12059264472339338100]$ |
$0$ |
$0$ |
$36$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$, $C_2$ |
1.3.ad 2 $\times$ 1.3.ac $\times$ 1.3.ab |
| 4.3.aj_bq_aev_jy |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )^{3}$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$1$ |
$3$ |
$-5$ |
$[-5, 13, 58, 133, 265, 646, 2011, 6541, 20254, 60253]$ |
$8$ |
$[8, 12096, 1536416, 80510976, 3840744248, 250890587136, 21073303936952, 1848011586011136, 154514490015638816, 12407390297278675776]$ |
$0$ |
$0$ |
$42$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.3.ad $\times$ 1.3.ac 3 |
| 4.3.ai_bc_aci_eb |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-4$ |
$[-4, 2, 8, 86, 296, 746, 2264, 6758, 19304, 58082]$ |
$3$ |
$[3, 2793, 254016, 45785649, 4283299443, 287570497536, 23682517231971, 1909235236551825, 147240958586250816, 11960388150768149673]$ |
$0$ |
$0$ |
$72$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.3.ad 2 $\times$ 2.3.ac_b |
| 4.3.ai_bd_aco_eq |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-4$ |
$[-4, 4, 14, 96, 336, 838, 2376, 7040, 19922, 58564]$ |
$4$ |
$[4, 3920, 341824, 52998400, 5070660404, 326947819520, 24919076318756, 1992815309721600, 151936029738601024, 12058002552079778000]$ |
$0$ |
$0$ |
$36$ |
$24$ |
$12$ |
\(\Q(\sqrt{-3}) \), \(\Q(i, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.3.ad 2 $\times$ 2.3.ac_c |
| 4.3.ai_be_acu_ff |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 + x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{3}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$1$ |
$3$ |
$-4$ |
$[-4, 6, 20, 102, 356, 882, 2348, 6918, 19820, 57846]$ |
$5$ |
$[5, 5145, 439040, 56517825, 5473190525, 346961018880, 24589833484445, 1956789130794225, 151162379345089280, 11912402839226961225]$ |
$0$ |
$0$ |
$42$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.3.ad 3 $\times$ 1.3.b |
| 4.3.ai_bf_adb_fx |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 45 x^{5} + 27 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-4$ |
$[-4, 8, 23, 84, 296, 773, 2089, 6532, 20039, 59268]$ |
$5$ |
$[5, 5425, 457940, 44078125, 4326589525, 300106399600, 21852060841280, 1845111414453125, 152838760198077380, 12202985346955860625]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), 6.0.1342367.1 |
$C_2$, $A_4\times C_2$ |
1.3.ad $\times$ 3.3.af_n_az |
| 4.3.ai_bf_ada_fu |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - 2 x + 4 x^{2} - 6 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-4$ |
$[-4, 8, 26, 104, 356, 890, 2264, 6656, 19682, 57848]$ |
$6$ |
$[6, 6468, 550368, 56840784, 5473263966, 351231648768, 23674748355222, 1880431371506688, 150082676736082272, 11912820414139488228]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-8 -2 \sqrt{3}})\) |
$C_2$, $D_{4}$ |
1.3.ad 2 $\times$ 2.3.ac_e |
| 4.3.ai_bg_adk_gw |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )^{2}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-4$ |
$[-4, 10, 20, 26, 156, 730, 2292, 6426, 19100, 59050]$ |
$4$ |
$[4, 4624, 391876, 21381376, 2428715524, 283130410000, 23991364017604, 1816019815366656, 145706642016575236, 12158462041948282384]$ |
$0$ |
$0$ |
$42$ |
$40$ |
$4$ |
\(\Q(\zeta_{8})\) |
$C_2^2$ |
2.3.ae_i 2 |
| 4.3.ai_bg_adh_gm |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )( 1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-4$ |
$[-4, 10, 29, 82, 281, 799, 2180, 6610, 20333, 60085]$ |
$6$ |
$[6, 6804, 584136, 43164576, 4095464736, 310007984832, 22788608466462, 1866925407215232, 155128934657036088, 12372374984414505984]$ |
$0$ |
$0$ |
$12$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-26 -6 \sqrt{13}})\) |
$C_2$, $C_2$, $C_4$ |
1.3.ad $\times$ 1.3.ac $\times$ 2.3.ad_f |
| 4.3.ai_bg_adg_gj |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - 2 x + 5 x^{2} - 6 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-4$ |
$[-4, 10, 32, 102, 336, 874, 2208, 6470, 19760, 58810]$ |
$7$ |
$[7, 7889, 680512, 54662881, 5079693647, 343587786752, 23073342565007, 1827315445641777, 150688359407419456, 12108904870630602209]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-9 -2 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.3.ad 2 $\times$ 2.3.ac_f |
| 4.3.ai_bh_ado_he |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - x + 3 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$2$ |
$2$ |
$-4$ |
$[-4, 12, 32, 56, 196, 774, 2404, 6688, 19256, 58332]$ |
$6$ |
$[6, 7140, 631008, 31558800, 2844704886, 300359808000, 25239404286102, 1889625817497600, 146877530321315808, 12011040839153825700]$ |
$0$ |
$0$ |
$48$ |
$24$ |
$12$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \), \(\Q(\zeta_{8})\) |
$C_2$, $C_2$, $C_2^2$ |
1.3.ad $\times$ 1.3.ab $\times$ 2.3.ae_i |
| 4.3.ai_bh_adn_hb |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 5 x + 15 x^{2} - 31 x^{3} + 45 x^{4} - 45 x^{5} + 27 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-4$ |
$[-4, 12, 35, 76, 246, 813, 2369, 6788, 20069, 59632]$ |
$7$ |
$[7, 8281, 732844, 40585181, 3533486887, 315571420528, 24860761811648, 1917568997154629, 153059630035416076, 12278172330073214201]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), 6.0.400967.1 |
$C_2$, $A_4\times C_2$ |
1.3.ad $\times$ 3.3.af_p_abf |
| 4.3.ai_bh_adm_gy |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} )( 1 + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$1$ |
$3$ |
$-4$ |
$[-4, 12, 38, 96, 296, 846, 2264, 6528, 19874, 59532]$ |
$8$ |
$[8, 9408, 834176, 50878464, 4336544168, 329612967936, 23678218350536, 1843693075660800, 151574224374586496, 12257112584296966848]$ |
$0$ |
$0$ |
$42$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$, $C_2$ |
1.3.ad 2 $\times$ 1.3.ac $\times$ 1.3.a |
| 4.3.ai_bi_ads_hm |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} )^{2}( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-4$ |
$[-4, 14, 44, 82, 196, 638, 2068, 6426, 19772, 60014]$ |
$8$ |
$[8, 9792, 903944, 42614784, 2886151048, 248946177600, 21641775795592, 1816019815366656, 150768372127835144, 12357774548336619072]$ |
$0$ |
$0$ |
$42$ |
$40$ |
$8$ |
\(\Q(\sqrt{-2}) \), \(\Q(\zeta_{8})\) |
$C_2$, $C_2^2$ |
1.3.ac 2 $\times$ 2.3.ae_i |
| 4.3.ai_bi_ads_hn |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - x + 3 x^{2} )^{2}$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-4$ |
$[-4, 14, 44, 86, 236, 818, 2516, 6950, 19412, 57614]$ |
$9$ |
$[9, 11025, 1016064, 46580625, 3331944729, 318637670400, 26552368104201, 1966215181100625, 148057827801940224, 11865407116631000625]$ |
$0$ |
$0$ |
$54$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.3.ad 2 $\times$ 1.3.ab 2 |
| 4.3.ai_bi_adr_hk |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )( 1 - 3 x + 7 x^{2} - 9 x^{3} + 9 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-4$ |
$[-4, 14, 47, 106, 281, 803, 2222, 6370, 19361, 59189]$ |
$10$ |
$[10, 12180, 1122520, 57002400, 4066084000, 311728294080, 23231717873290, 1799908010409600, 147649492269375880, 12186375001164672000]$ |
$0$ |
$0$ |
$12$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-9 +2 \sqrt{5}})\) |
$C_2$, $C_2$, $D_{4}$ |
1.3.ad $\times$ 1.3.ac $\times$ 2.3.ad_h |
| 4.3.ai_bj_adw_hw |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )^{2}$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$2$ |
$2$ |
$-4$ |
$[-4, 16, 56, 112, 236, 682, 2180, 6688, 19928, 59296]$ |
$12$ |
$[12, 15120, 1455552, 62899200, 3380489772, 264095354880, 22767589553196, 1889625817497600, 151979936138960832, 12207936683852355600]$ |
$0$ |
$0$ |
$48$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$, $C_2$ |
1.3.ad $\times$ 1.3.ac 2 $\times$ 1.3.ab |
| 4.3.ai_bk_aea_ig |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} )^{4}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$1$ |
$3$ |
$-4$ |
$[-4, 18, 68, 138, 236, 546, 1844, 6426, 20444, 60978]$ |
$16$ |
$[16, 20736, 2085136, 84934656, 3429742096, 218889236736, 19522293907216, 1816019815366656, 156005942621967376, 12560354365595832576]$ |
$0$ |
$0$ |
$42$ |
$24$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
1.3.ac 4 |
| 4.3.ah_t_ay_y |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - x - 2 x^{2} - 3 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-3$ |
$[-3, -1, 12, 107, 267, 818, 2433, 6611, 19956, 59039]$ |
$4$ |
$[4, 2352, 313600, 58828224, 3833913964, 318637670400, 25583626756636, 1867179827525376, 152206785136134400, 12155794379587396272]$ |
$0$ |
$0$ |
$54$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}, \sqrt{-11})\) |
$C_2$, $C_2^2$ |
1.3.ad 2 $\times$ 2.3.ab_ac |
| 4.3.ah_u_abe_bn |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - x - x^{2} - 3 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-3$ |
$[-3, 1, 15, 117, 302, 847, 2531, 6773, 19905, 59296]$ |
$5$ |
$[5, 3185, 356720, 67283125, 4435836400, 330847811840, 26727999291355, 1913590813168125, 151807494193431440, 12208565650804140800]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-18 +2 \sqrt{29}})\) |
$C_2$, $D_{4}$ |
1.3.ad 2 $\times$ 2.3.ab_ab |
| 4.3.ah_v_abl_cf |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 6 x^{2} - 7 x^{3} + 18 x^{4} - 36 x^{5} + 27 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-3$ |
$[-3, 3, 15, 107, 277, 711, 2251, 6403, 19140, 59043]$ |
$5$ |
$[5, 3465, 321020, 57882825, 3993666025, 274969038960, 23543819129605, 1809002263293225, 146011266846851840, 12156510723031191825]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), 6.0.2461019.1 |
$C_2$, $D_{6}$ |
1.3.ad $\times$ 3.3.ae_g_ah |
| 4.3.ah_v_abk_cc |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 + 2 x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{3}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$1$ |
$3$ |
$-3$ |
$[-3, 3, 18, 123, 327, 846, 2517, 6771, 19494, 58803]$ |
$6$ |
$[6, 4116, 395136, 72342816, 4896017706, 329612967936, 26564029141866, 1913695797127296, 148676055648494976, 12107028012374894676]$ |
$0$ |
$0$ |
$42$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.3.ad 3 $\times$ 1.3.c |
| 4.3.ah_w_abr_cu |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 7 x^{2} - 10 x^{3} + 21 x^{4} - 36 x^{5} + 27 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-3$ |
$[-3, 5, 18, 109, 297, 722, 2265, 6637, 19440, 59585]$ |
$6$ |
$[6, 4452, 363384, 60422544, 4355437746, 279337641408, 23702199325314, 1874503567302912, 148248758281499064, 12268605764220463812]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), 6.0.7181504.1 |
$C_2$, $S_4\times C_2$ |
1.3.ad $\times$ 3.3.ae_h_ak |
| 4.3.ah_w_abq_cr |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - x + x^{2} - 3 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-3$ |
$[-3, 5, 21, 125, 342, 827, 2433, 6725, 19173, 58400]$ |
$7$ |
$[7, 5145, 433552, 73907925, 5190222352, 321210005760, 25589480443093, 1900351978468125, 146252994459889072, 12024597112399737600]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-26 +2 \sqrt{21}})\) |
$C_2$, $D_{4}$ |
1.3.ad 2 $\times$ 2.3.ab_b |
| 4.3.ah_x_aby_dm |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )( 1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$1$ |
$3$ |
$-3$ |
$[-3, 7, 18, 91, 267, 646, 2097, 6643, 19494, 58807]$ |
$6$ |
$[6, 4788, 344736, 48301344, 3824938986, 250890587136, 21939467263818, 1876183595395200, 148662203360249376, 12107841369080712948]$ |
$0$ |
$0$ |
$42$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-2}, \sqrt{-3})\) |
$C_2$, $C_2$, $C_2^2$ |
1.3.ad $\times$ 1.3.ac $\times$ 2.3.ac_b |
| 4.3.ah_x_abx_dj |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 8 x^{2} - 13 x^{3} + 24 x^{4} - 36 x^{5} + 27 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-3$ |
$[-3, 7, 21, 107, 307, 727, 2237, 6803, 19740, 59567]$ |
$7$ |
$[7, 5537, 409444, 59672249, 4537455167, 281119337072, 23392114502071, 1922148223120489, 150528923543557888, 12264624935213421617]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), 6.0.10816643.1 |
$C_2$, $A_4\times C_2$ |
1.3.ad $\times$ 3.3.ae_i_an |
| 4.3.ah_x_abw_dg |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - x + 2 x^{2} - 3 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-3$ |
$[-3, 7, 24, 123, 347, 802, 2321, 6707, 19176, 58327]$ |
$8$ |
$[8, 6272, 476672, 72077824, 5294214808, 310927425536, 24317685973624, 1894394635241472, 146275717043144192, 12010242165980304512]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-9 +2 \sqrt{17}})\) |
$C_2$, $D_{4}$ |
1.3.ad 2 $\times$ 2.3.ab_c |
| 4.3.ah_y_ace_eb |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 9 x^{2} - 17 x^{3} + 27 x^{4} - 36 x^{5} + 27 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-3$ |
$[-3, 9, 21, 85, 272, 687, 2139, 6869, 20055, 58864]$ |
$7$ |
$[7, 5929, 400624, 45706661, 3908457392, 266033565952, 22379220236513, 1942216848112541, 152965130185763728, 12119527096636999424]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), 6.0.10338167.1 |
$C_2$, $S_4\times C_2$ |
1.3.ad $\times$ 3.3.ae_j_ar |
| 4.3.ah_y_acd_dy |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )( 1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$2$ |
$2$ |
$-3$ |
$[-3, 9, 24, 101, 307, 738, 2209, 6925, 20112, 59289]$ |
$8$ |
$[8, 6720, 463904, 55910400, 4528043608, 285245291520, 23085014729848, 1958316775833600, 153402593732216864, 12206659206053928000]$ |
$0$ |
$0$ |
$24$ |
$24$ |
$12$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \), \(\Q(i, \sqrt{5})\) |
$C_2$, $C_2$, $C_2^2$ |
1.3.ad $\times$ 1.3.ac $\times$ 2.3.ac_c |
| 4.3.ah_y_acc_dv |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - x + 3 x^{2} - 3 x^{3} + 9 x^{4} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$4$ |
$1$ |
$3$ |
$2$ |
$2$ |
$-3$ |
$[-3, 9, 27, 117, 342, 783, 2223, 6741, 19521, 58464]$ |
$9$ |
$[9, 7497, 529200, 67150629, 5192572464, 303286636800, 23234300923311, 1904096980028061, 148884520287358800, 12037866219491196672]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-34 +2 \sqrt{13}})\) |
$C_2$, $D_{4}$ |
1.3.ad 2 $\times$ 2.3.ab_d |
| 4.3.ah_z_acn_fa |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )( 1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$3$ |
$1$ |
$-3$ |
$[-3, 11, 15, 31, 212, 791, 2237, 6495, 19851, 59846]$ |
$6$ |
$[6, 5508, 343674, 22847184, 3077562336, 307605413700, 23403352250802, 1834606210793472, 151367919900582942, 12322899257743899648]$ |
$0$ |
$0$ |
$16$ |
$24$ |
$4$ |
\(\Q(\zeta_{8})\), \(\Q(\sqrt{-26 -6 \sqrt{13}})\) |
$C_2^2$, $C_4$ |
2.3.ae_i $\times$ 2.3.ad_f |
| 4.3.ah_z_acl_et |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 10 x^{2} - 21 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-3$ |
$[-3, 11, 21, 59, 237, 719, 2139, 6659, 19740, 57731]$ |
$7$ |
$[7, 6321, 407092, 32622681, 3349212307, 277908681456, 22350531758359, 1880571277251849, 150525368480881408, 11889101913430315161]$ |
$0$ |
$0$ |
$18$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), 6.0.309123.1 |
$C_2$, $D_{6}$ |
1.3.ad $\times$ 3.3.ae_k_av |
| 4.3.ah_z_ack_eq |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 10 x^{2} - 20 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-3$ |
$[-3, 11, 24, 75, 267, 746, 2209, 6931, 20328, 58731]$ |
$8$ |
$[8, 7168, 468608, 40628224, 3823530328, 288872464384, 23100875366584, 1960516736761856, 155090381688685184, 12092309005923908608]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), 6.0.2296688.1 |
$C_2$, $S_4\times C_2$ |
1.3.ad $\times$ 3.3.ae_k_au |
| 4.3.ah_z_acj_en |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 10 x^{2} - 19 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-3$ |
$[-3, 11, 27, 91, 297, 767, 2223, 6979, 20412, 58931]$ |
$9$ |
$[9, 8001, 531468, 49614201, 4332861549, 296714332656, 23230256952681, 1974715900036425, 155745282861778176, 12133301575821043401]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), 6.0.11822771.1 |
$C_2$, $S_4\times C_2$ |
1.3.ad $\times$ 3.3.ae_k_at |
| 4.3.ah_z_aci_ek |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} )( 1 + x + 3 x^{2} )( 1 - 3 x + 3 x^{2} )^{2}$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-3$ |
$[-3, 11, 30, 107, 327, 782, 2181, 6803, 20010, 58571]$ |
$10$ |
$[10, 8820, 595840, 59623200, 4887498550, 302705786880, 22780004400310, 1922914262505600, 152621475670814080, 12059264472339338100]$ |
$0$ |
$0$ |
$36$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$, $C_2$ |
1.3.ad 2 $\times$ 1.3.ac $\times$ 1.3.b |
| 4.3.ah_ba_acr_fi |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 + 3 x^{2} )( 1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$1$ |
$3$ |
$-3$ |
$[-3, 13, 24, 45, 227, 838, 2321, 6413, 19392, 59293]$ |
$8$ |
$[8, 7616, 490784, 26930176, 3258722968, 327058457600, 24316960184056, 1811776064716800, 147899391592223264, 12208097778913566656]$ |
$0$ |
$0$ |
$72$ |
$24$ |
$12$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \), \(\Q(\zeta_{8})\) |
$C_2$, $C_2$, $C_2^2$ |
1.3.ad $\times$ 1.3.a $\times$ 2.3.ae_i |
| 4.3.ah_ba_acq_ff |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - x + 3 x^{2} )( 1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-3$ |
$[-3, 13, 27, 61, 252, 835, 2349, 6757, 20007, 59128]$ |
$9$ |
$[9, 8505, 553392, 33722325, 3604685904, 326324194560, 24620803914051, 1908965547359325, 152584301835349776, 12173484255729350400]$ |
$0$ |
$0$ |
$12$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-26 -6 \sqrt{13}})\) |
$C_2$, $C_2$, $C_4$ |
1.3.ad $\times$ 1.3.ab $\times$ 2.3.ad_f |
| 4.3.ah_ba_acp_fb |
$4$ |
$\F_{3}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 7 x + 26 x^{2} - 67 x^{3} + 131 x^{4} - 201 x^{5} + 234 x^{6} - 189 x^{7} + 81 x^{8}$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-3$ |
$[-3, 13, 30, 73, 242, 688, 1999, 6401, 19776, 58558]$ |
$9$ |
$[9, 8433, 556983, 38058129, 3443813559, 266687359281, 20994047917929, 1808033357296737, 150786355400594739, 12057431016972414753]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
8.0.371495353.1 |
$C_2 \wr S_4$ |
simple |
| 4.3.ah_ba_acp_fc |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 4 x + 11 x^{2} - 22 x^{3} + 33 x^{4} - 36 x^{5} + 27 x^{6} )$ |
$[0,0,0,\frac{1}{2},\frac{1}{2},1,1,1]$ |
$1$ |
$3$ |
$1$ |
$3$ |
$1$ |
$-3$ |
$[-3, 13, 30, 77, 277, 826, 2321, 6893, 20280, 58793]$ |
$10$ |
$[10, 9380, 616840, 41459600, 3983713550, 321699331520, 24298968752110, 1948662891884800, 154713550731961480, 12105231000843656900]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), 6.0.5169344.1 |
$C_2$, $S_4\times C_2$ |
1.3.ad $\times$ 3.3.ae_l_aw |
| 4.3.ah_ba_aco_ey |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 39 x^{4} - 45 x^{5} + 27 x^{6} )$ |
$[0,0,0,0,1,1,1,1]$ |
$0$ |
$4$ |
$0$ |
$4$ |
$0$ |
$-3$ |
$[-3, 13, 33, 89, 267, 673, 1922, 6417, 20229, 59993]$ |
$10$ |
$[10, 9300, 621490, 46500000, 3863596550, 261827522100, 20243733754240, 1813169850000000, 154314037806166930, 12353429416140532500]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \), 6.0.1342367.1 |
$C_2$, $A_4\times C_2$ |
1.3.ac $\times$ 3.3.af_n_az |
| 4.3.ah_ba_aco_ez |
$4$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}( 1 - x + 5 x^{2} - 3 x^{3} + 9 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1,1]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$2$ |
$-3$ |
$[-3, 13, 33, 93, 302, 811, 2237, 6821, 20229, 58528]$ |
$11$ |
$[11, 10241, 681296, 50191141, 4407635056, 314606141696, 23385096417001, 1928181068114301, 154310471689556336, 12051248646952798976]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-42 +2 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.3.ad 2 $\times$ 2.3.ab_f |
