| 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 |
| 3.2.ag_s_abg |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$4$ |
$0$ |
$3$ |
$0$ |
$3$ |
$-3$ |
$[-3, 5, 21, 41, 57, 65, 81, 161, 417, 1025]$ |
$1$ |
$[1, 125, 2197, 15625, 68921, 274625, 1442897, 11390625, 111284641, 1076890625]$ |
$0$ |
$0$ |
$25$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.2.ac 3 |
| 3.2.af_n_aw |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$-2$ |
$[-2, 6, 13, 18, 38, 87, 152, 242, 481, 1086]$ |
$1$ |
$[1, 95, 988, 4275, 39401, 375440, 2491763, 15736275, 125716084, 1141643975]$ |
$0$ |
$0$ |
$12$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ac $\times$ 2.2.ad_f |
| 3.2.af_o_ay |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$1$ |
$2$ |
$-2$ |
$[-2, 8, 22, 32, 38, 56, 110, 224, 454, 968]$ |
$2$ |
$[2, 200, 2366, 10000, 36982, 236600, 1813198, 14580000, 119844998, 1017005000]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac 2 $\times$ 1.2.ab |
| 3.2.ae_i_am |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$4$ |
$0$ |
$3$ |
$0$ |
$3$ |
$-1$ |
$[-1, 5, 5, 17, 49, 65, 97, 257, 545, 1025]$ |
$1$ |
$[1, 65, 325, 4225, 54161, 274625, 1632737, 16769025, 142869025, 1073741825]$ |
$0$ |
$0$ |
$25$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2^2$ |
1.2.ac $\times$ 2.2.ac_c |
| 3.2.ae_j_ap |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
|
$1 - 4 x + 9 x^{2} - 15 x^{3} + 18 x^{4} - 16 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-1$ |
$[-1, 7, 8, 7, 24, 52, 90, 231, 575, 1092]$ |
$1$ |
$[1, 71, 421, 2059, 25621, 209237, 1560896, 15222187, 151446751, 1147846421]$ |
$0$ |
$0$ |
$14$ |
$42$ |
$7$ |
\(\Q(\zeta_{7})\) |
$C_6$ |
simple |
| 3.2.ae_j_ao |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$2$ |
$1$ |
$-1$ |
$[-1, 7, 11, 23, 59, 91, 111, 223, 515, 987]$ |
$2$ |
$[2, 140, 806, 5600, 72242, 394940, 1813198, 14716800, 134765618, 1036672700]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.1088.2 |
$C_2$, $D_{4}$ |
1.2.ac $\times$ 2.2.ac_d |
| 3.2.ae_k_ar |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 9, 14, 9, 19, 78, 181, 305, 518, 1029]$ |
$2$ |
$[2, 152, 1064, 2736, 21142, 323456, 3131242, 20142432, 135386552, 1078157432]$ |
$0$ |
$0$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ab $\times$ 2.2.ad_f |
| 3.2.ae_k_aq |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$4$ |
$0$ |
$3$ |
$0$ |
$3$ |
$-1$ |
$[-1, 9, 17, 25, 49, 81, 97, 161, 449, 1089]$ |
$3$ |
$[3, 225, 1521, 5625, 55473, 342225, 1647201, 11390625, 118688193, 1144130625]$ |
$0$ |
$0$ |
$25$ |
$24$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.2.ac 2 $\times$ 1.2.a |
| 3.2.ae_l_as |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$-1$ |
$[-1, 11, 23, 23, 19, 47, 139, 287, 491, 911]$ |
$4$ |
$[4, 320, 2548, 6400, 19844, 203840, 2278532, 18662400, 129063844, 960449600]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac $\times$ 1.2.ab 2 |
| 3.2.ad_c_b |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 2 x^{2} + x^{3} + 4 x^{4} - 12 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$0$ |
$[0, 0, 3, 28, 35, 87, 168, 252, 570, 1015]$ |
$1$ |
$[1, 29, 301, 8149, 34861, 375347, 2863288, 16436533, 149808001, 1062528419]$ |
$1$ |
$0$ |
$14$ |
$42$ |
$7$ |
\(\Q(\zeta_{7})\) |
$C_6$ |
simple |
| 3.2.ad_d_ac |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 2 x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$0$ |
$[0, 2, 3, 26, 30, 47, 126, 194, 471, 1082]$ |
$1$ |
$[1, 35, 208, 6475, 30791, 203840, 2045639, 13111875, 124128784, 1136957675]$ |
$1$ |
$0$ |
$18$ |
$24$ |
$12$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2$, $C_2^2$ |
1.2.ac $\times$ 2.2.ab_ab |
| 3.2.ad_e_ae |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
✓ |
$( 1 - 2 x + 2 x^{2} )( 1 - x - 2 x^{3} + 4 x^{4} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$2$ |
$1$ |
$0$ |
$[0, 4, 6, 32, 50, 64, 154, 256, 474, 1104]$ |
$2$ |
$[2, 80, 338, 10400, 57482, 256880, 2525098, 16660800, 124272122, 1161136400]$ |
$1$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.2312.1 |
$C_2$, $D_{4}$ |
1.2.ac $\times$ 2.2.ab_a |
| 3.2.ad_f_ah |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 12 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 6, 6, 22, 40, 42, 126, 318, 564, 1126]$ |
$2$ |
$[2, 92, 302, 6256, 42842, 180596, 2062538, 21270400, 147805142, 1184409932]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
6.0.679024.1 |
$S_4\times C_2$ |
simple |
| 3.2.ad_f_ag |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$2$ |
$1$ |
$0$ |
$[0, 6, 9, 34, 60, 63, 126, 242, 405, 966]$ |
$3$ |
$[3, 135, 468, 11475, 73923, 252720, 2074341, 15801075, 108519372, 1014593175]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.2873.1 |
$C_2$, $D_{4}$ |
1.2.ac $\times$ 2.2.ab_b |
| 3.2.ad_g_ak |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
✓ |
$( 1 - x + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$1$ |
$2$ |
$0$ |
$[0, 8, 6, 8, 30, 56, 126, 320, 582, 968]$ |
$2$ |
$[2, 104, 350, 2704, 29062, 236600, 2051758, 21464352, 153858950, 1014031304]$ |
$1$ |
$1$ |
$22$ |
$24$ |
$12$ |
\(\Q(\sqrt{-7}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2^2$ |
1.2.ab $\times$ 2.2.ac_c |
| 3.2.ad_g_aj |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 3 x + 6 x^{2} - 9 x^{3} + 12 x^{4} - 12 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 8, 9, 20, 45, 59, 126, 332, 594, 983]$ |
$3$ |
$[3, 153, 513, 5661, 46923, 235467, 2042904, 22423221, 157333509, 1031414463]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.465831.1 |
$A_4\times C_2$ |
simple |
| 3.2.ad_g_ai |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
✓ |
$( 1 + x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$1$ |
$2$ |
$0$ |
$[0, 8, 12, 32, 60, 56, 84, 224, 444, 968]$ |
$4$ |
$[4, 200, 676, 10000, 73964, 236600, 1481204, 14580000, 117531388, 1017005000]$ |
$1$ |
$1$ |
$22$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac 2 $\times$ 1.2.b |
| 3.2.ad_h_am |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$0$ |
$[0, 10, 9, 2, 30, 103, 168, 242, 513, 1150]$ |
$3$ |
$[3, 171, 684, 1539, 31713, 467856, 2844579, 15736275, 134079732, 1212927111]$ |
$0$ |
$0$ |
$12$ |
$24$ |
$6$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.a $\times$ 2.2.ad_f |
| 3.2.ad_h_al |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - x + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$0$ |
$[0, 10, 12, 14, 40, 82, 140, 286, 552, 930]$ |
$4$ |
$[4, 224, 868, 3584, 38764, 340256, 2278532, 18837504, 145132204, 979023584]$ |
$1$ |
$1$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \), 4.0.1088.2 |
$C_2$, $D_{4}$ |
1.2.ab $\times$ 2.2.ac_d |
| 3.2.ad_h_ak |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$2$ |
$1$ |
$0$ |
$[0, 10, 15, 26, 50, 55, 70, 226, 555, 1050]$ |
$5$ |
$[5, 275, 1040, 6875, 56375, 228800, 1305715, 14911875, 145492880, 1100721875]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), 4.0.1025.1 |
$C_2$, $D_{4}$ |
1.2.ac $\times$ 2.2.ab_d |
| 3.2.ad_i_am |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$1$ |
$2$ |
$0$ |
$[0, 12, 18, 16, 30, 72, 126, 224, 486, 1032]$ |
$6$ |
$[6, 360, 1638, 3600, 29766, 294840, 2069934, 14580000, 127818054, 1080505800]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$, $C_2$ |
1.2.ac $\times$ 1.2.ab $\times$ 1.2.a |
| 3.2.ad_j_an |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - x + 2 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$0$ |
$[0, 14, 24, 14, 0, 38, 168, 350, 528, 854]$ |
$8$ |
$[8, 512, 2744, 4096, 10648, 175616, 2863288, 23887872, 138991832, 907039232]$ |
$1$ |
$0$ |
$14$ |
$14$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
1.2.ab 3 |
| 3.2.ac_ac_i |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 2 x^{2} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$4$ |
$0$ |
$3$ |
$0$ |
$3$ |
$1$ |
$[1, -3, 13, 9, 41, 33, 113, 161, 481, 897]$ |
$1$ |
$[1, 5, 637, 2025, 39401, 156065, 1822577, 11390625, 125599201, 946609025]$ |
$0$ |
$0$ |
$25$ |
$24$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{2}) \) |
$C_2$, $C_2$ |
1.2.ac $\times$ 2.2.a_ae |
| 3.2.ac_ab_g |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - 3 x^{2} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$1$ |
$[1, -1, 13, 23, 41, 83, 113, 287, 481, 1139]$ |
$2$ |
$[2, 20, 962, 6400, 44362, 355940, 1841674, 18662400, 125611226, 1199992100]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(i, \sqrt{7})\) |
$C_2$, $C_2^2$ |
1.2.ac $\times$ 2.2.a_ad |
| 3.2.ac_a_d |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 3 x^{3} - 8 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 1, 10, 25, 21, 70, 99, 273, 586, 1101]$ |
$2$ |
$[2, 32, 632, 6976, 23342, 283136, 1655194, 17984128, 155066888, 1154401952]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.1539727.2 |
$D_{6}$ |
simple |
| 3.2.ac_a_e |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
✓ |
$( 1 - 2 x + 2 x^{2} )( 1 - 2 x^{2} + 4 x^{4} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$4$ |
$0$ |
$3$ |
$0$ |
$3$ |
$1$ |
$[1, 1, 13, 33, 41, 97, 113, 257, 481, 961]$ |
$3$ |
$[3, 45, 1053, 11025, 40713, 426465, 1837041, 16769025, 126584289, 1010700225]$ |
$1$ |
$0$ |
$25$ |
$24$ |
$24$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.2.ac $\times$ 2.2.a_ac |
| 3.2.ac_b_a |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 2 x + x^{2} + 2 x^{4} - 8 x^{5} + 8 x^{6}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$2$ |
$1$ |
$1$ |
$[1, 3, 7, 23, 11, 51, 127, 255, 619, 1043]$ |
$2$ |
$[2, 44, 386, 5984, 16742, 212300, 2105602, 16683392, 164730518, 1094290604]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.2580992.1 |
$D_{6}$ |
simple |
| 3.2.ac_b_b |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + x^{2} + x^{3} + 2 x^{4} - 8 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 3, 10, 31, 26, 72, 134, 263, 631, 1068]$ |
$3$ |
$[3, 63, 657, 9891, 26763, 289737, 2173944, 17180667, 168486993, 1118987793]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.2369943.1 |
$S_4\times C_2$ |
simple |
| 3.2.ac_b_c |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x^{2} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$1$ |
$[1, 3, 13, 39, 41, 87, 113, 191, 481, 903]$ |
$4$ |
$[4, 80, 988, 14400, 39524, 375440, 1879868, 12960000, 125716084, 952528400]$ |
$0$ |
$0$ |
$12$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ac $\times$ 2.2.a_ab |
| 3.2.ac_c_ad |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - x + 2 x^{2} )( 1 - x - x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$1$ |
$[1, 5, 4, 17, 11, 38, 155, 257, 508, 1025]$ |
$2$ |
$[2, 56, 224, 4144, 16522, 175616, 2570626, 16783200, 133677152, 1073731736]$ |
$1$ |
$1$ |
$14$ |
$42$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2$, $C_2^2$ |
1.2.ab $\times$ 2.2.ab_ab |
| 3.2.ac_c_ac |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
|
|
✓ |
✓ |
$1 - 2 x + 2 x^{2} - 2 x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3},\frac{2}{3}]$ |
$3$ |
$0$ |
$3$ |
$3$ |
$0$ |
$1$ |
$[1, 5, 7, 25, 21, 53, 169, 289, 601, 1105]$ |
$3$ |
$[3, 81, 387, 7209, 23493, 219429, 2866377, 18865953, 159327513, 1161423441]$ |
$2$ |
$1$ |
$2$ |
$2$ |
$1$ |
6.0.1142512.1 |
$S_4\times C_2$ |
simple |
| 3.2.ac_c_ab |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 2 x^{2} - x^{3} + 4 x^{4} - 8 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 5, 10, 33, 31, 62, 155, 257, 586, 1065]$ |
$4$ |
$[4, 104, 592, 11024, 31604, 246272, 2553436, 16778528, 154949488, 1118339144]$ |
$2$ |
$1$ |
$2$ |
$2$ |
$1$ |
6.0.2464727.1 |
$S_4\times C_2$ |
simple |
| 3.2.ac_c_a |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 + 2 x + 2 x^{2} )( 1 - 2 x + 2 x^{2} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$4$ |
$0$ |
$3$ |
$0$ |
$3$ |
$1$ |
$[1, 5, 13, 41, 41, 65, 113, 161, 481, 1025]$ |
$5$ |
$[5, 125, 845, 15625, 42025, 274625, 1851505, 11390625, 126091745, 1076890625]$ |
$0$ |
$0$ |
$25$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.2.ac 2 $\times$ 1.2.c |
| 3.2.ac_d_ag |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 2 x + 3 x^{2} - 6 x^{3} + 6 x^{4} - 8 x^{5} + 8 x^{6}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$2$ |
$1$ |
$1$ |
$[1, 7, 1, 7, 21, 43, 141, 255, 397, 987]$ |
$2$ |
$[2, 68, 146, 2176, 22082, 183668, 2299978, 16720384, 106675922, 1036838228]$ |
$1$ |
$1$ |
$4$ |
$4$ |
$1$ |
6.0.399424.1 |
$D_{6}$ |
simple |
| 3.2.ac_d_af |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 2 x + 3 x^{2} - 5 x^{3} + 6 x^{4} - 8 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 7, 4, 15, 26, 52, 176, 311, 481, 1072]$ |
$3$ |
$[3, 99, 243, 4059, 26763, 216513, 3024024, 20786139, 125737191, 1122520509]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.3194271.1 |
$S_4\times C_2$ |
simple |
| 3.2.ac_d_ae |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - x + 2 x^{2} )( 1 - x - 2 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$1$ |
$[1, 7, 7, 23, 31, 55, 183, 319, 511, 1047]$ |
$4$ |
$[4, 128, 364, 6656, 30844, 221312, 3173132, 21325824, 133831516, 1096565888]$ |
$2$ |
$1$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \), 4.0.2312.1 |
$C_2$, $D_{4}$ |
1.2.ab $\times$ 2.2.ab_a |
| 3.2.ac_d_ad |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 2 x + 3 x^{2} - 3 x^{3} + 6 x^{4} - 8 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 7, 10, 31, 36, 52, 162, 279, 505, 1032]$ |
$5$ |
$[5, 155, 515, 10075, 36275, 207545, 2721640, 18386875, 132237065, 1080668525]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.2256319.1 |
$A_4\times C_2$ |
simple |
| 3.2.ac_d_ac |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 + x^{2} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$1$ |
$[1, 7, 13, 39, 41, 43, 113, 191, 481, 1147]$ |
$6$ |
$[6, 180, 702, 14400, 44526, 189540, 1823142, 12960000, 126467406, 1208880900]$ |
$0$ |
$0$ |
$12$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{3}, \sqrt{-5})\) |
$C_2$, $C_2^2$ |
1.2.ac $\times$ 2.2.a_b |
| 3.2.ac_e_ai |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 + 2 x^{2} )( 1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$4$ |
$0$ |
$3$ |
$0$ |
$3$ |
$1$ |
$[1, 9, 1, 1, 41, 81, 113, 257, 577, 1089]$ |
$3$ |
$[3, 117, 225, 1521, 43593, 342225, 1863921, 16769025, 152373825, 1140785217]$ |
$0$ |
$0$ |
$25$ |
$24$ |
$24$ |
\(\Q(\sqrt{-2}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2^2$ |
1.2.a $\times$ 2.2.ac_c |
| 3.2.ac_e_ah |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 + x + 2 x^{2} )( 1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$1$ |
$[1, 9, 4, 9, 41, 78, 155, 305, 508, 1029]$ |
$4$ |
$[4, 152, 304, 2736, 42284, 323456, 2557916, 20142432, 132772912, 1078157432]$ |
$1$ |
$1$ |
$8$ |
$12$ |
$6$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.b $\times$ 2.2.ad_f |
| 3.2.ac_e_ag |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
|
|
✓ |
✓ |
$1 - 2 x + 4 x^{2} - 6 x^{3} + 8 x^{4} - 8 x^{5} + 8 x^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3},\frac{2}{3}]$ |
$3$ |
$0$ |
$3$ |
$3$ |
$0$ |
$1$ |
$[1, 9, 7, 17, 41, 69, 169, 321, 457, 929]$ |
$5$ |
$[5, 185, 395, 4625, 40025, 277685, 2851945, 21538625, 120507785, 978891425]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
6.0.503792.1 |
$S_4\times C_2$ |
simple |
| 3.2.ac_e_af |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - x + 2 x^{2} )( 1 - x + x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 9, 10, 25, 41, 54, 155, 305, 442, 909]$ |
$6$ |
$[6, 216, 504, 7344, 39666, 217728, 2606694, 20225376, 116867016, 958171896]$ |
$1$ |
$1$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \), 4.0.2873.1 |
$C_2$, $D_{4}$ |
1.2.ab $\times$ 2.2.ab_b |
| 3.2.ac_e_ae |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} + 4 x^{4} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$4$ |
$0$ |
$3$ |
$0$ |
$3$ |
$1$ |
$[1, 9, 13, 33, 41, 33, 113, 257, 481, 1089]$ |
$7$ |
$[7, 245, 637, 11025, 43337, 156065, 1865969, 16769025, 125599201, 1145180225]$ |
$0$ |
$0$ |
$25$ |
$24$ |
$24$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.2.ac $\times$ 2.2.a_c |
| 3.2.ac_f_ai |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 + 2 x^{2} )( 1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$2$ |
$1$ |
$1$ |
$[1, 11, 7, 7, 51, 107, 127, 223, 547, 1051]$ |
$6$ |
$[6, 252, 558, 2016, 58146, 492156, 2069934, 14716800, 143731314, 1101401532]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \), 4.0.1088.2 |
$C_2$, $D_{4}$ |
1.2.a $\times$ 2.2.ac_d |
| 3.2.ac_f_ah |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 2 x + 5 x^{2} - 7 x^{3} + 10 x^{4} - 8 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 11, 10, 15, 46, 80, 134, 263, 451, 876]$ |
$7$ |
$[7, 287, 637, 3731, 46067, 339521, 2170504, 17285723, 118627873, 927374777]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.400967.1 |
$A_4\times C_2$ |
simple |
| 3.2.ac_f_ag |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$1$ |
$[1, 11, 13, 23, 41, 47, 113, 287, 481, 911]$ |
$8$ |
$[8, 320, 728, 6400, 39688, 203840, 1861336, 18662400, 126572264, 960449600]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$, $C_2$ |
1.2.ac $\times$ 1.2.ab $\times$ 1.2.b |
| 3.2.ac_g_ai |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$4$ |
$0$ |
$3$ |
$0$ |
$3$ |
$1$ |
$[1, 13, 13, 9, 41, 97, 113, 161, 481, 1153]$ |
$9$ |
$[9, 405, 1053, 2025, 44649, 426465, 1880433, 11390625, 126584289, 1215569025]$ |
$0$ |
$0$ |
$25$ |
$24$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.2.ac $\times$ 1.2.a 2 |
| 3.2.ac_g_ah |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$1$ |
$[1, 13, 16, 17, 31, 46, 99, 289, 592, 993]$ |
$10$ |
$[10, 440, 1120, 4400, 30250, 197120, 1640810, 19087200, 156684640, 1039511000]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \), 4.0.1025.1 |
$C_2$, $D_{4}$ |
1.2.ab $\times$ 2.2.ab_d |
| 3.2.ac_h_ai |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 + 2 x^{2} )( 1 - x + 2 x^{2} )^{2}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$1$ |
$[1, 15, 19, 7, 11, 63, 155, 287, 523, 975]$ |
$12$ |
$[12, 576, 1764, 2304, 15972, 254016, 2601156, 18662400, 137650212, 1020419136]$ |
$0$ |
$0$ |
$18$ |
$24$ |
$2$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.2.ab 2 $\times$ 1.2.a |
| 3.2.ab_ac_e |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 - 2 x^{2} )^{2}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$1$ |
$2$ |
$2$ |
$[2, 0, 14, 0, 22, 24, 142, 224, 518, 840]$ |
$2$ |
$[2, 8, 686, 1296, 21142, 134456, 2290318, 14580000, 135260678, 893968328]$ |
$0$ |
$0$ |
$22$ |
$24$ |
$2$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{2}) \) |
$C_2$, $C_2$ |
1.2.ab $\times$ 2.2.a_ae |
