| 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 |
| 2.2.ae_i |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x + 2 x^{2} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$-1$ |
$[-1, 5, 17, 33, 49, 65, 97, 193, 449, 1025]$ |
$1$ |
$[1, 25, 169, 625, 1681, 4225, 12769, 50625, 231361, 1050625]$ |
$0$ |
$0$ |
$11$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.2.ac 2 |
| 2.2.ad_f |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 5 x^{2} - 6 x^{3} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$0$ |
$[0, 6, 9, 10, 30, 87, 168, 274, 513, 1086]$ |
$1$ |
$[1, 19, 76, 171, 961, 5776, 22051, 69939, 261364, 1113799]$ |
$1$ |
$1$ |
$4$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2^2$ |
simple |
| 2.2.ad_g |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 2 x + 2 x^{2} )( 1 - x + 2 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$0$ |
$[0, 8, 18, 24, 30, 56, 126, 256, 486, 968]$ |
$2$ |
$[2, 40, 182, 400, 902, 3640, 16046, 64800, 249158, 992200]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac $\times$ 1.2.ab |
| 2.2.ac_c |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
|
|
✓ |
✓ |
✓ |
$1 - 2 x + 2 x^{2} - 4 x^{3} + 4 x^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$1$ |
$[1, 5, 1, 9, 41, 65, 113, 289, 577, 1025]$ |
$1$ |
$[1, 13, 25, 169, 1321, 4225, 14449, 74529, 297025, 1047553]$ |
$1$ |
$1$ |
$11$ |
$24$ |
$12$ |
\(\Q(\zeta_{12})\) |
$C_2^2$ |
simple |
| 2.2.ac_d |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 3 x^{2} - 4 x^{3} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$1$ |
$[1, 7, 7, 15, 51, 91, 127, 255, 547, 987]$ |
$2$ |
$[2, 28, 62, 224, 1762, 6076, 16046, 65408, 280178, 1011388]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.1088.2 |
$D_{4}$ |
simple |
| 2.2.ac_e |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
✓ |
$( 1 - 2 x + 2 x^{2} )( 1 + 2 x^{2} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$1$ |
$[1, 9, 13, 17, 41, 81, 113, 193, 481, 1089]$ |
$3$ |
$[3, 45, 117, 225, 1353, 5265, 14577, 50625, 246753, 1116225]$ |
$1$ |
$1$ |
$11$ |
$24$ |
$8$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.2.ac $\times$ 1.2.a |
| 2.2.ac_f |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$1$ |
$[1, 11, 19, 15, 11, 47, 155, 319, 523, 911]$ |
$4$ |
$[4, 64, 196, 256, 484, 3136, 20164, 82944, 268324, 937024]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
1.2.ab 2 |
| 2.2.ab_ab |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
|
|
$1 - x - x^{2} - 2 x^{3} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$2$ |
$[2, 2, -1, 18, 22, 47, 142, 226, 503, 1082]$ |
$1$ |
$[1, 7, 16, 259, 751, 3136, 18103, 58275, 258064, 1109227]$ |
$0$ |
$0$ |
$6$ |
$12$ |
$3$ |
\(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2^2$ |
simple |
| 2.2.ab_a |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - x - 2 x^{3} + 4 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$2$ |
$[2, 4, 2, 24, 42, 64, 170, 288, 506, 1104]$ |
$2$ |
$[2, 16, 26, 416, 1402, 3952, 22346, 74048, 258362, 1132816]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.2312.1 |
$D_{4}$ |
simple |
| 2.2.ab_b |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + x^{2} - 2 x^{3} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$[2, 6, 5, 26, 52, 63, 142, 274, 437, 966]$ |
$3$ |
$[3, 27, 36, 459, 1803, 3888, 18357, 70227, 225612, 989847]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.2873.1 |
$D_{4}$ |
simple |
| 2.2.ab_c |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 2 x + 2 x^{2} )( 1 + x + 2 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$2$ |
$[2, 8, 8, 24, 52, 56, 100, 256, 476, 968]$ |
$4$ |
$[4, 40, 52, 400, 1804, 3640, 13108, 64800, 244348, 992200]$ |
$1$ |
$1$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ac $\times$ 1.2.b |
| 2.2.ab_d |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + 3 x^{2} - 2 x^{3} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$[2, 10, 11, 18, 42, 55, 86, 258, 587, 1050]$ |
$5$ |
$[5, 55, 80, 275, 1375, 3520, 11555, 66275, 302480, 1073875]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.1025.1 |
$D_{4}$ |
simple |
| 2.2.ab_e |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 + 2 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$2$ |
$[2, 12, 14, 8, 22, 72, 142, 256, 518, 1032]$ |
$6$ |
$[6, 72, 126, 144, 726, 4536, 18318, 64800, 265734, 1054152]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$2$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.2.ab $\times$ 1.2.a |
| 2.2.a_ae |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 2 x^{2} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$3$ |
$[3, -3, 9, 1, 33, 33, 129, 193, 513, 897]$ |
$1$ |
$[1, 1, 49, 81, 961, 2401, 16129, 50625, 261121, 923521]$ |
$0$ |
$0$ |
$11$ |
$24$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$C_2$ |
simple |
| 2.2.a_ad |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
|
$1 - 3 x^{2} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$3$ |
$[3, -1, 9, 15, 33, 83, 129, 319, 513, 1139]$ |
$2$ |
$[2, 4, 74, 256, 1082, 5476, 16298, 82944, 261146, 1170724]$ |
$0$ |
$0$ |
$6$ |
$12$ |
$2$ |
\(\Q(i, \sqrt{7})\) |
$C_2^2$ |
simple |
| 2.2.a_ac |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
|
|
✓ |
✓ |
|
$1 - 2 x^{2} + 4 x^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$3$ |
$[3, 1, 9, 25, 33, 97, 129, 289, 513, 961]$ |
$3$ |
$[3, 9, 81, 441, 993, 6561, 16257, 74529, 263169, 986049]$ |
$0$ |
$0$ |
$11$ |
$24$ |
$6$ |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
$C_2^2$ |
simple |
| 2.2.a_ab |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x^{2} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$3$ |
$[3, 3, 9, 31, 33, 87, 129, 223, 513, 903]$ |
$4$ |
$[4, 16, 76, 576, 964, 5776, 16636, 57600, 261364, 929296]$ |
$1$ |
$1$ |
$4$ |
$6$ |
$2$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2^2$ |
simple |
| 2.2.a_a |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
✓ |
$( 1 - 2 x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$3$ |
$[3, 5, 9, 33, 33, 65, 129, 193, 513, 1025]$ |
$5$ |
$[5, 25, 65, 625, 1025, 4225, 16385, 50625, 262145, 1050625]$ |
$1$ |
$1$ |
$11$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.2.ac $\times$ 1.2.c |
| 2.2.a_b |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x^{2} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$3$ |
$[3, 7, 9, 31, 33, 43, 129, 223, 513, 1147]$ |
$6$ |
$[6, 36, 54, 576, 1086, 2916, 16134, 57600, 262926, 1179396]$ |
$1$ |
$1$ |
$4$ |
$12$ |
$2$ |
\(\Q(\sqrt{3}, \sqrt{-5})\) |
$C_2^2$ |
simple |
| 2.2.a_c |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
|
|
✓ |
✓ |
✓ |
$1 + 2 x^{2} + 4 x^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$3$ |
$[3, 9, 9, 25, 33, 33, 129, 289, 513, 1089]$ |
$7$ |
$[7, 49, 49, 441, 1057, 2401, 16513, 74529, 261121, 1117249]$ |
$1$ |
$1$ |
$11$ |
$24$ |
$6$ |
\(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2^2$ |
simple |
| 2.2.a_d |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 2 x^{2} )( 1 + x + 2 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$3$ |
$[3, 11, 9, 15, 33, 47, 129, 319, 513, 911]$ |
$8$ |
$[8, 64, 56, 256, 968, 3136, 16472, 82944, 263144, 937024]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$2$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.ab $\times$ 1.2.b |
| 2.2.a_e |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 + 2 x^{2} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$3$ |
$[3, 13, 9, 1, 33, 97, 129, 193, 513, 1153]$ |
$9$ |
$[9, 81, 81, 81, 1089, 6561, 16641, 50625, 263169, 1185921]$ |
$0$ |
$0$ |
$11$ |
$24$ |
$2$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
1.2.a 2 |
| 2.2.b_ab |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
|
|
$1 + x - x^{2} + 2 x^{3} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$4$ |
$[4, 2, 19, 18, 44, 47, 116, 226, 523, 1082]$ |
$7$ |
$[7, 7, 196, 259, 1477, 3136, 14749, 58275, 268324, 1109227]$ |
$0$ |
$0$ |
$6$ |
$12$ |
$3$ |
\(\Q(\sqrt{-3}, \sqrt{-7})\) |
$C_2^2$ |
simple |
| 2.2.b_a |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 + x + 2 x^{3} + 4 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$4$ |
$[4, 4, 16, 24, 24, 64, 88, 288, 520, 1104]$ |
$8$ |
$[8, 16, 152, 416, 808, 3952, 11768, 74048, 265544, 1132816]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.2312.1 |
$D_{4}$ |
simple |
| 2.2.b_b |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + x^{2} + 2 x^{3} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$4$ |
$[4, 6, 13, 26, 14, 63, 116, 274, 589, 966]$ |
$9$ |
$[9, 27, 108, 459, 549, 3888, 15003, 70227, 303588, 989847]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.2873.1 |
$D_{4}$ |
simple |
| 2.2.b_c |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$4$ |
$[4, 8, 10, 24, 14, 56, 158, 256, 550, 968]$ |
$10$ |
$[10, 40, 70, 400, 550, 3640, 20590, 64800, 282310, 992200]$ |
$1$ |
$1$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.2.ab $\times$ 1.2.c |
| 2.2.b_d |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + 3 x^{2} + 2 x^{3} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$4$ |
$[4, 10, 7, 18, 24, 55, 172, 258, 439, 1050]$ |
$11$ |
$[11, 55, 44, 275, 781, 3520, 22649, 66275, 226556, 1073875]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.1025.1 |
$D_{4}$ |
simple |
| 2.2.b_e |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 + 2 x^{2} )( 1 + x + 2 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$4$ |
$[4, 12, 4, 8, 44, 72, 116, 256, 508, 1032]$ |
$12$ |
$[12, 72, 36, 144, 1452, 4536, 14964, 64800, 260604, 1054152]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.2.a $\times$ 1.2.b |
| 2.2.c_c |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
|
|
✓ |
✓ |
✓ |
$1 + 2 x + 2 x^{2} + 4 x^{3} + 4 x^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$5$ |
$[5, 5, 17, 9, 25, 65, 145, 289, 449, 1025]$ |
$13$ |
$[13, 13, 169, 169, 793, 4225, 18577, 74529, 231361, 1047553]$ |
$1$ |
$1$ |
$11$ |
$24$ |
$12$ |
\(\Q(\zeta_{12})\) |
$C_2^2$ |
simple |
| 2.2.c_d |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x + 3 x^{2} + 4 x^{3} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 7, 11, 15, 15, 91, 131, 255, 479, 987]$ |
$14$ |
$[14, 28, 98, 224, 574, 6076, 16562, 65408, 245294, 1011388]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.1088.2 |
$D_{4}$ |
simple |
| 2.2.c_e |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
✓ |
$( 1 + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$5$ |
$[5, 9, 5, 17, 25, 81, 145, 193, 545, 1089]$ |
$15$ |
$[15, 45, 45, 225, 825, 5265, 18705, 50625, 279585, 1116225]$ |
$1$ |
$1$ |
$11$ |
$24$ |
$8$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.2.a $\times$ 1.2.c |
| 2.2.c_f |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 + x + 2 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$5$ |
$[5, 11, -1, 15, 55, 47, 103, 319, 503, 911]$ |
$16$ |
$[16, 64, 16, 256, 1936, 3136, 13456, 82944, 258064, 937024]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
1.2.b 2 |
| 2.2.d_f |
$2$ |
$\F_{2}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 3 x + 5 x^{2} + 6 x^{3} + 4 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$6$ |
$[6, 6, 9, 10, 36, 87, 90, 274, 513, 1086]$ |
$19$ |
$[19, 19, 76, 171, 1159, 5776, 11989, 69939, 261364, 1113799]$ |
$1$ |
$1$ |
$4$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2^2$ |
simple |
| 2.2.d_g |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 + x + 2 x^{2} )( 1 + 2 x + 2 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$6$ |
$[6, 8, 0, 24, 36, 56, 132, 256, 540, 968]$ |
$20$ |
$[20, 40, 20, 400, 1100, 3640, 16820, 64800, 276860, 992200]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.2.b $\times$ 1.2.c |
| 2.2.e_i |
$2$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 + 2 x + 2 x^{2} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$7$ |
$[7, 5, 1, 33, 17, 65, 161, 193, 577, 1025]$ |
$25$ |
$[25, 25, 25, 625, 625, 4225, 21025, 50625, 297025, 1050625]$ |
$0$ |
$0$ |
$11$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.2.c 2 |
| 2.3.ag_p |
$2$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
✓ |
✓ |
|
$( 1 - 3 x + 3 x^{2} )^{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$-2$ |
$[-2, 4, 28, 100, 298, 838, 2350, 6724, 19684, 58564]$ |
$1$ |
$[1, 49, 784, 8281, 73441, 614656, 5148361, 44129449, 387459856, 3458263249]$ |
$0$ |
$0$ |
$9$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.3.ad 2 |
| 2.3.af_m |
$2$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 3 x + 3 x^{2} )( 1 - 2 x + 3 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$-1$ |
$[-1, 9, 38, 105, 269, 738, 2183, 6609, 19874, 59289]$ |
$2$ |
$[2, 84, 1064, 8736, 65582, 536256, 4769438, 43365504, 391199816, 3500898324]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.3.ad $\times$ 1.3.ac |
| 2.3.ae_i |
$2$ |
$\F_{3}$ |
$3$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 4 x + 8 x^{2} - 12 x^{3} + 9 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$0$ |
$[0, 10, 24, 54, 200, 730, 2240, 6494, 19392, 59050]$ |
$2$ |
$[2, 68, 626, 4624, 49282, 532100, 4898098, 42614784, 381715394, 3486898628]$ |
$1$ |
$1$ |
$8$ |
$24$ |
$4$ |
\(\Q(\zeta_{8})\) |
$C_2^2$ |
simple |
| 2.3.ae_j |
$2$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 3 x + 3 x^{2} )( 1 - x + 3 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$0$ |
$[0, 12, 36, 84, 240, 774, 2352, 6756, 19548, 58332]$ |
$3$ |
$[3, 105, 1008, 6825, 57723, 564480, 5152899, 44342025, 384782832, 3444620025]$ |
$1$ |
$1$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.3.ad $\times$ 1.3.ab |
| 2.3.ae_k |
$2$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 2 x + 3 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$0$ |
$[0, 14, 48, 110, 240, 638, 2016, 6494, 20064, 60014]$ |
$4$ |
$[4, 144, 1444, 9216, 58564, 467856, 4418404, 42614784, 394975876, 3544059024]$ |
$1$ |
$1$ |
$8$ |
$8$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
1.3.ac 2 |
| 2.3.ad_f |
$2$ |
$\F_{3}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 5 x^{2} - 9 x^{3} + 9 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$1$ |
$[1, 11, 19, 59, 256, 791, 2185, 6563, 20143, 59846]$ |
$3$ |
$[3, 81, 549, 4941, 62448, 578097, 4778049, 43050933, 396546543, 3534057216]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.2197.1 |
$C_4$ |
simple |
| 2.3.ad_g |
$2$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
|
✓ |
✓ |
✓ |
$( 1 - 3 x + 3 x^{2} )( 1 + 3 x^{2} )$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$1$ |
$[1, 13, 28, 73, 271, 838, 2269, 6481, 19684, 59293]$ |
$4$ |
$[4, 112, 784, 5824, 66124, 614656, 4964572, 42515200, 387459856, 3501133552]$ |
$1$ |
$1$ |
$9$ |
$24$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.3.ad $\times$ 1.3.a |
| 2.3.ad_h |
$2$ |
$\F_{3}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 7 x^{2} - 9 x^{3} + 9 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$1$ |
$[1, 15, 37, 83, 256, 795, 2227, 6323, 19171, 58950]$ |
$5$ |
$[5, 145, 1055, 6525, 62000, 581305, 4870955, 41505525, 377427305, 3480928000]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.1525.1 |
$D_{4}$ |
simple |
| 2.3.ad_i |
$2$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 3 x^{2} )( 1 - x + 3 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$1$ |
$[1, 17, 46, 89, 211, 674, 2185, 6641, 19738, 59057]$ |
$6$ |
$[6, 180, 1368, 7200, 51546, 492480, 4773642, 43574400, 388496952, 3487086900]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.3.ac $\times$ 1.3.ab |
| 2.3.ac_b |
$2$ |
$\F_{3}$ |
$3$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + x^{2} - 6 x^{3} + 9 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$2$ |
$[2, 8, 8, 68, 242, 638, 2102, 6596, 19304, 58568]$ |
$3$ |
$[3, 57, 324, 5529, 58323, 467856, 4600011, 43264425, 380016036, 3458495577]$ |
$1$ |
$1$ |
$8$ |
$24$ |
$3$ |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
$C_2^2$ |
simple |
| 2.3.ac_c |
$2$ |
$\F_{3}$ |
$3$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 2 x^{2} - 6 x^{3} + 9 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$2$ |
$[2, 10, 14, 78, 282, 730, 2214, 6878, 19922, 59050]$ |
$4$ |
$[4, 80, 436, 6400, 69044, 531920, 4840196, 45158400, 392133604, 3486722000]$ |
$2$ |
$2$ |
$4$ |
$8$ |
$4$ |
\(\Q(i, \sqrt{5})\) |
$C_2^2$ |
simple |
| 2.3.ac_d |
$2$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 3 x + 3 x^{2} )( 1 + x + 3 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$2$ |
$[2, 12, 20, 84, 302, 774, 2186, 6756, 19820, 58332]$ |
$5$ |
$[5, 105, 560, 6825, 74525, 564480, 4776245, 44342025, 390136880, 3444620025]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.3.ad $\times$ 1.3.b |
| 2.3.ac_e |
$2$ |
$\F_{3}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 4 x^{2} - 6 x^{3} + 9 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$[2, 14, 26, 86, 302, 782, 2102, 6494, 19682, 58334]$ |
$6$ |
$[6, 132, 702, 6864, 74526, 571428, 4598502, 42611712, 387350262, 3444740772]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.7488.1 |
$D_{4}$ |
simple |
| 2.3.ac_f |
$2$ |
$\F_{3}$ |
$3$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 5 x^{2} - 6 x^{3} + 9 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$[2, 16, 32, 84, 282, 766, 2046, 6308, 19760, 59296]$ |
$7$ |
$[7, 161, 868, 6601, 69167, 558992, 4481687, 41408073, 388913476, 3501441041]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.4672.2 |
$D_{4}$ |
simple |
| 2.3.ac_g |
$2$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 2 x + 3 x^{2} )( 1 + 3 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$2$ |
$[2, 18, 38, 78, 242, 738, 2102, 6366, 19874, 60018]$ |
$8$ |
$[8, 192, 1064, 6144, 59048, 536256, 4599176, 41779200, 391199816, 3544297152]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$2$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.3.ac $\times$ 1.3.a |
