| 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.ab_a_a |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
|
|
✓ |
✓ |
$1 - x - 4 x^{5} + 8 x^{6}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$3$ |
$0$ |
$2$ |
$[2, 4, 8, 16, 12, 88, 156, 288, 548, 984]$ |
$4$ |
$[4, 56, 556, 4144, 16564, 381416, 2586476, 19037536, 143325124, 1029850136]$ |
$3$ |
$2$ |
$2$ |
$2$ |
$1$ |
6.0.839056.1 |
$S_4\times C_2$ |
simple |
| 3.2.ab_b_ad |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + x^{2} - 3 x^{3} + 2 x^{4} - 4 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 6, 2, 14, 22, 78, 170, 222, 542, 1166]$ |
$4$ |
$[4, 80, 244, 3200, 25084, 326960, 2899124, 14566400, 142200028, 1231624400]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
6.0.503792.1 |
$S_4\times C_2$ |
simple |
| 3.2.ab_b_b |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - x + 2 x^{2} )( 1 - x^{2} + 4 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$2$ |
$[2, 6, 14, 30, 22, 78, 142, 254, 518, 846]$ |
$8$ |
$[8, 128, 1064, 9216, 21208, 323456, 2362312, 16588800, 135386552, 899558528]$ |
$3$ |
$2$ |
$8$ |
$6$ |
$2$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.ab $\times$ 2.2.a_ab |
| 3.2.ab_c_ac |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
|
|
✓ |
✓ |
$1 - x + 2 x^{2} - 2 x^{3} + 4 x^{4} - 4 x^{5} + 8 x^{6}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$3$ |
$0$ |
$2$ |
$[2, 8, 8, 24, 32, 80, 184, 224, 440, 1008]$ |
$8$ |
$[8, 176, 488, 5984, 31768, 332816, 3193352, 14852288, 116449976, 1056031856]$ |
$3$ |
$2$ |
$2$ |
$2$ |
$1$ |
6.0.2296688.1 |
$S_4\times C_2$ |
simple |
| 3.2.ab_d_ad |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + 3 x^{2} - 3 x^{3} + 6 x^{4} - 4 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$2$ |
$[2, 10, 8, 22, 42, 70, 156, 222, 386, 1050]$ |
$10$ |
$[10, 260, 430, 5200, 44050, 279500, 2611010, 14684800, 104258230, 1100633300]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
6.0.3307504.1 |
$S_4\times C_2$ |
simple |
| 3.2.a_b_a |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 + 2 x^{2} )( 1 - x^{2} + 4 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$3$ |
$[3, 7, 9, 23, 33, 103, 129, 191, 513, 967]$ |
$12$ |
$[12, 144, 684, 5184, 31812, 467856, 2146044, 12960000, 134079732, 1012003344]$ |
$3$ |
$2$ |
$12$ |
$24$ |
$2$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.a $\times$ 2.2.a_ab |
| 3.2.a_c_ab |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x^{2} - x^{3} + 4 x^{4} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$3$ |
$[3, 9, 6, 25, 43, 78, 129, 177, 510, 1069]$ |
$14$ |
$[14, 224, 392, 5824, 45794, 326144, 2103374, 12218752, 133422296, 1121769824]$ |
$3$ |
$2$ |
$2$ |
$2$ |
$1$ |
6.0.6660007.1 |
$S_4\times C_2$ |
simple |
| 3.2.a_c_b |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x^{2} + x^{3} + 4 x^{4} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$3$ |
$[3, 9, 12, 25, 23, 78, 129, 177, 516, 1069]$ |
$16$ |
$[16, 224, 832, 5824, 24496, 326144, 2098672, 12218752, 135024448, 1121769824]$ |
$3$ |
$2$ |
$2$ |
$2$ |
$1$ |
6.0.6660007.1 |
$S_4\times C_2$ |
simple |
| 3.2.b_a_a |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
|
|
✓ |
✓ |
$1 + x + 4 x^{5} + 8 x^{6}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$3$ |
$0$ |
$4$ |
$[4, 4, 10, 16, 54, 88, 102, 288, 478, 984]$ |
$14$ |
$[14, 56, 686, 4144, 62174, 381416, 1694518, 19037536, 125011838, 1029850136]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
6.0.839056.1 |
$S_4\times C_2$ |
simple |
| 3.2.b_b_ab |
$3$ |
$\F_{2}$ |
$2$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 + x + 2 x^{2} )( 1 - x^{2} + 4 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$4$ |
$[4, 6, 4, 30, 44, 78, 116, 254, 508, 846]$ |
$16$ |
$[16, 128, 304, 9216, 42416, 323456, 1929776, 16588800, 132772912, 899558528]$ |
$2$ |
$2$ |
$8$ |
$6$ |
$2$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.2.b $\times$ 2.2.a_ab |
| 3.2.b_b_d |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + x^{2} + 3 x^{3} + 2 x^{4} + 4 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$4$ |
$[4, 6, 16, 14, 44, 78, 88, 222, 484, 1166]$ |
$20$ |
$[20, 80, 1340, 3200, 49100, 326960, 1530220, 14566400, 126969020, 1231624400]$ |
$3$ |
$2$ |
$2$ |
$2$ |
$1$ |
6.0.503792.1 |
$S_4\times C_2$ |
simple |
| 3.2.b_c_c |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
|
|
|
✓ |
✓ |
$1 + x + 2 x^{2} + 2 x^{3} + 4 x^{4} + 4 x^{5} + 8 x^{6}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$3$ |
$0$ |
$4$ |
$[4, 8, 10, 24, 34, 80, 74, 224, 586, 1008]$ |
$22$ |
$[22, 176, 682, 5984, 33242, 332816, 1351834, 14852288, 154874698, 1056031856]$ |
$3$ |
$2$ |
$2$ |
$2$ |
$1$ |
6.0.2296688.1 |
$S_4\times C_2$ |
simple |
| 3.2.b_d_d |
$3$ |
$\F_{2}$ |
$2$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + 3 x^{2} + 3 x^{3} + 6 x^{4} + 4 x^{5} + 8 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$4$ |
$[4, 10, 10, 22, 24, 70, 102, 222, 640, 1050]$ |
$26$ |
$[26, 260, 650, 5200, 24986, 279500, 1714102, 14684800, 171253550, 1100633300]$ |
$3$ |
$2$ |
$2$ |
$2$ |
$1$ |
6.0.3307504.1 |
$S_4\times C_2$ |
simple |
