| 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 |
| 2.8.ak_bp |
$2$ |
$\F_{2^{3}}$ |
$2$ |
|
|
|
✓ |
|
|
✓ |
|
$( 1 - 5 x + 8 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$-1$ |
$[-1, 47, 503, 4191, 33319, 264143, 2102743, 16789183, 134232839, 1073721647]$ |
$16$ |
$[16, 3136, 258064, 17172736, 1091905936, 69244764736, 4409781602704, 281675802240000, 18016426864880656, 1152899840893573696]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
1.8.af 2 |
| 2.8.aj_bk |
$2$ |
$\F_{2^{3}}$ |
$2$ |
|
|
|
|
✓ |
|
✓ |
|
$( 1 - 5 x + 8 x^{2} )( 1 - 4 x + 8 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$0$ |
$[0, 56, 540, 4272, 33300, 263144, 2097900, 16775008, 134208900, 1073731736]$ |
$20$ |
$[20, 3640, 276860, 17508400, 1091278100, 68981883880, 4399611554540, 281437900380000, 18013213645806980, 1152910673773058200]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.8.af $\times$ 1.8.ae |
| 2.8.ah_bc |
$2$ |
$\F_{2^{3}}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 4 x + 8 x^{2} )( 1 - 3 x + 8 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$2$ |
$[2, 72, 590, 4304, 32902, 261144, 2093086, 16770976, 134223350, 1073792232]$ |
$30$ |
$[30, 4680, 304110, 17643600, 1078134150, 68457593880, 4389525719070, 281370287671200, 18015152855242230, 1152975630858503400]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-23}) \) |
$C_2$, $C_2$ |
1.8.ae $\times$ 1.8.ad |
| 2.8.ab_ah |
$2$ |
$\F_{2^{3}}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
|
|
$1 - x - 7 x^{2} - 8 x^{3} + 64 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$8$ |
$[8, 50, 467, 4194, 32488, 263135, 2099896, 16778434, 134264051, 1073755250]$ |
$49$ |
$[49, 3283, 240100, 17179939, 1064579929, 68979769600, 4403804428681, 281495379287619, 18020616547992100, 1152935918697336403]$ |
$0$ |
$0$ |
$6$ |
$12$ |
$3$ |
\(\Q(\sqrt{-3}, \sqrt{-31})\) |
$C_2^2$ |
simple |
| 2.8.ab_q |
$2$ |
$\F_{2^{3}}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - x + 8 x^{2} )( 1 + 8 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$8$ |
$[8, 96, 536, 3872, 32488, 263664, 2099896, 16767808, 134194568, 1073793936]$ |
$72$ |
$[72, 6480, 274968, 15876000, 1064599272, 69118706160, 4403803196088, 281317163400000, 18011290161096072, 1152977459634752400]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$2$ |
\(\Q(\sqrt{-31}) \), \(\Q(\sqrt{-2}) \) |
$C_2$, $C_2$ |
1.8.ab $\times$ 1.8.a |
| 2.8.a_ap |
$2$ |
$\F_{2^{3}}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
|
$1 - 15 x^{2} + 64 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$9$ |
$[9, 35, 513, 3903, 32769, 261155, 2097153, 16774783, 134217729, 1073768675]$ |
$50$ |
$[50, 2500, 261650, 16000000, 1073755250, 68460722500, 4398049840850, 281434176000000, 18014398777478450, 1152950336902562500]$ |
$0$ |
$0$ |
$6$ |
$12$ |
$2$ |
\(\Q(i, \sqrt{31})\) |
$C_2^2$ |
simple |
| 2.8.a_ai |
$2$ |
$\F_{2^{3}}$ |
$2$ |
✓ |
|
✓ |
|
|
✓ |
✓ |
|
$1 - 8 x^{2} + 64 x^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$9$ |
$[9, 49, 513, 4225, 32769, 264193, 2097153, 16785409, 134217729, 1073676289]$ |
$57$ |
$[57, 3249, 263169, 17313921, 1073709057, 69257922561, 4398044413953, 281612466003969, 18014398777917441, 1152851139083829249]$ |
$0$ |
$0$ |
$11$ |
$24$ |
$6$ |
\(\Q(\sqrt{-2}, \sqrt{-3})\) |
$C_2^2$ |
simple |
| 2.8.b_ah |
$2$ |
$\F_{2^{3}}$ |
$2$ |
✓ |
|
✓ |
✓ |
|
|
|
|
$1 + x - 7 x^{2} + 8 x^{3} + 64 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$10$ |
$[10, 50, 559, 4194, 33050, 263135, 2094410, 16778434, 134171407, 1073755250]$ |
$67$ |
$[67, 3283, 287296, 17179939, 1082996107, 68979769600, 4392299447323, 281495379287619, 18008182080706624, 1152935918697336403]$ |
$0$ |
$0$ |
$6$ |
$12$ |
$3$ |
\(\Q(\sqrt{-3}, \sqrt{-31})\) |
$C_2^2$ |
simple |
| 2.8.b_q |
$2$ |
$\F_{2^{3}}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 + 8 x^{2} )( 1 + x + 8 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$10$ |
$[10, 96, 490, 3872, 33050, 263664, 2094410, 16767808, 134240890, 1073793936]$ |
$90$ |
$[90, 6480, 251370, 15876000, 1083015450, 69118706160, 4392298214730, 281317163400000, 18017507394738810, 1152977459634752400]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$2$ |
\(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-31}) \) |
$C_2$, $C_2$ |
1.8.a $\times$ 1.8.b |
| 2.8.h_bc |
$2$ |
$\F_{2^{3}}$ |
$2$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 + 3 x + 8 x^{2} )( 1 + 4 x + 8 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$16$ |
$[16, 72, 436, 4304, 32636, 261144, 2101220, 16770976, 134212108, 1073792232]$ |
$156$ |
$[156, 4680, 225108, 17643600, 1069417596, 68457593880, 4406583961572, 281370287671200, 18013643979532812, 1152975630858503400]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.8.d $\times$ 1.8.e |
| 2.8.j_bk |
$2$ |
$\F_{2^{3}}$ |
$2$ |
|
|
|
|
✓ |
|
✓ |
|
$( 1 + 4 x + 8 x^{2} )( 1 + 5 x + 8 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$18$ |
$[18, 56, 486, 4272, 32238, 263144, 2096406, 16775008, 134226558, 1073731736]$ |
$182$ |
$[182, 3640, 249158, 17508400, 1056477422, 68981883880, 4396478407958, 281437900380000, 18015583662465662, 1152910673773058200]$ |
$0$ |
$0$ |
$6$ |
$8$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.8.e $\times$ 1.8.f |
| 2.8.k_bp |
$2$ |
$\F_{2^{3}}$ |
$2$ |
|
|
|
✓ |
|
|
✓ |
|
$( 1 + 5 x + 8 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$19$ |
$[19, 47, 523, 4191, 32219, 264143, 2091563, 16789183, 134202619, 1073721647]$ |
$196$ |
$[196, 3136, 268324, 17172736, 1055860036, 69244764736, 4386335432164, 281675802240000, 18012370805110276, 1152899840893573696]$ |
$0$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
1.8.f 2 |
