Invariants
Base field: | $\F_{2^{3}}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 3 x + 8 x^{2} )( 1 - 7 x + 27 x^{2} - 56 x^{3} + 64 x^{4} )$ |
$1 - 10 x + 56 x^{2} - 193 x^{3} + 448 x^{4} - 640 x^{5} + 512 x^{6}$ | |
Frobenius angles: | $\pm0.195988130520$, $\pm0.322067999368$, $\pm0.361652535788$ |
Angle rank: | $3$ (numerical) |
Isomorphism classes: | 9 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $3$ |
Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $174$ | $323640$ | $163179288$ | $72174956400$ | $35119392164274$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $77$ | $614$ | $4297$ | $32709$ | $261134$ | $2096555$ | $16785169$ | $134238782$ | $1073703757$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{3}}$.
Endomorphism algebra over $\F_{2^{3}}$The isogeny class factors as 1.8.ad $\times$ 2.8.ah_bb and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
Twist | Extension degree | Common base change |
---|---|---|
3.8.ae_o_abf | $2$ | (not in LMFDB) |
3.8.e_o_bf | $2$ | (not in LMFDB) |
3.8.k_ce_hl | $2$ | (not in LMFDB) |