Invariants
Base field: | $\F_{2^{3}}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 5 x + 8 x^{2} )( 1 - 7 x + 27 x^{2} - 56 x^{3} + 64 x^{4} )$ |
$1 - 12 x + 70 x^{2} - 247 x^{3} + 560 x^{4} - 768 x^{5} + 512 x^{6}$ | |
Frobenius angles: | $\pm0.154919815756$, $\pm0.195988130520$, $\pm0.361652535788$ |
Angle rank: | $3$ (numerical) |
Isomorphism classes: | 3 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $116$ | $251720$ | $148557488$ | $71621891600$ | $35547546243836$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-3$ | $61$ | $564$ | $4265$ | $33107$ | $263134$ | $2101369$ | $16789201$ | $134224332$ | $1073643261$ |
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.af $\times$ 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.ac_a_x | $2$ | (not in LMFDB) |
3.8.c_a_ax | $2$ | (not in LMFDB) |
3.8.m_cs_jn | $2$ | (not in LMFDB) |