Invariants
Base field: | $\F_{2^{3}}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 5 x + 8 x^{2} )( 1 - 6 x + 19 x^{2} - 48 x^{3} + 64 x^{4} )$ |
$1 - 11 x + 57 x^{2} - 191 x^{3} + 456 x^{4} - 704 x^{5} + 512 x^{6}$ | |
Frobenius angles: | $\pm0.0864530894824$, $\pm0.154919815756$, $\pm0.468973809368$ |
Angle rank: | $3$ (numerical) |
Isomorphism classes: | 24 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $120$ | $231840$ | $128793240$ | $66565900800$ | $35216945352600$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $58$ | $490$ | $3966$ | $32798$ | $264058$ | $2102714$ | $16782014$ | $134225230$ | $1073828218$ |
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.ag_t 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.ab_ad_ab | $2$ | (not in LMFDB) |
3.8.b_ad_b | $2$ | (not in LMFDB) |
3.8.l_cf_hj | $2$ | (not in LMFDB) |