Invariants
Base field: | $\F_{2^{3}}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 5 x + 8 x^{2} )( 1 - 5 x + 13 x^{2} - 40 x^{3} + 64 x^{4} )$ |
$1 - 10 x + 46 x^{2} - 145 x^{3} + 368 x^{4} - 640 x^{5} + 512 x^{6}$ | |
Frobenius angles: | $\pm0.0644257339289$, $\pm0.154919815756$, $\pm0.530510095142$ |
Angle rank: | $3$ (numerical) |
Isomorphism classes: | 15 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $132$ | $227304$ | $120901968$ | $66087728784$ | $35454761137092$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $57$ | $458$ | $3937$ | $33019$ | $263646$ | $2097703$ | $16777697$ | $134248634$ | $1073798097$ |
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.af_n 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.a_ae_ap | $2$ | (not in LMFDB) |
3.8.a_ae_p | $2$ | (not in LMFDB) |
3.8.k_bu_fp | $2$ | (not in LMFDB) |