Invariants
Base field: | $\F_{2^{3}}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 11 x + 59 x^{2} - 203 x^{3} + 472 x^{4} - 704 x^{5} + 512 x^{6}$ |
Frobenius angles: | $\pm0.00711186824812$, $\pm0.232753009462$, $\pm0.435766170796$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.1142512.1 |
Galois group: | $S_4\times C_2$ |
Isomorphism classes: | 1 |
This isogeny class is simple and geometrically simple, not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $126$ | $247212$ | $135957906$ | $67179366576$ | $34807453882866$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $62$ | $520$ | $4006$ | $32418$ | $261818$ | $2096008$ | $16762078$ | $134150398$ | $1073615782$ |
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 endomorphism algebra of this simple isogeny class is 6.0.1142512.1. |
Base change
This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^{3}}$.
Subfield | Primitive Model |
$\F_{2}$ | 3.2.b_ab_af |
Twists
Below is a list of all twists of this isogeny class.
Twist | Extension degree | Common base change |
---|---|---|
3.8.l_ch_hv | $2$ | (not in LMFDB) |