Invariants
Base field: | $\F_{13}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 15 x + 109 x^{2} - 489 x^{3} + 1417 x^{4} - 2535 x^{5} + 2197 x^{6}$ |
Frobenius angles: | $\pm0.0482491347716$, $\pm0.243527616942$, $\pm0.379270569548$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.296888383.1 |
Galois group: | $S_4\times C_2$ |
This isogeny class is simple and geometrically 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $685$ | $4632655$ | $10907274865$ | $23331278233575$ | $51035015651132425$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $163$ | $2261$ | $28603$ | $370199$ | $4821799$ | $62738696$ | $815711123$ | $10604342747$ | $137857710463$ |
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 $\F_{13}$.
Endomorphism algebra over $\F_{13}$The endomorphism algebra of this simple isogeny class is 6.0.296888383.1. |
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 |
---|---|---|
3.13.p_ef_sv | $2$ | (not in LMFDB) |