Invariants
Base field: | $\F_{13}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 15 x + 110 x^{2} - 496 x^{3} + 1430 x^{4} - 2535 x^{5} + 2197 x^{6}$ |
Frobenius angles: | $\pm0.0520504550069$, $\pm0.271344466885$, $\pm0.356632440861$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.5611187.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $692$ | $4694528$ | $11023593908$ | $23408287410176$ | $51013925488225472$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $165$ | $2285$ | $28697$ | $370044$ | $4818669$ | $62726733$ | $815717937$ | $10604604599$ | $137858847500$ |
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 6.0.5611187.1. |
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_eg_tc | $2$ | (not in LMFDB) |