Invariants
Base field: | $\F_{13}$ |
Dimension: | $3$ |
L-polynomial: | $1 - 16 x + 121 x^{2} - 550 x^{3} + 1573 x^{4} - 2704 x^{5} + 2197 x^{6}$ |
Frobenius angles: | $\pm0.0339662302293$, $\pm0.236468595294$, $\pm0.337737339224$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.12178624.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $622$ | $4454764$ | $10900314262$ | $23442910445104$ | $51088586067563662$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-2$ | $156$ | $2260$ | $28740$ | $370588$ | $4820016$ | $62722910$ | $815673180$ | $10604396206$ | $137858106216$ |
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 6.0.12178624.2. |
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.q_er_ve | $2$ | (not in LMFDB) |