Invariants
Base field: | $\F_{19}$ |
Dimension: | $3$ |
L-polynomial: | $1 + 6 x - 6 x^{2} - 144 x^{3} - 114 x^{4} + 2166 x^{5} + 6859 x^{6}$ |
Frobenius angles: | $\pm0.138106922050$, $\pm0.731501495324$, $\pm0.880842547929$ |
Angle rank: | $3$ (numerical) |
Number field: | 6.0.379750680000.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $8768$ | $41314816$ | $317699431424$ | $2226414615201792$ | $15177128498780571968$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $26$ | $314$ | $6752$ | $131090$ | $2475446$ | $47061548$ | $893934914$ | $16983834530$ | $322687706528$ | $6131074866074$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{19}$.
Endomorphism algebra over $\F_{19}$The endomorphism algebra of this simple isogeny class is 6.0.379750680000.1. |
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 |
---|---|---|
3.19.ag_ag_fo | $2$ | (not in LMFDB) |