Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 61 x + 1441 x^{2} - 15616 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.0492306350850$, $\pm0.129653471103$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.97625.1 |
Galois group: | $D_{4}$ |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $51301$ | $4240284155$ | $281305144678996$ | $18446318368618006355$ | $1208925205185227318292541$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $196$ | $64698$ | $16767091$ | $4294868178$ | $1099511068956$ | $281474982310143$ | $72057594300532876$ | $18446744079428907618$ | $4722366482964176679091$ | $1208925819615887872910698$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{8}}$.
Endomorphism algebra over $\F_{2^{8}}$The endomorphism algebra of this simple isogeny class is 4.0.97625.1. |
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 |
---|---|---|
2.256.cj_cdl | $2$ | (not in LMFDB) |