Invariants
Base field: | $\F_{2^{10}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 122 x + 5761 x^{2} - 124928 x^{3} + 1048576 x^{4}$ |
Frobenius angles: | $\pm0.0233129119208$, $\pm0.136899915147$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.999488.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $929288$ | $1095991115744$ | $1152833347268645576$ | $1208923955545968593714048$ | $1267650571063861667459848790088$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $903$ | $1045215$ | $1073659719$ | $1099509932415$ | $1125899880939463$ | $1152921504481615839$ | $1180591620725657417991$ | $1208925819614898342951423$ | $1237940039285377124117418759$ | $1267650600228228627908040537055$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{10}}$.
Endomorphism algebra over $\F_{2^{10}}$The endomorphism algebra of this simple isogeny class is 4.0.999488.2. |
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 |
---|---|---|
2.1024.es_inp | $2$ | (not in LMFDB) |