Invariants
Base field: | $\F_{2^{10}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 119 x + 5581 x^{2} - 121856 x^{3} + 1048576 x^{4}$ |
Frobenius angles: | $\pm0.0758283833176$, $\pm0.152360144022$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.166673585.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $932183$ | $1096371188339$ | $1152858897304603664$ | $1208925261029977561309715$ | $1267650627595277929621612962723$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $906$ | $1045578$ | $1073683515$ | $1099511119746$ | $1125899931149446$ | $1152921506373935751$ | $1180591620791274340554$ | $1208925819617051394770466$ | $1237940039285446132297065315$ | $1267650600228230867844253503778$ |
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 4.0.166673585.1. |
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 |
---|---|---|
2.1024.ep_igr | $2$ | (not in LMFDB) |