Invariants
Base field: | $\F_{2^{10}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 123 x + 5829 x^{2} - 125952 x^{3} + 1048576 x^{4}$ |
Frobenius angles: | $\pm0.0662686946492$, $\pm0.107542209239$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1968625.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $928331$ | $1095877107211$ | $1152827210442336176$ | $1208923766346577526080195$ | $1267650570971606337270640360871$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $902$ | $1045106$ | $1073654003$ | $1099509760338$ | $1125899880857522$ | $1152921504874231991$ | $1180591620758647190078$ | $1208925819616827877541698$ | $1237940039285471276397239627$ | $1267650600228232691811030426506$ |
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 4.0.1968625.1. |
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.et_iqf | $2$ | (not in LMFDB) |