Invariants
Base field: | $\F_{2^{10}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 118 x + 5511 x^{2} - 120832 x^{3} + 1048576 x^{4}$ |
Frobenius angles: | $\pm0.0490179712428$, $\pm0.173198423717$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.6769728.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $933138$ | $1096472609244$ | $1152862843706930286$ | $1208925250329445072805088$ | $1267650614943247340626217122338$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $907$ | $1045675$ | $1073687191$ | $1099511110015$ | $1125899919912187$ | $1152921505443873739$ | $1180591620738879788359$ | $1208925819614671735565503$ | $1237940039285354419448715691$ | $1267650600228227832394456806955$ |
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 4.0.6769728.2. |
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.eo_idz | $2$ | (not in LMFDB) |