Invariants
Base field: | $\F_{2^{10}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 8 x - 159 x^{2} - 8192 x^{3} + 1048576 x^{4}$ |
Frobenius angles: | $\pm0.205257621131$, $\pm0.735510757239$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.149350032.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1040218$ | $1099113062724$ | $1152890470103202106$ | $1208930038224502123323648$ | $1267650635534099477144686846138$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $1017$ | $1048195$ | $1073712921$ | $1099515464575$ | $1125899938200537$ | $1152921505631535619$ | $1180591620792333810489$ | $1208925819611625189972223$ | $1237940039285343668795297721$ | $1267650600228228170315560289155$ |
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 4.0.149350032.2. |
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.i_agd | $2$ | (not in LMFDB) |