Invariants
Base field: | $\F_{5^{4}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 92 x + 3351 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
Frobenius angles: | $\pm0.0226935499136$, $\pm0.181059151180$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.33123600.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $336385$ | $151901038065$ | $59598221306468740$ | $23283027173235188647785$ | $9094947052991048445719364625$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $534$ | $388864$ | $244114314$ | $152587646884$ | $95367432010374$ | $59604644801528134$ | $37252902982047725814$ | $23283064365179278167364$ | $14551915228357720097033034$ | $9094947017728980147058390624$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{5^{4}}$.
Endomorphism algebra over $\F_{5^{4}}$The endomorphism algebra of this simple isogeny class is 4.0.33123600.1. |
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 |
---|---|---|
2.625.do_eyx | $2$ | (not in LMFDB) |