Invariants
Base field: | $\F_{5^{4}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 92 x + 3359 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
Frobenius angles: | $\pm0.0742530806974$, $\pm0.165990880443$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.7219856.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $336393$ | $151907341761$ | $59598760502780676$ | $23283052119724556073033$ | $9094947887906422168688508393$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $534$ | $388880$ | $244116522$ | $152587810372$ | $95367440765094$ | $59604645180466118$ | $37252902996038017878$ | $23283064365632857148932$ | $14551915228370845665192810$ | $9094947017729322208151469200$ |
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 4.0.7219856.1. |
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_ezf | $2$ | (not in LMFDB) |