Invariants
Base field: | $\F_{5^{4}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 48 x + 625 x^{2} )( 1 - 44 x + 625 x^{2} )$ |
$1 - 92 x + 3362 x^{2} - 57500 x^{3} + 390625 x^{4}$ | |
Frobenius angles: | $\pm0.0903344706017$, $\pm0.157542425424$ |
Angle rank: | $2$ (numerical) |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $336396$ | $151909705680$ | $59598962701730028$ | $23283061464588750028800$ | $9094948199552013841188153516$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $534$ | $388886$ | $244117350$ | $152587871614$ | $95367444032934$ | $59604645320718806$ | $37252903001125391190$ | $23283064365792128873854$ | $14551915228375148687738934$ | $9094947017729419614762939926$ |
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 isogeny class factors as 1.625.abw $\times$ 1.625.abs and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.