Invariants
Base field: | $\F_{5^{4}}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 49 x + 625 x^{2} )( 1 - 46 x + 625 x^{2} )$ |
$1 - 95 x + 3504 x^{2} - 59375 x^{3} + 390625 x^{4}$ | |
Frobenius angles: | $\pm0.0637685608585$, $\pm0.128188433698$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $334660$ | $151801776000$ | $59595646525928080$ | $23282986201460040384000$ | $9094946812024219172806855300$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $531$ | $388609$ | $244103766$ | $152587378369$ | $95367429483651$ | $59604644964754654$ | $37252902994149941811$ | $23283064365700887449089$ | $14551915228375364769864246$ | $9094947017729483040000702049$ |
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.abx $\times$ 1.625.abu 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.
Twists
Below is a list of all twists of this isogeny class.
Twist | Extension degree | Common base change |
---|---|---|
2.625.ad_abmq | $2$ | (not in LMFDB) |
2.625.d_abmq | $2$ | (not in LMFDB) |
2.625.dr_feu | $2$ | (not in LMFDB) |