Properties

Label 2.625.adp_fbg
Base Field $\F_{5^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{5^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 47 x + 625 x^{2} )( 1 - 46 x + 625 x^{2} )$
Frobenius angles:  $\pm0.110824686604$, $\pm0.128188433698$
Angle rank:  $2$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 335820 151876609920 59598106375173120 23283048017878968614400 9094948130978993416376009100 3552713714994581251298615244226560 1387778781559245817396443727360110749580 542101086256494093614950235812542126769305600 211758236813784433138617642436074387903758455034880 82718061255305500689141663355134714590349180341217225600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 533 388801 244113842 152587783489 95367443313893 59604645382626526 37252903005498054197 23283064365977171996929 14551915228381238117188178 9094947017729582897888484001

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The isogeny class factors as 1.625.abv $\times$ 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:
All geometric endomorphisms are defined over $\F_{5^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.625.ab_abjc$2$(not in LMFDB)
2.625.b_abjc$2$(not in LMFDB)
2.625.dp_fbg$2$(not in LMFDB)