Properties

Label 2.625.adp_fbc
Base Field $\F_{5^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{5^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 93 x + 3408 x^{2} - 58125 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0765374170745$, $\pm0.151561343062$
Angle rank:  $2$ (numerical)
Number field:  4.0.5380024.1
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 335816 151873457632 59597833844252288 23283035227241569726336 9094947695679946550517761096 3552713703014537722442993070905344 1387778781278870668949196567997367502344 542101086250787464010042264432116780453682688 211758236813683140970788778596112531331985401151104 82718061255303966858182359227201090402217214280194782432

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 533 388793 244112726 152587699665 95367438749453 59604645181634750 37252902997971791117 23283064365732074121697 14551915228374277372417526 9094947017729414251391004233

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.5380024.1.
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.dp_fbc$2$(not in LMFDB)