Properties

Label 2.625.ads_fgq
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:  $1 - 96 x + 3552 x^{2} - 60000 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0487724642706$, $\pm0.118311861587$
Angle rank:  $2$ (numerical)
Number field:  4.0.1229056.2
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
$A(\F_{q^r})$ 334082 151764766468 59594450336321474 23282956846813150755856 9094946203907983996969941122 3552713678982153029098604693041156 1387778780954225794723640130598183652162 542101086247354396918361686176019244874989568 211758236813662651601696652553694565650701898424578 82718061255304156104056304637839320005935381102361553668

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 530 388514 244098866 152587185990 95367423107090 59604644778438242 37252902989257171634 23283064365584625012862 14551915228372869353694866 9094947017729435059194895394

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.1229056.2.
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.ds_fgq$2$(not in LMFDB)