Properties

Label 2.625.adq_fdb
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:  $( 1 - 47 x + 625 x^{2} )^{2}$
Frobenius angles:  $\pm0.110824686604$, $\pm0.110824686604$
Angle rank:  $1$ (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 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
$A(\F_{q^r})$ 335241 151840370889 59596980471005184 23283022119922727318025 9094947648106872037487293161 3552713707631750105700258712387584 1387778781474462885533364750853735186569 542101086256070718392927977768083565271913225 211758236813797122090637960350980070950981764448256 82718061255306038246267171712633858082363146845274097929

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 532 388708 244109230 152587613764 95367438250612 59604645259098718 37252903003222179700 23283064365958988169604 14551915228382110095331342 9094947017729642002919493028

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The isogeny class factors as 1.625.abv 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-291}) \)$)$
All geometric endomorphisms are defined over $\F_{5^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.625.a_abkx$2$(not in LMFDB)
2.625.dq_fdb$2$(not in LMFDB)
2.625.bv_ciy$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.625.a_abkx$2$(not in LMFDB)
2.625.dq_fdb$2$(not in LMFDB)
2.625.bv_ciy$3$(not in LMFDB)
2.625.a_bkx$4$(not in LMFDB)
2.625.abv_ciy$6$(not in LMFDB)