Properties

Label 2.625.adq_fcv
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:  $1 - 94 x + 3453 x^{2} - 58750 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0472783280743$, $\pm0.149997419122$
Angle rank:  $2$ (numerical)
Number field:  4.0.16248384.1
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
$A(\F_{q^r})$ 335235 151835641905 59596567276511340 23283002417598852594825 9094946962588397639667003675 3552713688187747276371046563031440 1387778781000280262790583994830910260635 542101086245848451837985588301973125132204425 211758236813599748701452082296796684763442443821740 82718061255302619482932040928062381707987031630563919025

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 532 388696 244107538 152587484644 95367431062432 59604644932882486 37252902990493436848 23283064365519945164164 14551915228368546699304882 9094947017729266105915533976

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.16248384.1.
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.dq_fcv$2$(not in LMFDB)