Properties

Label 2.625.adp_fbb
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:  $1 - 93 x + 3407 x^{2} - 58125 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0701326688218$, $\pm0.154721810855$
Angle rank:  $2$ (numerical)
Number field:  4.0.28730709.1
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
$A(\F_{q^r})$ 335815 151872669565 59597765711573215 23283032028056573811525 9094947586633456223306249200 3552713700002424182879681996343445 1387778781207843678738544867392983707735 542101086249320420243324701767531285247786725 211758236813656346049348278479550398161978535260535 82718061255303536586197545390409858350584249772445267200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 533 388791 244112447 152587678699 95367437606018 59604645131099871 37252902996065174867 23283064365669065071699 14551915228372436039436953 9094947017729366942485963326

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.28730709.1.
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_fbb$2$(not in LMFDB)