Properties

Label 2.625.adp_fbd
Base field $\F_{5^{4}}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{5^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 93 x + 3409 x^{2} - 58125 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0831736883744$, $\pm0.147926818132$
Angle rank:  $2$ (numerical)
Number field:  4.0.1573221.2
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $335817$ $151874245701$ $59597901976951809$ $23283038425816307082213$ $9094947804637745432907103632$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $533$ $388795$ $244113005$ $152587720627$ $95367439891958$ $59604645232054843$ $37252902999868383269$ $23283064365794388672547$ $14551915228376078167239917$ $9094947017729459493964414750$

Jacobians and polarizations

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{5^{4}}$.

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.1573221.2.

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_fbd$2$(not in LMFDB)