Properties

Label 2.625.ado_eza
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

Related objects

Downloads

Learn more

Invariants

Base field:  $\F_{5^{4}}$
Dimension:  $2$
L-polynomial:  $1 - 92 x + 3354 x^{2} - 57500 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0466455273859$, $\pm0.176167524581$
Angle rank:  $2$ (numerical)
Number field:  4.0.1325376.2
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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $336388$ $151903401936$ $59598423504934756$ $23283036532745666147328$ $9094947366742346999040908068$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $534$ $388870$ $244115142$ $152587708222$ $95367435300294$ $59604644944470598$ $37252902987366429078$ $23283064365354301674622$ $14551915228362925109877750$ $9094947017729122590988610950$

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 4.0.1325376.2.

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.do_eza$2$(not in LMFDB)