Properties

Label 2.625.adr_fer
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:  $1 - 95 x + 3501 x^{2} - 59375 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0290941168115$, $\pm0.140487243861$
Angle rank:  $2$ (numerical)
Number field:  4.0.4189941.1
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
$A(\F_{q^r})$ 334657 151799411229 59595437729566537 23282976089367302716725 9094946452572333143055185152 3552713679596209585298569610152029 1387778780870773896157574925328902004417 542101086244037128726421977909571765750847525 211758236813574433532409168615400859615299001431897 82718061255302219063435103437595335470496162038459797504

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 531 388603 244102911 152587312099 95367425714526 59604644788740403 37252902987017026791 23283064365442149428899 14551915228366807054134771 9094947017729222079326246878

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.4189941.1.
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.dr_fer$2$(not in LMFDB)