Properties

Label 2.625.adq_fct
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:  $1 - 94 x + 3451 x^{2} - 58750 x^{3} + 390625 x^{4}$
Frobenius angles:  $\pm0.0263772007358$, $\pm0.155227168270$
Angle rank:  $2$ (numerical)
Number field:  4.0.601664.1
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
$A(\F_{q^r})$ 335233 151834065593 59596429545179200 23282995845275515592873 9094946733365078666128682353 3552713681650338862283693853516800 1387778780839107685155321767863812531313 542101086242303558062080156330817409983315913 211758236813528820357712888888550378256790187252800 82718061255301311464087921680783956125262427956573422553

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 532 388692 244106974 152587441572 95367428658852 59604644823202974 37252902986166993412 23283064365367693135812 14551915228363672540637374 9094947017729122287722688052

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The endomorphism algebra of this simple isogeny class is 4.0.601664.1.
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_fct$2$(not in LMFDB)