Properties

Label 2.61.aba_la
Base Field $\F_{61}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{61}$
Dimension:  $2$
L-polynomial:  $1 - 26 x + 286 x^{2} - 1586 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.0707655388053$, $\pm0.258010398137$
Angle rank:  $2$ (numerical)
Number field:  4.0.38000.1
Galois group:  $D_{4}$
Jacobians:  12

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 the Jacobians of 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2396 13465520 51514385756 191744911281920 713351235086432316 2654339967409974447920 9876823232904313082563196 36751689750051569664708177920 136753052553879288638308823299676 508858110651228833955749991673950000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 36 3618 226956 13848558 844606156 51520199538 3142739876676 191707291576158 11694146068320276 713342913108960898

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.38000.1.
All geometric endomorphisms are defined over $\F_{61}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.61.ba_la$2$(not in LMFDB)