Properties

Label 2.61.aba_lc
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:  $1 - 26 x + 288 x^{2} - 1586 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.107873325280$, $\pm0.243518934227$
Angle rank:  $2$ (numerical)
Number field:  4.0.454464.1
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2398 13481556 51550019422 191788022467536 713387030318426398 2654362261516381669044 9876833857984296715159582 36751693442659020899183514624 136753053274793617306973472258862 508858110544328123088082490732138676

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 36 3622 227112 13851670 844648536 51520632262 3142743257508 191707310837854 11694146129967732 713342912959102102

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.454464.1.
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_lc$2$(not in LMFDB)