Properties

Label 2.191.abx_blt
Base Field $\F_{191}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 981 x^{2} - 9359 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.122524293102$, $\pm0.179046122411$
Angle rank:  $2$ (numerical)
Number field:  4.0.585125.1
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28055 1314965905 48540654699605 1771255261948841405 64615379546177676250000 2357222686425126346810277305 85993803049233445098761355498905 3137139830401253035736371731729663605 114445997952480355214278167267282095679155 4175104451028537448391377986020596566820000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 143 36043 6966353 1330906923 254196205548 48551249214343 9273284526492143 1771197288870081603 338298681581845835573 64615048177862676323598

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.585125.1.
All geometric endomorphisms are defined over $\F_{191}$.

Base change

This is a primitive isogeny class.

Twists

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