Abelian variety isogeny class 2.191.aby_bms over $\F_{191}$

• Label: 2.191.aby_bms
• Base field: $\F_{191}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{191}$
Dimension:	$2$
L-polynomial:	$( 1 - 26 x + 191 x^{2} )( 1 - 24 x + 191 x^{2} )$
	$1 - 50 x + 1006 x^{2} - 9550 x^{3} + 36481 x^{4}$
Frobenius angles:	$\pm0.110219473395$, $\pm0.165219579186$
Angle rank:	$2$ (numerical)
Jacobians:	$20$

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$2$
Slopes:	$[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$27888$	$1313190144$	$48532078753200$	$1771226369864146944$	$64615308156361728468528$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$142$	$35994$	$6965122$	$1330885214$	$254195924702$	$48551246967258$	$9273284532928082$	$1771197289546194814$	$338298681597852110062$	$64615048178126992952154$

Jacobians and polarizations

This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=37x^6+69x^5+87x^4+4x^3+87x^2+69x+37$
• $y^2=159x^6+82x^5+161x^4+92x^3+37x^2+53x+37$
• $y^2=33x^6+x^5+19x^4+166x^3+19x^2+x+33$
• $y^2=186x^6+148x^5+94x^4+130x^3+94x^2+148x+186$
• $y^2=186x^6+48x^5+188x^4+103x^3+111x^2+8x+190$
• $y^2=159x^6+167x^5+52x^4+39x^3+x^2+152x+190$
• $y^2=146x^6+76x^5+110x^4+164x^3+137x^2+55x+114$
• $y^2=125x^6+36x^5+74x^4+6x^3+74x^2+36x+125$
• $y^2=114x^6+71x^5+117x^4+73x^3+117x^2+71x+114$
• $y^2=151x^6+88x^5+70x^4+84x^3+70x^2+88x+151$
• $y^2=28x^6+115x^5+160x^4+78x^3+160x^2+115x+28$
• $y^2=105x^6+164x^5+110x^4+56x^3+164x^2+188x+110$
• $y^2=45x^6+57x^5+139x^4+166x^3+165x^2+62x+125$
• $y^2=176x^6+42x^5+123x^4+131x^3+123x^2+42x+176$
• $y^2=48x^6+62x^5+74x^4+174x^3+167x^2+88x+59$
• $y^2=83x^6+115x^5+77x^4+53x^3+103x^2+158x+22$
• $y^2=190x^6+57x^5+65x^4+187x^3+65x^2+57x+190$
• $y^2=115x^6+47x^5+134x^4+125x^3+134x^2+47x+115$
• $y^2=69x^6+74x^5+174x^4+25x^3+174x^2+74x+69$
• $y^2=127x^6+8x^5+160x^4+128x^3+59x^2+121x+111$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{191}$.

Endomorphism algebra over $\F_{191}$

The isogeny class factors as 1.191.aba $\times$ 1.191.ay and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.191.aba : \(\Q(\sqrt{-22}) \).
• 1.191.ay : \(\Q(\sqrt{-47}) \).

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

Twist	Extension degree	Common base change
2.191.ac_aji	$2$	(not in LMFDB)
2.191.c_aji	$2$	(not in LMFDB)
2.191.by_bms	$2$	(not in LMFDB)