Abelian variety isogeny class 2.181.abv_bjc over $\F_{181}$

• Label: 2.181.abv_bjc
• Base field: $\F_{181}$
• 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:	$\F_{181}$
Dimension:	$2$
L-polynomial:	$( 1 - 25 x + 181 x^{2} )( 1 - 22 x + 181 x^{2} )$
	$1 - 47 x + 912 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:	$\pm0.120568372405$, $\pm0.195291079027$
Angle rank:	$2$ (numerical)
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$25120$	$1060767360$	$35157378359680$	$1151987094432576000$	$37738821994604977348000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$135$	$32377$	$5928990$	$1073330113$	$194265403875$	$35161846158742$	$6364291132695015$	$1151936659539125473$	$208500535073002862310$	$37738596846881618170177$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=95x^6+174x^5+158x^4+39x^3+11x^2+78x+84$
• $y^2=83x^6+137x^5+23x^4+130x^3+51x^2+153x+165$
• $y^2=66x^6+42x^5+180x^4+89x^3+164x^2+162x+140$
• $y^2=11x^6+162x^5+115x^4+83x^3+129x^2+103x+67$
• $y^2=6x^6+119x^5+132x^4+163x^3+128x^2+86x+131$
• $y^2=63x^6+170x^5+33x^4+81x^3+141x^2+176x+179$
• $y^2=39x^6+140x^5+54x^4+21x^3+172x^2+58x+166$
• $y^2=74x^6+109x^5+112x^4+147x^3+52x^2+153x+147$
• $y^2=89x^6+130x^5+152x^4+90x^3+64x^2+90x+150$
• $y^2=19x^6+86x^5+133x^4+170x^3+13x^2+173x+72$
• $y^2=18x^6+69x^5+78x^4+77x^3+20x^2+76x+134$
• $y^2=154x^6+173x^5+33x^4+178x^3+70x^2+18x+76$
• $y^2=110x^6+176x^5+42x^4+9x^3+66x^2+135x+86$
• $y^2=126x^6+121x^5+96x^4+75x^3+88x^2+161x+57$
• $y^2=107x^6+48x^5+31x^4+170x^3+19x^2+35x+154$
• $y^2=81x^6+165x^5+45x^4+43x^3+146x^2+31x+169$
• $y^2=112x^6+116x^5+147x^4+12x^3+41x^2+22x+88$
• $y^2=175x^6+19x^5+76x^4+146x^3+106x^2+124x+151$
• $y^2=174x^6+79x^5+53x^4+118x^3+27x^2+11x+159$
• $y^2=19x^6+114x^5+102x^4+143x^3+62x^2+157x+71$
• $y^2=89x^6+111x^5+152x^4+112x^3+23x^2+86x+33$
• $y^2=94x^6+163x^5+101x^4+14x^3+121x^2+27x+174$
• $y^2=63x^6+15x^5+155x^4+85x^3+47x^2+118x+6$
• $y^2=41x^6+115x^5+140x^4+176x^3+140x^2+144x+47$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{181}$.

Endomorphism algebra over $\F_{181}$

The isogeny class factors as 1.181.az $\times$ 1.181.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.181.az : \(\Q(\sqrt{-11}) \).
• 1.181.aw : \(\Q(\sqrt{-15}) \).

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
2.181.ad_ahg	$2$	(not in LMFDB)
2.181.d_ahg	$2$	(not in LMFDB)
2.181.bv_bjc	$2$	(not in LMFDB)