Abelian variety isogeny class 2.173.abv_bii over $\F_{173}$

• Label: 2.173.abv_bii
• Base field: $\F_{173}$
• 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:	$\F_{173}$
Dimension:	$2$
L-polynomial:	$( 1 - 26 x + 173 x^{2} )( 1 - 21 x + 173 x^{2} )$
	$1 - 47 x + 892 x^{2} - 8131 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0485897903475$, $\pm0.205732831898$
Angle rank:	$2$ (numerical)
Jacobians:	$21$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22644$	$883116000$	$26796102658416$	$802360782054000000$	$24013841202718894927044$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$127$	$29505$	$5175274$	$895746833$	$154964107307$	$26808754697190$	$4637914286350199$	$802359177069960193$	$138808137850704468562$	$24013807852292306846025$

Jacobians and polarizations

This isogeny class contains the Jacobians of 21 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=3x^6+62x^5+172x^4+39x^2+96x+80$
• $y^2=40x^6+46x^5+39x^4+165x^3+54x^2+15x+162$
• $y^2=50x^6+45x^5+21x^4+101x^3+4x^2+163x+134$
• $y^2=41x^6+48x^5+25x^4+100x^3+8x^2+70x+147$
• $y^2=46x^6+59x^5+10x^4+137x^3+41x^2+91x+82$
• $y^2=154x^6+123x^5+160x^4+64x^3+90x^2+98x+35$
• $y^2=129x^6+75x^5+112x^4+46x^3+3x^2+32x+107$
• $y^2=87x^6+170x^5+73x^4+138x^3+154x^2+46x+167$
• $y^2=100x^6+90x^5+56x^4+126x^3+10x^2+172x+75$
• $y^2=158x^6+109x^5+145x^4+59x^3+46x^2+61x+146$
• $y^2=10x^5+43x^4+133x^3+10x^2+55x$
• $y^2=168x^6+14x^5+94x^4+137x^3+117x^2+161x+3$
• $y^2=63x^6+164x^5+37x^4+161x^3+59x^2+171x+46$
• $y^2=78x^6+152x^5+3x^4+123x^3+148x^2+55x+73$
• $y^2=157x^6+19x^5+146x^4+56x^3+21x^2+26x+123$
• $y^2=72x^6+132x^5+164x^4+5x^3+131x^2+26x+3$
• $y^2=3x^6+169x^5+122x^4+73x^3+154x^2+49x+153$
• $y^2=65x^6+66x^5+77x^4+5x^3+79x^2+120x+99$
• $y^2=52x^6+121x^5+36x^4+172x^3+110x^2+52x+42$
• $y^2=126x^6+53x^5+73x^4+116x^3+147x^2+28$
• $y^2=38x^6+75x^5+57x^4+90x^3+50x^2+123x+166$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{173}$.

Endomorphism algebra over $\F_{173}$

The isogeny class factors as 1.173.aba $\times$ 1.173.av and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.173.aba : \(\Q(\sqrt{-1}) \).
• 1.173.av : \(\Q(\sqrt{-251}) \).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.173.af_ahs	$2$	(not in LMFDB)
2.173.f_ahs	$2$	(not in LMFDB)
2.173.bv_bii	$2$	(not in LMFDB)