# Properties

 Label 2.173.abv_bii Base Field $\F_{173}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{173}$ Dimension: $2$ L-polynomial: $( 1 - 26 x + 173 x^{2} )( 1 - 21 x + 173 x^{2} )$ Frobenius angles: $\pm0.0485897903475$, $\pm0.205732831898$ Angle rank: $2$ (numerical) Jacobians: 21

This isogeny class is not 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 21 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22644 883116000 26796102658416 802360782054000000 24013841202718894927044 718709291817427459471104000 21510249113517197758200562606596 643780250156606239613876808024000000 19267699137141907018008637764849806997744 576662967574467440312519312529753892089900000

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

## Decomposition and endomorphism algebra

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

## 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)
Below is a list of all 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) 2.173.az_qo $4$ (not in LMFDB) 2.173.ar_kc $4$ (not in LMFDB) 2.173.r_kc $4$ (not in LMFDB) 2.173.z_qo $4$ (not in LMFDB)