# Properties

 Label 2.173.abu_bhn 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: $( 1 - 25 x + 173 x^{2} )( 1 - 21 x + 173 x^{2} )$ Frobenius angles: $\pm0.100717649571$, $\pm0.205732831898$ Angle rank: $2$ (numerical) Jacobians: 42

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 42 curves, and hence is principally polarizable:

• $y^2=166x^6+169x^5+148x^4+104x^3+85x^2+15x+143$
• $y^2=87x^6+56x^5+48x^4+93x^3+32x^2+121x+45$
• $y^2=145x^6+154x^5+76x^4+28x^3+104x^2+101x+104$
• $y^2=70x^6+2x^5+168x^4+118x^3+x^2+66x+76$
• $y^2=129x^6+25x^5+49x^4+95x^3+105x^2+141x+34$
• $y^2=14x^6+10x^5+25x^4+164x^3+160x^2+29x+73$
• $y^2=95x^6+77x^5+61x^4+103x^3+97x^2+37x+132$
• $y^2=114x^6+54x^5+17x^4+71x^3+101x^2+33x+112$
• $y^2=8x^6+63x^5+55x^4+87x^3+34x^2+2x+5$
• $y^2=131x^6+28x^5+25x^4+116x^3+29x^2+72x+110$
• $y^2=15x^6+83x^5+121x^4+88x^3+16x^2+14x+85$
• $y^2=39x^6+62x^5+24x^4+167x^3+100x^2+48x+70$
• $y^2=64x^6+158x^5+108x^4+51x^3+20x^2+60x+132$
• $y^2=96x^6+95x^5+27x^4+170x^3+112x^2+158x+153$
• $y^2=172x^6+121x^5+37x^4+161x^3+119x^2+144x+124$
• $y^2=34x^6+117x^5+116x^4+134x^3+102x^2+151x+142$
• $y^2=14x^6+102x^5+33x^4+80x^3+100x^2+119x+2$
• $y^2=91x^6+89x^5+60x^4+160x^3+2x^2+11x+167$
• $y^2=171x^6+116x^5+169x^4+151x^3+140x^2+67x+115$
• $y^2=62x^6+130x^5+158x^4+27x^3+169x^2+40x+108$
• and 22 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22797 884637585 26803519496208 802388604578081625 24013930738364481950397 718709550259888705123307520 21510249796945308659028315026373 643780251826900989334563911164115625 19267699140912511004343907100983319248272 576662967582237714701138078621429197939645425

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 128 29556 5176706 895777892 154964685088 26808764337414 4637914433706976 802359179151689668 138808137877868610698 24013807852615882117236

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The isogeny class factors as 1.173.az $\times$ 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.173.ae_agx $2$ (not in LMFDB) 2.173.e_agx $2$ (not in LMFDB) 2.173.bu_bhn $2$ (not in LMFDB)