Properties

 Label 2.173.abv_bil 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: $1 - 47 x + 895 x^{2} - 8131 x^{3} + 29929 x^{4}$ Frobenius angles: $\pm0.0881869395452$, $\pm0.191285016768$ Angle rank: $2$ (numerical) Number field: 4.0.1935557.1 Galois group: $D_{4}$ Jacobians: 18

This isogeny class is simple and geometrically 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 18 curves, and hence is principally polarizable:

• $y^2=167x^6+92x^5+103x^4+104x^3+106x^2+12x+143$
• $y^2=3x^6+136x^5+11x^4+10x^3+23x^2+138x+148$
• $y^2=15x^6+6x^5+58x^4+97x^3+162x^2+51x+150$
• $y^2=120x^6+85x^5+170x^4+147x^3+163x^2+26x+77$
• $y^2=18x^6+120x^5+101x^4+145x^3+80x^2+143x+44$
• $y^2=72x^6+121x^5+26x^4+102x^3+14x^2+169x+40$
• $y^2=108x^6+17x^5+23x^4+60x^3+86x^2+29x+163$
• $y^2=103x^6+136x^5+37x^4+31x^3+32x^2+51x+2$
• $y^2=44x^6+138x^5+10x^4+112x^3+67x^2+164x+3$
• $y^2=42x^6+145x^5+128x^4+59x^3+14x^2+85x+51$
• $y^2=165x^6+13x^5+169x^4+5x^3+14x^2+3x+130$
• $y^2=120x^6+108x^5+50x^4+60x^3+151x^2+94x+127$
• $y^2=59x^6+117x^5+172x^4+105x^3+27x^2+117x+35$
• $y^2=36x^6+165x^5+114x^4+27x^3+49x^2+161x+36$
• $y^2=161x^6+14x^5+16x^4+124x^3+155x^2+93x+79$
• $y^2=89x^6+156x^5+3x^4+54x^3+10x^2+102x+88$
• $y^2=58x^6+112x^5+32x^4+163x^3+109x^2+71x+105$
• $y^2=10x^6+69x^5+90x^4+130x^3+145x^2+127x+86$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 22647 883300941 26798296309443 802374923595026421 24013906206530330034192 718709528842278431312091357 21510249833146758795490279296867 643780252013139864891546365931978213 19267699141213841933977291950633403696551 576662967581889765667151030412422145898434816

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 127 29511 5175697 895762619 154964526782 26808763538511 4637914441512521 802359179383803763 138808137880039455535 24013807852601392577046

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
 The endomorphism algebra of this simple isogeny class is 4.0.1935557.1.
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.bv_bil $2$ (not in LMFDB)