Invariants
Base field: | $\F_{173}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 45 x + 843 x^{2} - 7785 x^{3} + 29929 x^{4}$ |
Frobenius angles: | $\pm0.0769286473055$, $\pm0.234964715490$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.17004349.1 |
Galois group: | $D_{4}$ |
Jacobians: | $17$ |
This isogeny class is simple and geometrically 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $22943$ | $885668629$ | $26805259424531$ | $802381386475467301$ | $24013868660564699460368$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $129$ | $29591$ | $5177043$ | $895769835$ | $154964284494$ | $26808754980647$ | $4637914283058843$ | $802359177446497459$ | $138808137867701921289$ | $24013807852701957868886$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 17 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=43x^6+107x^5+159x^4+47x^3+74x^2+69x+70$
- $y^2=84x^6+142x^5+101x^4+162x^3+134x^2+137x+73$
- $y^2=171x^6+23x^5+96x^4+32x^3+125x^2+14x+133$
- $y^2=6x^6+138x^5+163x^4+161x^3+82x^2+12x+60$
- $y^2=82x^6+94x^5+57x^4+154x^3+170x^2+30x+170$
- $y^2=105x^6+159x^5+18x^4+97x^3+11x^2+53x+87$
- $y^2=48x^6+25x^5+61x^4+2x^3+70x^2+138x+42$
- $y^2=101x^6+135x^5+11x^4+84x^3+15x^2+13x+63$
- $y^2=139x^6+31x^5+7x^4+18x^3+47x^2+90x+76$
- $y^2=127x^6+129x^5+45x^4+140x^3+137x^2+67x+67$
- $y^2=93x^6+4x^5+111x^4+35x^3+150x^2+89x+128$
- $y^2=52x^6+129x^5+12x^4+139x^3+154x^2+95x+153$
- $y^2=60x^6+65x^5+136x^4+x^3+4x^2+95x+82$
- $y^2=141x^6+138x^5+65x^4+28x^3+125x^2+42x+79$
- $y^2=90x^6+12x^5+46x^4+53x^3+155x^2+120x+117$
- $y^2=40x^6+3x^5+136x^4+22x^3+151x^2+162x+51$
- $y^2=79x^6+146x^5+94x^4+119x^3+25x^2+98x+11$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{173}$.
Endomorphism algebra over $\F_{173}$The endomorphism algebra of this simple isogeny class is 4.0.17004349.1. |
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.bt_bgl | $2$ | (not in LMFDB) |