Invariants
Base field: | $\F_{173}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 45 x + 851 x^{2} - 7785 x^{3} + 29929 x^{4}$ |
Frobenius angles: | $\pm0.145147992759$, $\pm0.197931037552$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.9725.1 |
Galois group: | $D_{4}$ |
Jacobians: | $11$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $22951$ | $886161061$ | $26810859451819$ | $802415155191647301$ | $24014009244398486526736$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $129$ | $29607$ | $5178123$ | $895807531$ | $154965191694$ | $26808771455943$ | $4637914510420803$ | $802359179578468723$ | $138808137871611331209$ | $24013807852348734248022$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 11 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=103x^6+12x^5+18x^3+107x^2+119x+81$
- $y^2=60x^6+170x^5+2x^4+167x^3+3x^2+78x+111$
- $y^2=45x^6+94x^5+33x^4+31x^3+73x^2+114x+148$
- $y^2=3x^6+124x^5+28x^4+42x^3+72x^2+160x+51$
- $y^2=163x^6+37x^5+41x^4+154x^3+137x^2+30x+149$
- $y^2=2x^6+164x^5+132x^4+127x^3+67x^2+112x+80$
- $y^2=62x^6+106x^5+132x^4+154x^3+70x^2+131x+74$
- $y^2=2x^6+109x^5+102x^4+149x^3+137x^2+154x+51$
- $y^2=62x^6+165x^5+42x^4+163x^3+102x^2+68x+40$
- $y^2=25x^6+34x^5+26x^4+145x^3+48x^2+170x+43$
- $y^2=171x^6+97x^5+76x^4+92x^3+72x^2+158x+80$
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 4.0.9725.1. |
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_bgt | $2$ | (not in LMFDB) |