Invariants
Base field: | $\F_{173}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 46 x + 869 x^{2} - 7958 x^{3} + 29929 x^{4}$ |
Frobenius angles: | $\pm0.0814447409702$, $\pm0.214601179315$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.6884928.2 |
Galois group: | $D_{4}$ |
Jacobians: | $14$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $22795$ | $884514385$ | $26802088280620$ | $802379675022474025$ | $24013891603602758580475$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $128$ | $29552$ | $5176430$ | $895767924$ | $154964432548$ | $26808759371774$ | $4637914355265844$ | $802359178169168356$ | $138808137869094191750$ | $24013807852591803172832$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=81x^6+157x^5+87x^4+160x^3+37x^2+135x+69$
- $y^2=14x^6+85x^5+6x^4+3x^3+28x^2+111x+5$
- $y^2=113x^6+11x^5+25x^4+137x^3+126x^2+70x+114$
- $y^2=55x^6+93x^5+162x^4+145x^3+34x^2+8x+94$
- $y^2=71x^6+18x^5+25x^4+27x^3+118x^2+156x+58$
- $y^2=24x^6+35x^5+98x^4+151x^3+170x^2+16x+103$
- $y^2=x^6+129x^5+20x^4+129x^3+86x^2+138x+44$
- $y^2=128x^6+123x^5+77x^4+153x^3+67x^2+86x+70$
- $y^2=5x^6+26x^5+43x^4+155x^3+77x^2+150x+57$
- $y^2=41x^6+128x^5+8x^4+108x^3+73x^2+126x+120$
- $y^2=26x^6+7x^5+73x^4+149x^3+112x^2+46x+37$
- $y^2=147x^6+54x^5+30x^4+82x^3+26x^2+131x+13$
- $y^2=41x^6+9x^5+98x^4+167x^3+15x^2+80x+146$
- $y^2=78x^6+171x^5+110x^4+37x^3+120x^2+76x+49$
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 4.0.6884928.2. |
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.bu_bhl | $2$ | (not in LMFDB) |