Invariants
Base field: | $\F_{167}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 46 x + 857 x^{2} - 7682 x^{3} + 27889 x^{4}$ |
Frobenius angles: | $\pm0.0558069158019$, $\pm0.207406191075$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.2875968.2 |
Galois group: | $D_{4}$ |
Jacobians: | $8$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $21019$ | $766668025$ | $21682109682052$ | $604971287016069625$ | $16871961020557309209379$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $122$ | $27488$ | $4655348$ | $777801684$ | $129892240402$ | $21691963677926$ | $3622557564190750$ | $604967115954496036$ | $101029508514287983916$ | $16871927924723441268368$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=86x^6+9x^5+9x^4+79x^3+46x^2+107x+33$
- $y^2=16x^6+89x^5+141x^4+78x^3+158x^2+162x+43$
- $y^2=8x^6+131x^5+4x^4+131x^3+121x^2+118x+163$
- $y^2=67x^6+7x^5+163x^4+33x^3+151x^2+92x+153$
- $y^2=51x^6+45x^5+61x^4+14x^3+139x^2+69x+101$
- $y^2=81x^6+3x^5+59x^4+120x^3+150x^2+109x+76$
- $y^2=145x^6+163x^5+63x^4+89x^3+31x^2+83x+3$
- $y^2=35x^6+148x^5+41x^4+123x^3+155x^2+117x+151$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{167}$.
Endomorphism algebra over $\F_{167}$The endomorphism algebra of this simple isogeny class is 4.0.2875968.2. |
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 |
---|---|---|
2.167.bu_bgz | $2$ | (not in LMFDB) |