Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 800 x^{2} - 7172 x^{3} + 26569 x^{4}$ |
Frobenius angles: | $\pm0.0544015131199$, $\pm0.235892031164$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.8966400.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20154$ | $697046244$ | $18750605251914$ | $498319254842977296$ | $13239650694675594215514$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $120$ | $26234$ | $4329648$ | $705922870$ | $115063745040$ | $18755367361418$ | $3057125150181096$ | $498311412708741214$ | $81224760516570400824$ | $13239635966951191063514$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=25x^6+132x^5+29x^4+19x^3+46x^2+83x+95$
- $y^2=68x^6+80x^5+75x^4+54x^3+148x^2+7x+43$
- $y^2=114x^6+45x^5+x^4+142x^3+78x^2+32x+54$
- $y^2=140x^6+92x^5+36x^4+116x^3+58x^2+93x+70$
- $y^2=92x^6+72x^5+44x^4+41x^3+112x^2+145x+31$
- $y^2=109x^6+18x^4+110x^3+36x^2+133x+158$
- $y^2=157x^6+98x^5+26x^4+28x^3+67x^2+156x+60$
- $y^2=123x^6+82x^5+160x^4+12x^3+98x^2+158x+24$
- $y^2=141x^6+35x^5+160x^4+58x^3+20x^2+28x+161$
- $y^2=113x^6+125x^5+3x^4+89x^3+24x^2+111x+97$
- $y^2=126x^6+112x^5+155x^4+126x^3+29x^2+x+147$
- $y^2=66x^6+39x^5+150x^4+122x^3+55x^2+30x+86$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{163}$.
Endomorphism algebra over $\F_{163}$The endomorphism algebra of this simple isogeny class is 4.0.8966400.1. |
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 |
---|---|---|
2.163.bs_beu | $2$ | (not in LMFDB) |