Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 798 x^{2} - 7172 x^{3} + 26569 x^{4}$ |
Frobenius angles: | $\pm0.0236068181920$, $\pm0.241413415058$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.39744.5 |
Galois group: | $D_{4}$ |
Jacobians: | $28$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20152$ | $696936768$ | $18749460156856$ | $498312833339802624$ | $13239625329965910743032$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $120$ | $26230$ | $4329384$ | $705913774$ | $115063524600$ | $18755363155750$ | $3057125083076520$ | $498311411768505694$ | $81224760504261240312$ | $13239635966787143560150$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=89x^6+117x^5+116x^4+110x^3+60x^2+151x+131$
- $y^2=12x^6+5x^5+105x^4+44x^3+39x^2+8x+106$
- $y^2=2x^6+101x^5+145x^4+135x^3+52x^2+39x+26$
- $y^2=98x^6+18x^5+113x^4+82x^3+78x+98$
- $y^2=59x^6+56x^5+93x^4+162x^3+14x^2+x+52$
- $y^2=11x^6+90x^5+26x^4+57x^3+117x^2+72x+65$
- $y^2=130x^6+5x^5+51x^4+151x^3+120x^2+116x+127$
- $y^2=105x^6+136x^5+17x^4+10x^3+36x^2+32x+130$
- $y^2=38x^6+43x^5+46x^4+156x^3+15x^2+55x+136$
- $y^2=117x^6+136x^5+10x^4+59x^3+78x^2+130x+116$
- $y^2=21x^6+31x^5+110x^4+155x^3+26x^2+133x+81$
- $y^2=73x^6+112x^5+4x^4+56x^3+123x^2+62x+106$
- $y^2=70x^6+116x^5+141x^4+39x^3+51x^2+143x+68$
- $y^2=29x^6+127x^5+62x^4+45x^3+132x^2+117x+146$
- $y^2=116x^6+54x^5+47x^4+150x^3+106x^2+155x+5$
- $y^2=159x^6+113x^5+22x^4+105x^3+25x^2+52x+79$
- $y^2=129x^6+138x^5+84x^4+157x^3+41x^2+108x+130$
- $y^2=122x^6+140x^5+82x^4+32x^3+41x^2+45x+107$
- $y^2=96x^6+6x^5+19x^4+103x^3+117x^2+112x+81$
- $y^2=88x^6+54x^5+85x^4+88x^3+79x^2+20x+60$
- $y^2=14x^6+129x^5+29x^4+97x^3+70x^2+140x+82$
- $y^2=141x^6+96x^5+56x^4+33x^3+66x^2+106x+8$
- $y^2=29x^6+155x^5+67x^4+155x^3+70x^2+156x+31$
- $y^2=24x^6+58x^5+138x^4+96x^3+113x^2+70x+25$
- $y^2=34x^6+85x^5+92x^4+108x^3+138x^2+137x+15$
- $y^2=32x^6+98x^5+88x^4+154x^3+155x^2+127x+127$
- $y^2=113x^6+26x^5+52x^4+79x^3+102x^2+64x+147$
- $y^2=78x^6+124x^5+151x^4+70x^3+48x^2+121x+68$
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 4.0.39744.5. |
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_bes | $2$ | (not in LMFDB) |