Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 23 x + 163 x^{2} )( 1 - 21 x + 163 x^{2} )$ |
$1 - 44 x + 809 x^{2} - 7172 x^{3} + 26569 x^{4}$ | |
Frobenius angles: | $\pm0.143017980409$, $\pm0.192621479609$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $18$ |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20163$ | $697538985$ | $18755758417968$ | $498348012083632425$ | $13239762329938211361723$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $120$ | $26252$ | $4330836$ | $705963604$ | $115064715240$ | $18755385038534$ | $3057125402510712$ | $498311415406419556$ | $81224760532955930028$ | $13239635966844261699932$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=66x^6+98x^5+55x^4+14x^3+115x^2+124x+148$
- $y^2=127x^6+144x^5+160x^4+162x^3+111x^2+69x+27$
- $y^2=57x^6+81x^5+75x^4+149x^3+86x^2+34x+113$
- $y^2=110x^6+21x^5+125x^4+106x^3+2x^2+131x+142$
- $y^2=13x^6+80x^5+129x^4+46x^3+149x^2+13x+123$
- $y^2=96x^6+142x^5+151x^4+153x^3+91x^2+59x+35$
- $y^2=3x^6+153x^5+86x^4+133x^3+80x^2+17x+18$
- $y^2=162x^6+113x^5+155x^4+26x^3+43x^2+160x+48$
- $y^2=70x^6+52x^5+9x^4+51x^3+49x^2+12x+159$
- $y^2=128x^6+18x^5+153x^4+16x^3+76x^2+3x+153$
- $y^2=89x^6+84x^5+51x^4+27x^3+x^2+151x+76$
- $y^2=95x^6+88x^5+106x^4+162x^3+149x^2+62x+93$
- $y^2=154x^6+140x^5+114x^4+27x^3+28x^2+69x+101$
- $y^2=70x^6+87x^5+140x^4+149x^3+144x^2+15x+63$
- $y^2=130x^6+73x^5+59x^4+95x^3+66x^2+8x+116$
- $y^2=85x^6+39x^5+113x^4+65x^3+4x^2+121x+65$
- $y^2=76x^6+35x^5+28x^4+44x^3+106x^2+65x+42$
- $y^2=8x^6+8x^5+109x^4+55x^3+68x^2+82x+102$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{163}$.
Endomorphism algebra over $\F_{163}$The isogeny class factors as 1.163.ax $\times$ 1.163.av and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ac_agb | $2$ | (not in LMFDB) |
2.163.c_agb | $2$ | (not in LMFDB) |
2.163.bs_bfd | $2$ | (not in LMFDB) |