Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 18 x + 83 x^{2} )( 1 - 12 x + 83 x^{2} )$ |
$1 - 30 x + 382 x^{2} - 2490 x^{3} + 6889 x^{4}$ | |
Frobenius angles: | $\pm0.0496118990883$, $\pm0.271155063531$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $30$ |
Isomorphism classes: | 200 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4752$ | $46531584$ | $326888355024$ | $2252392220491776$ | $15515905884131066832$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $54$ | $6754$ | $571698$ | $47460430$ | $3939006294$ | $326939250418$ | $27136036291698$ | $2252292120115294$ | $186940254961923894$ | $15516041191968600514$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 30 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=82x^6+49x^5+63x^4+23x^3+63x^2+49x+82$
- $y^2=82x^6+11x^5+20x^4+55x^3+25x^2+22x+34$
- $y^2=18x^6+82x^5+57x^4+79x^3+57x^2+82x+18$
- $y^2=46x^6+29x^5+33x^4+79x^3+40x^2+75x+5$
- $y^2=51x^6+49x^5+44x^4+65x^3+78x^2+54x+73$
- $y^2=27x^6+20x^5+9x^4+48x^3+79x^2+33x+46$
- $y^2=39x^6+13x^5+72x^4+42x^3+72x^2+13x+39$
- $y^2=69x^6+21x^5+69x^4+36x^3+58x^2+24x+74$
- $y^2=73x^6+46x^5+63x^4+15x^3+58x^2+81x+35$
- $y^2=70x^6+19x^5+5x^4+16x^3+39x^2+67x+12$
- $y^2=36x^6+67x^5+66x^4+62x^3+65x^2+8x+28$
- $y^2=36x^6+24x^5+18x^4+12x^3+48x^2+36x+11$
- $y^2=5x^6+49x^5+36x^4+57x^3+36x^2+49x+5$
- $y^2=73x^6+38x^5+51x^4+20x^3+53x^2+11x+82$
- $y^2=16x^6+79x^5+56x^4+4x^3+74x^2+18x+59$
- $y^2=24x^6+54x^5+62x^4+57x^3+59x^2+55x+57$
- $y^2=19x^6+28x^5+2x^4+8x^3+9x^2+58x+60$
- $y^2=13x^6+82x^5+61x^4+40x^3+65x^2+35x+5$
- $y^2=40x^6+74x^5+44x^4+81x^3+3x^2+80x+16$
- $y^2=60x^6+x^5+5x^4+65x^3+38x^2+18x+13$
- $y^2=29x^6+27x^5+51x^4+59x^3+43x^2+35x+31$
- $y^2=28x^6+39x^5+6x^4+20x^3+10x^2+8x+67$
- $y^2=79x^6+58x^5+29x^4+72x^3+29x^2+58x+79$
- $y^2=55x^6+54x^5+39x^4+82x^3+75x^2+76x+34$
- $y^2=18x^6+56x^5+64x^4+80x^3+24x^2+41x+42$
- $y^2=39x^6+59x^5+29x^4+46x^3+36x^2+18x+74$
- $y^2=35x^6+12x^5+77x^4+73x^3+28x^2+49x+62$
- $y^2=79x^6+37x^5+4x^4+45x^3+76x^2+74x+22$
- $y^2=78x^6+30x^5+9x^4+9x^3+15x^2+79x+52$
- $y^2=67x^6+10x^5+79x^4+44x^3+28x^2+51x+24$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{83}$.
Endomorphism algebra over $\F_{83}$The isogeny class factors as 1.83.as $\times$ 1.83.am 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 |
---|---|---|
2.83.ag_aby | $2$ | (not in LMFDB) |
2.83.g_aby | $2$ | (not in LMFDB) |
2.83.be_os | $2$ | (not in LMFDB) |