Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 18 x + 83 x^{2} )( 1 - 11 x + 83 x^{2} )$ |
$1 - 29 x + 364 x^{2} - 2407 x^{3} + 6889 x^{4}$ | |
Frobenius angles: | $\pm0.0496118990883$, $\pm0.293691115068$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $12$ |
Isomorphism classes: | 75 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4818$ | $46686420$ | $326972779848$ | $2252319104455200$ | $15515738364469272798$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $55$ | $6777$ | $571846$ | $47458889$ | $3938963765$ | $326938855554$ | $27136035922127$ | $2252292158712721$ | $186940255498983778$ | $15516041194833651657$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=74x^6+2x^5+64x^4+39x^3+79x^2+67x+24$
- $y^2=20x^6+27x^5+15x^4+79x^3+6x^2+26x+14$
- $y^2=50x^6+18x^5+29x^4+46x^3+58x^2+49x+42$
- $y^2=20x^6+64x^5+33x^4+70x^3+5x^2+14x+13$
- $y^2=31x^6+17x^5+73x^4+59x^3+42x^2+47x+19$
- $y^2=42x^6+21x^5+53x^4+82x^3+7x^2+65x+55$
- $y^2=73x^6+22x^5+9x^4+50x^3+56x^2+59x+66$
- $y^2=19x^6+55x^5+31x^4+19x^3+18x^2+36x+36$
- $y^2=36x^6+63x^5+54x^3+56x^2+38x+53$
- $y^2=67x^6+35x^5+42x^4+10x^3+25x^2+65x+33$
- $y^2=15x^6+65x^5+80x^4+24x^3+56x^2+22x+72$
- $y^2=7x^6+16x^5+72x^4+8x^3+53x^2+57x+72$
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.al 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.ah_abg | $2$ | (not in LMFDB) |
2.83.h_abg | $2$ | (not in LMFDB) |
2.83.bd_oa | $2$ | (not in LMFDB) |