Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 17 x + 83 x^{2} )( 1 - 14 x + 83 x^{2} )$ |
$1 - 31 x + 404 x^{2} - 2573 x^{3} + 6889 x^{4}$ | |
Frobenius angles: | $\pm0.117184483028$, $\pm0.221078141621$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $8$ |
Isomorphism classes: | 20 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4690$ | $46421620$ | $326976463240$ | $2252839361735200$ | $15516640638323543950$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $53$ | $6737$ | $571850$ | $47469849$ | $3939192823$ | $326941647554$ | $27136058240869$ | $2252292254304241$ | $186940255255274510$ | $15516041187750459857$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=26x^6+3x^5+17x^4+43x^3+76x^2+43x+42$
- $y^2=5x^6+48x^5+46x^4+14x^3+49x^2+54x+72$
- $y^2=28x^5+31x^4+60x^3+43x^2+81x+58$
- $y^2=29x^6+79x^5+24x^4+70x^3+63x^2+19x+2$
- $y^2=35x^6+50x^5+12x^4+62x^3+32x^2+49x+24$
- $y^2=57x^6+20x^5+64x^4+64x^3+23x^2+77x+43$
- $y^2=72x^6+9x^5+78x^4+x^3+40x^2+80x+23$
- $y^2=67x^6+20x^5+74x^4+21x^3+37x^2+75x+41$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{83}$.
Endomorphism algebra over $\F_{83}$The isogeny class factors as 1.83.ar $\times$ 1.83.ao 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.ad_acu | $2$ | (not in LMFDB) |
2.83.d_acu | $2$ | (not in LMFDB) |
2.83.bf_po | $2$ | (not in LMFDB) |