Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 16 x + 83 x^{2} )( 1 - 13 x + 83 x^{2} )$ |
$1 - 29 x + 374 x^{2} - 2407 x^{3} + 6889 x^{4}$ | |
Frobenius angles: | $\pm0.158801688027$, $\pm0.247123549255$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4828$ | $46831600$ | $327472019728$ | $2253215327224000$ | $15516800734120996948$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $55$ | $6797$ | $572716$ | $47477769$ | $3939233465$ | $326941566374$ | $27136053887627$ | $2252292200147281$ | $186940254799144468$ | $15516041184344168957$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=66x^6+12x^5+61x^4+x^3+44x^2+14x+70$
- $y^2=39x^6+x^5+22x^4+48x^3+43x^2+63x+62$
- $y^2=26x^6+67x^5+25x^4+69x^3+58x^2+72x+35$
- $y^2=76x^6+57x^5+57x^4+61x^3+71x^2+82x+35$
- $y^2=62x^6+66x^5+48x^4+25x^3+71x^2+6x+5$
- $y^2=14x^6+40x^5+28x^4+18x^3+59x^2+59x+13$
- $y^2=80x^6+23x^5+32x^4+10x^3+57x^2+61x+64$
- $y^2=37x^6+29x^5+40x^4+14x^3+8x^2+18x+47$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{83}$.
Endomorphism algebra over $\F_{83}$The isogeny class factors as 1.83.aq $\times$ 1.83.an 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_abq | $2$ | (not in LMFDB) |
2.83.d_abq | $2$ | (not in LMFDB) |
2.83.bd_ok | $2$ | (not in LMFDB) |