Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 31 x + 403 x^{2} - 2573 x^{3} + 6889 x^{4}$ |
Frobenius angles: | $\pm0.101476209234$, $\pm0.229218298306$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.795821.3 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
Isomorphism classes: | 12 |
This isogeny class is simple and geometrically 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4689$ | $46407033$ | $326923058475$ | $2252733493647789$ | $15516495934019559504$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $53$ | $6735$ | $571757$ | $47467619$ | $3939156088$ | $326941193475$ | $27136054023691$ | $2252292228683059$ | $186940255252513991$ | $15516041190289736550$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=12x^6+68x^5+71x^4+45x^3+59x^2+13x+6$
- $y^2=67x^6+53x^5+46x^4+13x^3+55x^2+15x+63$
- $y^2=57x^6+44x^5+11x^4+18x^3+16x^2+69x+40$
- $y^2=78x^6+62x^5+76x^4+46x^3+2x^2+35x+47$
- $y^2=72x^6+33x^5+5x^4+2x^3+11x^2+14x+13$
- $y^2=48x^6+76x^5+72x^4+64x^3+60x^2+27x+5$
- $y^2=60x^6+53x^5+57x^4+9x^3+26x^2+23x+58$
- $y^2=24x^5+22x^4+65x^3+44x^2+53x+61$
- $y^2=53x^6+21x^5+60x^4+46x^3+6x^2+66x+80$
- $y^2=13x^6+7x^5+68x^4+20x^3+32x^2+12x+54$
- $y^2=20x^6+60x^5+25x^4+21x^3+12x^2+15x+29$
- $y^2=22x^6+33x^5+16x^4+68x^3+74x^2+19x+19$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{83}$.
Endomorphism algebra over $\F_{83}$The endomorphism algebra of this simple isogeny class is 4.0.795821.3. |
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.bf_pn | $2$ | (not in LMFDB) |