Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 32 x + 419 x^{2} - 2656 x^{3} + 6889 x^{4}$ |
Frobenius angles: | $\pm0.0738974052033$, $\pm0.213660075367$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.325008.5 |
Galois group: | $D_{4}$ |
Jacobians: | $4$ |
Isomorphism classes: | 4 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4621$ | $46196137$ | $326648009572$ | $2252487468544729$ | $15516327194810226301$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $52$ | $6704$ | $571276$ | $47462436$ | $3939113252$ | $326940894542$ | $27136051698332$ | $2252292200952004$ | $186940254856644532$ | $15516041185416518384$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=21x^6+56x^5+3x^4+79x^3+44x^2+70x+74$
- $y^2=54x^6+14x^5+53x^4+27x^3+67x^2+32x+20$
- $y^2=49x^6+30x^5+12x^4+16x^3+56x^2+58x+39$
- $y^2=32x^6+81x^5+29x^4+17x^3+61x^2+78x+27$
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 4.0.325008.5. |
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.bg_qd | $2$ | (not in LMFDB) |