Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 18 x + 83 x^{2} )( 1 - 13 x + 83 x^{2} )$ |
$1 - 31 x + 400 x^{2} - 2573 x^{3} + 6889 x^{4}$ | |
Frobenius angles: | $\pm0.0496118990883$, $\pm0.247123549255$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $3$ |
Isomorphism classes: | 13 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4686$ | $46363284$ | $326762858664$ | $2252414757881376$ | $15516054496826400066$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $53$ | $6729$ | $571478$ | $47460905$ | $3939044023$ | $326939756418$ | $27136039294165$ | $2252292107260369$ | $186940254463791314$ | $15516041186398856889$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=75x^6+35x^5+82x^4+6x^3+20x^2+72x+16$
- $y^2=19x^6+13x^5+77x^4+73x^3+44x^2+21x+52$
- $y^2=42x^6+71x^5+27x^4+72x^3+77x^2+x+32$
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.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.af_acq | $2$ | (not in LMFDB) |
2.83.f_acq | $2$ | (not in LMFDB) |
2.83.bf_pk | $2$ | (not in LMFDB) |