Invariants
Base field: | $\F_{83}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 17 x + 83 x^{2} )( 1 - 16 x + 83 x^{2} )$ |
$1 - 33 x + 438 x^{2} - 2739 x^{3} + 6889 x^{4}$ | |
Frobenius angles: | $\pm0.117184483028$, $\pm0.158801688027$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 4 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4556$ | $46015600$ | $326488737008$ | $2252497671544000$ | $15516567521229784196$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $51$ | $6677$ | $570996$ | $47462649$ | $3939174261$ | $326942185574$ | $27136069575855$ | $2252292387907441$ | $186940256310269388$ | $15516041191812753557$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
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.aq 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.ab_aec | $2$ | (not in LMFDB) |
2.83.b_aec | $2$ | (not in LMFDB) |
2.83.bh_qw | $2$ | (not in LMFDB) |