Invariants
Base field: | $\F_{73}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 14 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$ |
$1 - 27 x + 328 x^{2} - 1971 x^{3} + 5329 x^{4}$ | |
Frobenius angles: | $\pm0.194368965322$, $\pm0.224822766824$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
Isomorphism classes: | 12 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3660$ | $28020960$ | $151713339120$ | $806979549974400$ | $4297988490122748300$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $47$ | $5257$ | $389990$ | $28416529$ | $2073246527$ | $151335256174$ | $11047399811831$ | $806460036337441$ | $58871585881905590$ | $4297625822674078057$ |
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 $\F_{73}$.
Endomorphism algebra over $\F_{73}$The isogeny class factors as 1.73.ao $\times$ 1.73.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 |
---|---|---|
2.73.ab_abk | $2$ | (not in LMFDB) |
2.73.b_abk | $2$ | (not in LMFDB) |
2.73.bb_mq | $2$ | (not in LMFDB) |