Invariants
Base field: | $\F_{5^{4}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 93 x + 3409 x^{2} - 58125 x^{3} + 390625 x^{4}$ |
Frobenius angles: | $\pm0.0831736883744$, $\pm0.147926818132$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1573221.2 |
Galois group: | $D_{4}$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $335817$ | $151874245701$ | $59597901976951809$ | $23283038425816307082213$ | $9094947804637745432907103632$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $533$ | $388795$ | $244113005$ | $152587720627$ | $95367439891958$ | $59604645232054843$ | $37252902999868383269$ | $23283064365794388672547$ | $14551915228376078167239917$ | $9094947017729459493964414750$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{5^{4}}$.
Endomorphism algebra over $\F_{5^{4}}$The endomorphism algebra of this simple isogeny class is 4.0.1573221.2. |
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 |
---|---|---|
2.625.dp_fbd | $2$ | (not in LMFDB) |