Invariants
Base field: | $\F_{173}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 891 x^{2} - 8131 x^{3} + 29929 x^{4}$ |
Frobenius angles: | $\pm0.0295549099493$, $\pm0.209571521819$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1295981.1 |
Galois group: | $D_{4}$ |
Jacobians: | $4$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $22643$ | $883054357$ | $26795371452119$ | $802356061053561989$ | $24013819389124717592848$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $127$ | $29503$ | $5175133$ | $895741563$ | $154963966542$ | $26808751691983$ | $4637914232111917$ | $802359176212931091$ | $138808137838487926399$ | $24013807852129267532118$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=86x^6+158x^5+3x^4+8x^3+98x^2+108x+57$
- $y^2=60x^6+95x^5+36x^4+131x^3+63x^2+19x+111$
- $y^2=87x^6+38x^5+164x^4+112x^3+138x^2+9x+71$
- $y^2=103x^6+57x^5+131x^4+112x^3+142x^2+17x+3$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{173}$.
Endomorphism algebra over $\F_{173}$The endomorphism algebra of this simple isogeny class is 4.0.1295981.1. |
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 |
---|---|---|
2.173.bv_bih | $2$ | (not in LMFDB) |