Invariants
Base field: | $\F_{193}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 52 x + 1060 x^{2} - 10036 x^{3} + 37249 x^{4}$ |
Frobenius angles: | $\pm0.0520524425611$, $\pm0.154252660331$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.219392.2 |
Galois group: | $D_{4}$ |
Jacobians: | $6$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28222$ | $1365888356$ | $51644053293598$ | $1925078071649230736$ | $71708923936354747887742$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $142$ | $36666$ | $7183702$ | $1387455654$ | $267785255382$ | $51682546540506$ | $9974730436952206$ | $1925122954256869758$ | $371548729922805430030$ | $71708904873242106177946$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=152x^6+112x^5+168x^4+63x^3+13x^2+61x+144$
- $y^2=147x^6+168x^5+165x^4+177x^3+119x^2+170x+10$
- $y^2=178x^6+81x^5+99x^4+189x^3+119x^2+16x+47$
- $y^2=72x^6+181x^5+48x^4+77x^3+164x^2+112x+83$
- $y^2=153x^6+153x^5+178x^4+178x^3+164x^2+76x+37$
- $y^2=76x^6+122x^5+149x^4+141x^3+131x^2+162x+172$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{193}$.
Endomorphism algebra over $\F_{193}$The endomorphism algebra of this simple isogeny class is 4.0.219392.2. |
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 |
---|---|---|
2.193.ca_bou | $2$ | (not in LMFDB) |