Invariants
Base field: | $\F_{79}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 30 x + 377 x^{2} - 2370 x^{3} + 6241 x^{4}$ |
Frobenius angles: | $\pm0.0611389541483$, $\pm0.250488236037$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1051200.1 |
Galois group: | $D_{4}$ |
Jacobians: | $4$ |
Isomorphism classes: | 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4219$ | $38051161$ | $242998519684$ | $1517245334760825$ | $9468319931884217779$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $50$ | $6096$ | $492860$ | $38953588$ | $3077070650$ | $243087045846$ | $19203900756230$ | $1517108729348068$ | $119851595608680740$ | $9468276084831125856$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=36x^6+37x^5+50x^4+2x^3+38x^2+46x+14$
- $y^2=23x^6+57x^5+53x^4+40x^3+42x^2+66x+34$
- $y^2=72x^6+11x^5+2x^4+34x^3+11x^2+28x+56$
- $y^2=x^6+41x^5+47x^4+73x^3+59x^2+17x+26$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{79}$.
Endomorphism algebra over $\F_{79}$The endomorphism algebra of this simple isogeny class is 4.0.1051200.1. |
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 |
---|---|---|
2.79.be_on | $2$ | (not in LMFDB) |