Invariants
Base field: | $\F_{79}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 31 x + 394 x^{2} - 2449 x^{3} + 6241 x^{4}$ |
Frobenius angles: | $\pm0.0495376346146$, $\pm0.227164728724$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.74273.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4156$ | $37886096$ | $242842943152$ | $1517180084007488$ | $9468343711423384516$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $49$ | $6069$ | $492544$ | $38951913$ | $3077078379$ | $243087280446$ | $19203902478733$ | $1517108719555569$ | $119851595179731712$ | $9468276078491614189$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=15x^6+63x^5+78x^4+24x^3+29x^2+5x+34$
- $y^2=27x^6+66x^5+38x^4+22x^3+4x^2+75x+59$
- $y^2=4x^6+64x^5+36x^4+71x^3+x^2+10x+65$
- $y^2=13x^6+26x^5+20x^4+8x^3+64x^2+16x+24$
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 4.0.74273.1. |
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.bf_pe | $2$ | (not in LMFDB) |