Invariants
Base field: | $\F_{79}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 27 x + 324 x^{2} - 2133 x^{3} + 6241 x^{4}$ |
Frobenius angles: | $\pm0.0529367503537$, $\pm0.321190347894$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.169000.2 |
Galois group: | $D_{4}$ |
Jacobians: | $14$ |
Isomorphism classes: | 28 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4406$ | $38446756$ | $243166593656$ | $1517030560377760$ | $9467934547461302546$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $53$ | $6161$ | $493202$ | $38948073$ | $3076945403$ | $243085960586$ | $19203899289677$ | $1517108808242353$ | $119851596583378958$ | $9468276088033885481$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=66x^6+42x^5+63x^4+78x^3+17x^2+60x+18$
- $y^2=35x^6+42x^5+11x^4+46x^3+6x^2+52x+66$
- $y^2=12x^6+16x^5+26x^4+25x^3+67x^2+41x+34$
- $y^2=25x^6+31x^5+58x^4+43x^3+57x^2+61x+32$
- $y^2=78x^6+24x^5+12x^4+2x^3+15x^2+4x+38$
- $y^2=67x^6+31x^5+54x^4+32x^3+75x^2+49x+35$
- $y^2=32x^6+31x^5+61x^4+48x^3+62x^2+71x+18$
- $y^2=57x^6+x^5+7x^4+34x^3+52x^2+11x+20$
- $y^2=28x^6+3x^5+43x^4+69x^3+77x^2+8x+71$
- $y^2=37x^6+10x^5+60x^4+38x^3+67x^2+46x+33$
- $y^2=4x^6+67x^5+23x^4+52x^3+65x^2+58x+53$
- $y^2=30x^6+8x^5+25x^3+56x^2+13x+74$
- $y^2=10x^6+75x^5+3x^4+74x^3+48x^2+41x+53$
- $y^2=28x^6+38x^5+15x^4+77x^3+44x^2+51x+59$
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 4.0.169000.2. |
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 |
---|---|---|
2.79.bb_mm | $2$ | (not in LMFDB) |