Invariants
Base field: | $\F_{79}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 28 x + 349 x^{2} - 2212 x^{3} + 6241 x^{4}$ |
Frobenius angles: | $\pm0.133486072685$, $\pm0.269804315525$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.232625.1 |
Galois group: | $D_{4}$ |
Jacobians: | $24$ |
Isomorphism classes: | 24 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4351$ | $38423681$ | $243446873536$ | $1517631847679705$ | $9468603404246763271$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $52$ | $6156$ | $493768$ | $38963508$ | $3077162772$ | $243087895326$ | $19203909331708$ | $1517108817593508$ | $119851596386235352$ | $9468276089264915356$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=69x^6+33x^5+15x^4+47x^3+x^2+76x+25$
- $y^2=74x^6+18x^5+23x^4+32x^3+42x+23$
- $y^2=59x^6+26x^5+67x^4+72x^3+43x^2+5x+2$
- $y^2=50x^6+68x^5+77x^4+75x^3+76x^2+27x+61$
- $y^2=38x^6+34x^5+29x^3+4x^2+60x+26$
- $y^2=35x^6+39x^5+24x^4+8x^3+40x^2+66x+43$
- $y^2=68x^6+2x^5+x^4+64x^3+16x^2+37x+8$
- $y^2=4x^6+73x^5+46x^4+42x^3+25x^2+49x+34$
- $y^2=43x^6+72x^5+41x^4+5x^3+77x^2+22$
- $y^2=17x^6+70x^5+18x^4+71x^3+33x^2+46x+36$
- $y^2=19x^6+52x^5+18x^4+25x^3+50x^2+76x+63$
- $y^2=59x^6+11x^5+45x^4+3x^3+33x^2+39x+78$
- $y^2=73x^6+9x^5+41x^4+5x^3+75x^2+37$
- $y^2=53x^6+21x^5+53x^4+60x^3+11x^2+71x+21$
- $y^2=27x^6+13x^5+64x^4+20x^3+71x^2+28x+31$
- $y^2=52x^6+61x^5+37x^4+52x^3+32x^2+76x+46$
- $y^2=46x^6+31x^5+3x^4+63x^3+7x^2+55x+59$
- $y^2=47x^6+69x^5+43x^4+4x^3+66x^2+59x+35$
- $y^2=39x^6+69x^5+49x^4+21x^3+65x^2+32x+62$
- $y^2=2x^6+54x^5+59x^4+32x^3+41x^2+5x+43$
- $y^2=54x^6+11x^5+20x^4+24x^3+15x^2+25x+46$
- $y^2=7x^6+65x^5+66x^4+4x^3+5x^2+36x+14$
- $y^2=53x^6+74x^5+73x^3+73x^2+38x+17$
- $y^2=7x^6+68x^5+47x^4+25x^3+35x^2+60x+77$
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 4.0.232625.1. |
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.bc_nl | $2$ | (not in LMFDB) |