Invariants
Base field: | $\F_{79}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 16 x + 79 x^{2} )( 1 - 14 x + 79 x^{2} )$ |
$1 - 30 x + 382 x^{2} - 2370 x^{3} + 6241 x^{4}$ | |
Frobenius angles: | $\pm0.143514932644$, $\pm0.211343260462$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $16$ |
Isomorphism classes: | 64 |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4224$ | $38117376$ | $243221387904$ | $1517650948915200$ | $9468827658790667904$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $50$ | $6106$ | $493310$ | $38963998$ | $3077235650$ | $243089005786$ | $19203918316430$ | $1517108835586558$ | $119851595744281490$ | $9468276078104526106$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=55x^6+39x^5+50x^4+72x^3+50x^2+39x+55$
- $y^2=69x^6+20x^5+58x^4+39x^3+14x^2+44x+41$
- $y^2=30x^6+16x^4+36x^3+16x^2+30$
- $y^2=34x^6+8x^5+5x^4+13x^3+20x^2+49x+43$
- $y^2=8x^6+29x^5+13x^4+53x^3+13x^2+29x+8$
- $y^2=72x^6+11x^5+72x^4+27x^3+50x^2+5x+73$
- $y^2=55x^6+41x^5+21x^4+24x^3+49x^2+74x+55$
- $y^2=47x^6+50x^5+71x^4+67x^3+15x^2+40x+48$
- $y^2=41x^6+32x^5+53x^4+9x^3+53x^2+32x+41$
- $y^2=15x^6+41x^5+67x^4+20x^3+67x^2+41x+15$
- $y^2=17x^6+43x^5+70x^4+74x^3+70x^2+43x+17$
- $y^2=37x^6+73x^5+48x^4+19x^3+69x^2+45x+43$
- $y^2=10x^6+13x^5+21x^4+59x^3+52x^2+36x+46$
- $y^2=15x^6+22x^5+64x^4+23x^3+64x^2+22x+15$
- $y^2=64x^6+24x^5+70x^4+67x^3+68x^2+30x+10$
- $y^2=73x^6+76x^5+15x^4+54x^3+15x^2+76x+73$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{79}$.
Endomorphism algebra over $\F_{79}$The isogeny class factors as 1.79.aq $\times$ 1.79.ao and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ac_aco | $2$ | (not in LMFDB) |
2.79.c_aco | $2$ | (not in LMFDB) |
2.79.be_os | $2$ | (not in LMFDB) |