Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 28 x + 342 x^{2} - 2212 x^{3} + 6241 x^{4}$ |
| Frobenius angles: | $\pm0.0597528064165$, $\pm0.298065699981$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.81216.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $28$ |
| Isomorphism classes: | 44 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4344$ | $38331456$ | $243155890872$ | $1517153508750336$ | $9468084732576602424$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $52$ | $6142$ | $493180$ | $38951230$ | $3076994212$ | $243086255422$ | $19203898317292$ | $1517108776887934$ | $119851596440343700$ | $9468276090625816702$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=3x^6+35x^5+34x^4+51x^3+11x^2+7x+25$
- $y^2=60x^6+58x^5+24x^4+4x^3+12x^2+63x+73$
- $y^2=26x^6+31x^5+66x^4+26x^3+8x^2+73x+69$
- $y^2=18x^6+35x^5+64x^4+38x^3+59x^2+75x+11$
- $y^2=67x^6+42x^5+36x^4+58x^3+77x^2+59x+71$
- $y^2=37x^6+46x^5+59x^4+37x^3+45x^2+21x+48$
- $y^2=59x^6+66x^5+32x^4+3x^3+32x^2+73x+50$
- $y^2=3x^6+5x^5+15x^4+24x^3+38x^2+20x+27$
- $y^2=71x^6+2x^5+59x^4+68x^3+66x^2+57x+1$
- $y^2=14x^6+63x^5+32x^4+66x^3+x^2+14x+29$
- $y^2=19x^6+44x^5+30x^4+74x^3+32x^2+11x+61$
- $y^2=78x^6+71x^5+50x^4+57x^3+34x^2+62x+71$
- $y^2=12x^6+29x^5+78x^4+77x^3+52x^2+28x+61$
- $y^2=28x^6+59x^5+7x^4+63x^3+44x^2+76x+67$
- $y^2=56x^6+69x^5+37x^4+59x^3+6x^2+64x+20$
- $y^2=71x^6+7x^5+6x^4+3x^3+10x^2+44x+8$
- $y^2=39x^6+10x^5+44x^4+28x^3+75x^2+27x+77$
- $y^2=25x^6+6x^5+35x^4+14x^3+62x^2+67x$
- $y^2=54x^5+17x^4+53x^3+28x^2+15x+47$
- $y^2=78x^6+71x^5+52x^4+7x^3+36x^2+59x+69$
- $y^2=69x^6+21x^5+76x^4+50x^3+75x^2+45x+14$
- $y^2=15x^6+32x^5+5x^4+46x^3+61x^2+8x+60$
- $y^2=14x^6+11x^5+72x^4+42x^3+65x^2+26x+66$
- $y^2=36x^6+24x^5+71x^4+70x^3+48x^2+64x+43$
- $y^2=77x^6+71x^5+71x^4+x^3+65x^2+28x+31$
- $y^2=72x^6+14x^5+23x^4+8x^3+48x^2+2x+28$
- $y^2=36x^6+41x^5+70x^4+31x^3+53x^2+50x+45$
- $y^2=3x^6+58x^5+15x^4+71x^3+78x^2+77x+42$
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 4.0.81216.1. |
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_ne | $2$ | (not in LMFDB) |