Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 + 2 x + 157 x^{2} + 158 x^{3} + 6241 x^{4}$ |
| Frobenius angles: | $\pm0.492582283879$, $\pm0.543363711118$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.6269504.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $27$ |
| Isomorphism classes: | 27 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $6559$ | $40921601$ | $242861588452$ | $1516209195669161$ | $9468451363166605999$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $82$ | $6552$ | $492580$ | $38926980$ | $3077113362$ | $243089106582$ | $19203903261982$ | $1517108697318084$ | $119851596490123900$ | $9468276089888381752$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 27 curves (of which all are hyperelliptic):
- $y^2=18 x^6+23 x^4+72 x^3+23 x^2+69 x+22$
- $y^2=24 x^6+27 x^5+41 x^4+16 x^3+57 x^2+62 x+33$
- $y^2=75 x^6+59 x^5+61 x^4+63 x^3+49 x^2+40 x+30$
- $y^2=7 x^6+72 x^5+45 x^4+69 x^3+69 x^2+17 x+2$
- $y^2=71 x^6+58 x^5+65 x^4+66 x^3+75 x^2+39 x+12$
- $y^2=47 x^6+44 x^5+49 x^4+8 x^3+66 x^2+36 x+47$
- $y^2=28 x^6+2 x^5+36 x^4+12 x^3+21 x^2+15 x+32$
- $y^2=43 x^6+73 x^5+52 x^4+41 x^3+48 x^2+33 x+47$
- $y^2=62 x^6+65 x^5+10 x^4+70 x^3+13 x^2+66 x+53$
- $y^2=78 x^6+13 x^5+69 x^4+78 x^3+11 x^2+36 x+60$
- $y^2=25 x^6+8 x^5+31 x^4+42 x^3+30 x^2+16 x+28$
- $y^2=5 x^6+52 x^5+78 x^4+71 x^3+24 x^2+33 x+17$
- $y^2=5 x^6+4 x^5+37 x^4+43 x^3+61 x^2+25 x+31$
- $y^2=61 x^6+44 x^5+57 x^4+53 x^3+26 x^2+23 x+64$
- $y^2=40 x^6+33 x^5+63 x^4+40 x^3+72 x^2+19 x+47$
- $y^2=77 x^6+31 x^5+36 x^4+48 x^3+28 x^2+30 x+69$
- $y^2=77 x^6+2 x^5+50 x^4+16 x^3+68 x^2+24 x+6$
- $y^2=69 x^6+69 x^5+27 x^4+64 x^3+42 x^2+48 x+73$
- $y^2=45 x^6+11 x^5+61 x^4+76 x^3+2 x^2+34 x+34$
- $y^2=62 x^6+71 x^5+30 x^4+76 x^3+8 x^2+62 x+49$
- $y^2=40 x^6+61 x^5+50 x^4+12 x^3+65 x^2+17 x+33$
- $y^2=44 x^6+23 x^5+74 x^4+76 x^3+34 x^2+32 x+16$
- $y^2=34 x^6+41 x^5+69 x^4+49 x^3+34 x^2+36 x+74$
- $y^2=75 x^6+35 x^5+58 x^4+30 x^3+59 x^2+62 x+27$
- $y^2=70 x^6+38 x^5+33 x^4+32 x^3+39 x^2+55 x+63$
- $y^2=8 x^6+48 x^5+17 x^4+44 x^3+64 x^2+35 x+6$
- $y^2=63 x^6+4 x^5+33 x^4+19 x^3+40 x^2+43 x+42$
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 4.0.6269504.2. |
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.ac_gb | $2$ | (not in LMFDB) |