Invariants
| Base field: | $\F_{79}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 28 x + 348 x^{2} - 2212 x^{3} + 6241 x^{4}$ |
| Frobenius angles: | $\pm0.123766042460$, $\pm0.274866475067$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.4776192.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $20$ |
| Isomorphism classes: | 20 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4350$ | $38410500$ | $243405298350$ | $1517563978266000$ | $9468531892360116750$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $52$ | $6154$ | $493684$ | $38961766$ | $3077139532$ | $243087690922$ | $19203908473228$ | $1517108824593406$ | $119851596574228276$ | $9468276091477167274$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=68x^6+27x^5+53x^4+13x^3+49x^2+48x+17$
- $y^2=58x^6+64x^5+11x^4+52x^3+34x^2+10x+74$
- $y^2=30x^6+37x^5+2x^4+32x^3+18x^2+72x+46$
- $y^2=78x^6+26x^5+29x^4+38x^3+58x^2+58x+65$
- $y^2=25x^6+25x^5+63x^4+54x^3+41x^2+59x+34$
- $y^2=12x^6+60x^5+36x^4+34x^3+56x^2+72x+20$
- $y^2=66x^6+17x^5+23x^4+30x^3+27x^2+13x+13$
- $y^2=24x^6+2x^5+35x^4+14x^3+13x^2+47x+61$
- $y^2=37x^6+37x^5+66x^4+45x^3+52x^2+39x+62$
- $y^2=73x^6+76x^5+28x^4+61x^3+54x^2+64x+7$
- $y^2=23x^6+62x^5+76x^4+60x^3+13x^2+39x+39$
- $y^2=21x^6+26x^5+11x^4+46x^3+62x^2+23x+27$
- $y^2=68x^6+7x^5+75x^4+34x^3+14x^2+55x+37$
- $y^2=42x^6+25x^5+63x^4+42x^3+2x^2+7x+68$
- $y^2=56x^6+33x^5+70x^4+53x^3+23x^2+11x+51$
- $y^2=36x^6+66x^5+32x^4+78x^3+67x^2+19x+21$
- $y^2=24x^6+74x^5+54x^4+50x^3+30x^2+42x+7$
- $y^2=59x^6+29x^5+25x^4+58x^3+76x^2+21x+35$
- $y^2=11x^6+47x^5+45x^4+48x^3+50x^2+20x+77$
- $y^2=61x^6+54x^5+14x^4+47x^3+25x^2+57x+57$
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 4.0.4776192.1. |
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_nk | $2$ | (not in LMFDB) |