Invariants
Base field: | $\F_{167}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 805 x^{2} - 7348 x^{3} + 27889 x^{4}$ |
Frobenius angles: | $\pm0.0434254521130$, $\pm0.247924377782$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.688337.1 |
Galois group: | $D_{4}$ |
Jacobians: | $34$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $21303$ | $768761361$ | $21687450639552$ | $604973402008177401$ | $16871923575591307449183$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $124$ | $27564$ | $4656496$ | $777804404$ | $129891952124$ | $21691955596014$ | $3622557435915668$ | $604967114690152228$ | $101029508510725282000$ | $16871927924858890758204$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 34 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=78x^6+153x^5+123x^4+145x^3+52x^2+164x+26$
- $y^2=110x^6+155x^5+146x^4+132x^3+87x^2+55x+117$
- $y^2=93x^6+123x^5+122x^4+66x^3+28x^2+62x+30$
- $y^2=104x^6+37x^5+50x^4+5x^3+77x+128$
- $y^2=60x^6+159x^5+119x^4+40x^3+139x^2+92x+107$
- $y^2=56x^6+34x^5+141x^4+139x^3+134x^2+24x+132$
- $y^2=47x^6+117x^5+126x^4+81x^3+16x^2+45x+67$
- $y^2=144x^6+112x^5+63x^4+160x^3+108x^2+61x+45$
- $y^2=24x^6+150x^5+135x^4+85x^3+58x^2+32x+31$
- $y^2=4x^6+141x^5+15x^4+139x^3+17x^2+73x+84$
- $y^2=2x^6+15x^5+163x^4+162x^3+141x^2+102x+63$
- $y^2=91x^6+73x^5+64x^4+77x^3+122x^2+38x+46$
- $y^2=85x^6+51x^5+77x^4+125x^3+5x^2+31x+120$
- $y^2=103x^6+19x^5+110x^4+88x^3+118x^2+85x+80$
- $y^2=129x^6+127x^5+43x^4+123x^3+156x^2+162x+121$
- $y^2=28x^6+69x^5+8x^4+64x^3+149x^2+131x+43$
- $y^2=16x^6+153x^5+30x^4+11x^3+100x^2+48x+139$
- $y^2=54x^6+105x^5+91x^4+48x^3+109x^2+147x+155$
- $y^2=92x^6+37x^5+69x^4+144x^3+108x^2+125x+128$
- $y^2=35x^6+121x^5+68x^4+105x^3+11x^2+107x+131$
- and 14 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{167}$.
Endomorphism algebra over $\F_{167}$The endomorphism algebra of this simple isogeny class is 4.0.688337.1. |
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 |
---|---|---|
2.167.bs_bez | $2$ | (not in LMFDB) |