Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 906 x^{2} - 8507 x^{3} + 32761 x^{4}$ |
Frobenius angles: | $\pm0.0635793485401$, $\pm0.221935502645$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.9265212.2 |
Galois group: | $D_{4}$ |
Jacobians: | $16$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $25114$ | $1060363308$ | $35152354711456$ | $1151953605373879488$ | $37738665315964174366594$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $135$ | $32365$ | $5928144$ | $1073298913$ | $194264597355$ | $35161829997658$ | $6364290873082431$ | $1151936656247343649$ | $208500535043671137936$ | $37738596846816604226965$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 16 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=26x^6+103x^5+85x^4+72x^3+102x^2+41x+22$
- $y^2=172x^6+97x^5+117x^4+66x^3+15x^2+143x+86$
- $y^2=92x^6+112x^5+111x^4+9x^3+127x^2+129x+23$
- $y^2=140x^6+122x^5+54x^4+79x^3+11x^2+139x+119$
- $y^2=96x^6+84x^5+87x^4+141x^3+x^2+135x+27$
- $y^2=161x^6+14x^5+105x^4+22x^3+135x^2+6x+165$
- $y^2=51x^6+69x^5+123x^4+19x^3+80x^2+129x+135$
- $y^2=97x^6+133x^5+75x^4+131x^3+90x^2+94x+169$
- $y^2=92x^6+82x^5+38x^4+80x^3+112x^2+17x+125$
- $y^2=97x^6+161x^5+43x^4+102x^3+175x^2+113x+71$
- $y^2=37x^6+32x^5+112x^4+57x^3+141x^2+26x+32$
- $y^2=106x^6+63x^5+178x^4+109x^3+34x^2+131x+24$
- $y^2=x^6+123x^5+116x^4+166x^3+134x^2+173x+67$
- $y^2=74x^6+86x^5+177x^4+130x^3+175x^2+35x+15$
- $y^2=127x^6+34x^5+101x^4+38x^3+37x^2+70x+164$
- $y^2=158x^6+78x^5+26x^4+113x^3+155x^2+73x+6$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{181}$.
Endomorphism algebra over $\F_{181}$The endomorphism algebra of this simple isogeny class is 4.0.9265212.2. |
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 |
---|---|---|
2.181.bv_biw | $2$ | (not in LMFDB) |