Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 48 x + 931 x^{2} - 8688 x^{3} + 32761 x^{4}$ |
Frobenius angles: | $\pm0.0444136033573$, $\pm0.208191558910$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.326928.1 |
Galois group: | $D_{4}$ |
Jacobians: | $10$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $24957$ | $1058900553$ | $35146462028868$ | $1151937843870675033$ | $37738635441619717040157$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $134$ | $32320$ | $5927150$ | $1073284228$ | $194264443574$ | $35161828794718$ | $6364290859209998$ | $1151936655814360324$ | $208500535030469248118$ | $37738596846512132676640$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=174x^6+16x^5+83x^4+116x^3+22x^2+175x+144$
- $y^2=161x^6+104x^5+31x^4+131x^3+126x^2+102x+31$
- $y^2=42x^6+56x^5+109x^4+47x^3+70x^2+50x+175$
- $y^2=55x^6+148x^5+142x^4+150x^3+5x^2+79x+74$
- $y^2=178x^6+141x^5+126x^4+119x^3+91x^2+81x+70$
- $y^2=120x^6+60x^5+32x^4+92x^3+173x^2+171x+95$
- $y^2=42x^6+114x^5+166x^4+171x^3+127x^2+120x+103$
- $y^2=76x^6+116x^5+20x^4+32x^3+139x^2+73x+35$
- $y^2=160x^6+132x^5+54x^4+131x^3+87x^2+54x+169$
- $y^2=173x^6+20x^5+40x^4+125x^3+19x^2+48x+132$
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 4.0.326928.1. |
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 |
---|---|---|
2.181.bw_bjv | $2$ | (not in LMFDB) |