Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 48 x + 932 x^{2} - 8688 x^{3} + 32761 x^{4}$ |
Frobenius angles: | $\pm0.0587985007366$, $\pm0.204345036706$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.3651840.3 |
Galois group: | $D_{4}$ |
Jacobians: | $20$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $24958$ | $1058967940$ | $35147317165438$ | $1151943736680090000$ | $37738664441509340762158$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $134$ | $32322$ | $5927294$ | $1073289718$ | $194264592854$ | $35161832027922$ | $6364290918055694$ | $1151936656742226718$ | $208500535043430152294$ | $37738596846676822148802$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=12x^6+168x^5+5x^4+9x^3+106x^2+48x+69$
- $y^2=84x^6+133x^5+49x^4+77x^3+16x^2+176x+118$
- $y^2=155x^6+176x^5+64x^4+146x^3+84x^2+118x+86$
- $y^2=24x^6+160x^5+126x^4+22x^3+65x^2+124x+22$
- $y^2=174x^6+106x^5+146x^4+86x^3+141x^2+2x+72$
- $y^2=136x^6+96x^5+20x^4+141x^3+55x^2+167x+30$
- $y^2=85x^6+174x^5+137x^4+70x^3+56x^2+46x+12$
- $y^2=109x^6+178x^5+144x^4+44x^3+108x^2+121x+38$
- $y^2=35x^6+38x^5+46x^4+73x^3+121x^2+53x+170$
- $y^2=141x^6+13x^5+71x^4+134x^3+20x^2+63x+146$
- $y^2=73x^6+126x^5+29x^4+95x^3+133x^2+164x+123$
- $y^2=164x^6+129x^5+105x^4+176x^3+179x^2+54x+31$
- $y^2=54x^6+40x^5+11x^4+153x^3+154x^2+67x+69$
- $y^2=53x^6+146x^5+132x^4+164x^3+156x^2+125x+53$
- $y^2=25x^6+132x^5+171x^4+38x^3+130x^2+33x+9$
- $y^2=110x^6+168x^5+42x^4+162x^3+164x^2+144x+118$
- $y^2=36x^6+60x^5+36x^4+114x^3+96x^2+42x+131$
- $y^2=176x^6+85x^5+152x^4+41x^3+143x^2+11x+158$
- $y^2=104x^6+31x^5+167x^4+50x^3+110x^2+29x+44$
- $y^2=95x^6+13x^5+158x^4+110x^3+74x^2+179x+60$
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 4.0.3651840.3. |
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_bjw | $2$ | (not in LMFDB) |