Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 48 x + 933 x^{2} - 8688 x^{3} + 32761 x^{4}$ |
Frobenius angles: | $\pm0.0712454186694$, $\pm0.200090328096$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.223225.1 |
Galois group: | $D_{4}$ |
Jacobians: | $26$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $24959$ | $1059035329$ | $35148172307600$ | $1151949625203197689$ | $37738693348157251730159$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $134$ | $32324$ | $5927438$ | $1073295204$ | $194264741654$ | $35161835230838$ | $6364290975562094$ | $1151936657623560004$ | $208500535055041922198$ | $37738596846807669294404$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 26 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=40x^6+48x^5+64x^4+175x^3+58x^2+26x+124$
- $y^2=78x^6+117x^5+177x^4+60x^3+41x^2+26x+34$
- $y^2=36x^6+44x^5+59x^4+37x^3+152x^2+76x+108$
- $y^2=107x^6+101x^5+162x^4+162x^3+127x^2+84x+124$
- $y^2=31x^6+40x^5+135x^4+10x^3+56x^2+34x+13$
- $y^2=72x^6+88x^5+2x^4+69x^3+6x^2+46x+36$
- $y^2=17x^6+131x^5+88x^4+31x^3+163x^2+30x+44$
- $y^2=58x^6+167x^5+7x^4+37x^3+29x^2+32x+53$
- $y^2=3x^6+122x^5+103x^4+169x^3+171x^2+107x+68$
- $y^2=139x^6+41x^5+138x^4+73x^3+172x^2+80x+147$
- $y^2=88x^6+66x^5+106x^4+108x^3+100x^2+167x+37$
- $y^2=92x^6+56x^5+176x^4+69x^3+105x^2+63x+88$
- $y^2=170x^6+33x^5+28x^4+11x^3+90x^2+177x+8$
- $y^2=54x^6+23x^5+94x^4+60x^3+16x^2+70x+93$
- $y^2=167x^6+8x^5+125x^4+80x^3+24x^2+115x+120$
- $y^2=41x^6+171x^5+4x^4+24x^3+136x^2+171x+2$
- $y^2=166x^6+32x^5+23x^4+11x^3+119x^2+20x+146$
- $y^2=109x^6+36x^5+16x^4+29x^3+49x^2+72x+66$
- $y^2=43x^6+84x^5+30x^4+5x^3+97x^2+13x+122$
- $y^2=97x^6+x^5+175x^4+15x^3+88x^2+127x+59$
- $y^2=71x^6+161x^5+157x^4+172x^3+38x^2+174x+126$
- $y^2=134x^6+53x^5+106x^4+34x^3+105x^2+175x+57$
- $y^2=107x^6+55x^5+91x^4+139x^2+60x+165$
- $y^2=87x^6+57x^5+87x^4+131x^3+166x^2+110x+77$
- $y^2=36x^6+51x^5+171x^4+113x^3+89x^2+101x+120$
- $y^2=6x^6+114x^5+162x^4+121x^3+63x^2+11x+175$
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 4.0.223225.1. |
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_bjx | $2$ | (not in LMFDB) |