Invariants
Base field: | $\F_{131}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 41 x + 679 x^{2} - 5371 x^{3} + 17161 x^{4}$ |
Frobenius angles: | $\pm0.0723194931602$, $\pm0.195750322624$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.783653.1 |
Galois group: | $D_{4}$ |
Jacobians: | $13$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $12429$ | $289011537$ | $5050505394639$ | $86731838853806493$ | $1488385759381050385584$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $91$ | $16839$ | $2246575$ | $294505475$ | $38579716136$ | $5053916054835$ | $662062643309249$ | $86730203491637203$ | $11361656652577246489$ | $1488377021704920979974$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 13 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=77x^6+37x^5+64x^4+38x^3+81x^2+19x+94$
- $y^2=116x^6+115x^5+27x^4+73x^3+130x^2+128x+14$
- $y^2=21x^6+95x^5+126x^4+55x^3+41x^2+94x+15$
- $y^2=103x^6+66x^5+62x^4+29x^3+125x^2+16x+22$
- $y^2=113x^6+15x^5+62x^4+38x^3+62x^2+115x+72$
- $y^2=96x^6+64x^5+5x^4+113x^3+115x^2+10x+72$
- $y^2=89x^6+108x^5+31x^4+47x^3+29x^2+89x+57$
- $y^2=115x^6+95x^5+51x^4+6x^3+110x^2+116x+14$
- $y^2=62x^6+72x^5+113x^4+51x^3+108x^2+8x+48$
- $y^2=67x^6+33x^5+7x^4+29x^3+53x^2+123x+80$
- $y^2=48x^6+64x^5+33x^4+14x^3+124x^2+75x+23$
- $y^2=117x^6+35x^5+41x^4+71x^3+17x^2+127x+56$
- $y^2=111x^6+13x^5+93x^4+112x^3+72x^2+125x+122$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{131}$.
Endomorphism algebra over $\F_{131}$The endomorphism algebra of this simple isogeny class is 4.0.783653.1. |
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 |
---|---|---|
2.131.bp_bad | $2$ | (not in LMFDB) |