Invariants
Base field: | $\F_{131}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 40 x + 660 x^{2} - 5240 x^{3} + 17161 x^{4}$ |
Frobenius angles: | $\pm0.114963764829$, $\pm0.198420417075$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.747776.1 |
Galois group: | $D_{4}$ |
Jacobians: | $12$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $12542$ | $289745284$ | $5052747391262$ | $86736990396085136$ | $1488395702033592915502$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $92$ | $16882$ | $2247572$ | $294522966$ | $38579973852$ | $5053919383522$ | $662062681572692$ | $86730203879732958$ | $11361656655869706812$ | $1488377021723341092402$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=14x^6+65x^5+5x^4+66x^3+32x^2+78x+93$
- $y^2=116x^6+78x^5+37x^4+118x^3+32x^2+96x+51$
- $y^2=24x^6+120x^5+115x^4+72x^3+127x^2+64x+124$
- $y^2=108x^6+92x^5+109x^4+32x^3+13x^2+104x+18$
- $y^2=130x^6+128x^5+127x^4+80x^3+84x^2+8x+47$
- $y^2=29x^6+126x^5+100x^4+45x^3+32x^2+34x+18$
- $y^2=42x^6+11x^5+90x^4+46x^3+4x^2+113x+88$
- $y^2=8x^6+111x^5+40x^4+119x^3+21x^2+111x+26$
- $y^2=86x^6+4x^5+77x^4+25x^3+112x^2+44x+17$
- $y^2=3x^6+86x^5+37x^4+38x^3+77x^2+8x+23$
- $y^2=5x^6+91x^5+74x^4+103x^3+3x^2+50x+69$
- $y^2=3x^6+98x^5+121x^4+106x^3+43x^2+39x+23$
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 4.0.747776.1. |
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.bo_zk | $2$ | (not in LMFDB) |