# Properties

 Label 2.131.g_b Base field $\F_{131}$ Dimension $2$ $p$-rank $2$ Ordinary yes Supersingular no Simple yes Geometrically simple yes Primitive yes Principally polarizable yes Contains a Jacobian yes

## Invariants

 Base field: $\F_{131}$ Dimension: $2$ L-polynomial: $1 + 6 x + x^{2} + 786 x^{3} + 17161 x^{4}$ Frobenius angles: $\pm0.300401032106$, $\pm0.822720592890$ Angle rank: $2$ (numerical) Number field: 4.0.724392000.1 Galois group: $D_{4}$ Jacobians: 576

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## Point counts

This isogeny class contains the Jacobians of 576 curves, and hence is principally polarizable:

• $y^2=102x^6+93x^5+84x^4+76x^3+101x^2+88x+75$
• $y^2=23x^6+19x^5+83x^3+16x^2+107x+104$
• $y^2=68x^6+31x^5+22x^4+95x^3+24x^2+48x+48$
• $y^2=95x^6+101x^5+85x^4+55x^3+19x^2+52x+56$
• $y^2=62x^6+31x^5+90x^4+8x^3+83x+69$
• $y^2=123x^6+29x^5+53x^4+58x^3+89x^2+109x+35$
• $y^2=68x^6+93x^5+66x^4+20x^3+57x^2+19x+5$
• $y^2=79x^6+39x^5+91x^4+113x^3+123x^2+21x+56$
• $y^2=55x^6+52x^5+49x^4+33x^3+25x^2+45x+113$
• $y^2=85x^6+17x^5+44x^4+74x^3+49x^2+55x+67$
• $y^2=56x^6+9x^5+127x^4+98x^3+61x^2+29x+130$
• $y^2=55x^6+91x^5+126x^4+8x^3+61x^2+104x+21$
• $y^2=48x^6+65x^5+65x^4+117x^3+71x^2+7x+36$
• $y^2=100x^6+83x^5+44x^4+92x^3+129x^2+124x+112$
• $y^2=18x^6+96x^5+86x^4+120x^3+2x^2+80x+80$
• $y^2=69x^6+67x^5+4x^4+38x^3+46x^2+96x+128$
• $y^2=59x^6+103x^5+120x^4+32x^3+35x^2+94x+99$
• $y^2=128x^6+22x^5+24x^4+91x^3+60x^2+16x+15$
• $y^2=126x^6+9x^5+64x^4+126x^3+70x^2+42x+112$
• $y^2=108x^6+25x^5+4x^4+99x^3+47x^2+77x+100$
• and 556 more

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $17955$ $293941305$ $5059662908580$ $86744524991098905$ $1488362726025477421875$

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $138$ $17128$ $2250648$ $294548548$ $38579119098$ $5053913893438$ $662062535692878$ $86730203442289348$ $11361656660456567448$ $1488377021750445489448$

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{131}$
 The endomorphism algebra of this simple isogeny class is 4.0.724392000.1.
All geometric endomorphisms are defined over $\F_{131}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
TwistExtension degreeCommon base change
2.131.ag_b$2$(not in LMFDB)