# Properties

 Label 2.181.abv_bja Base Field $\F_{181}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{181}$ Dimension: $2$ L-polynomial: $1 - 47 x + 910 x^{2} - 8507 x^{3} + 32761 x^{4}$ Frobenius angles: $\pm0.101095234702$, $\pm0.206548865791$ Angle rank: $2$ (numerical) Number field: 4.0.5395052.1 Galois group: $D_{4}$ Jacobians: 16

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 16 curves, and hence is principally polarizable:

• $y^2=3x^6+94x^5+140x^4+36x^3+17x^2+118x+7$
• $y^2=97x^6+79x^5+55x^4+10x^2+120x+132$
• $y^2=147x^6+76x^5+152x^4+41x^3+6x^2+116x+48$
• $y^2=24x^6+62x^5+4x^4+158x^3+45x^2+180x+59$
• $y^2=19x^6+98x^5+111x^4+74x^3+34x^2+140x+138$
• $y^2=104x^6+166x^5+108x^4+36x^3+146x^2+92x+19$
• $y^2=138x^6+129x^5+174x^4+118x^3+61x^2+95x+99$
• $y^2=107x^6+52x^5+28x^4+140x^3+33x^2+132x+146$
• $y^2=35x^6+54x^5+135x^4+52x^3+62x^2+7x+151$
• $y^2=50x^6+26x^5+104x^4+53x^3+115x^2+66x+122$
• $y^2=7x^6+157x^5+35x^4+68x^2+140x+145$
• $y^2=170x^6+88x^5+94x^4+156x^3+179x^2+29x+148$
• $y^2=31x^6+58x^5+150x^4+88x^3+66x^2+46x+6$
• $y^2=98x^6+78x^5+156x^4+142x^3+115x^2+92x+90$
• $y^2=8x^6+80x^5+105x^4+130x^3+x^2+64x+138$
• $y^2=97x^6+145x^5+17x^4+164x^3+149x^2+66x+55$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 25118 1060632668 35155703788448 1151975948559692672 37738770133589417846358 1236354612936908884486068992 40504199794471643475908992301702 1326958064538181042526605543263723008 43472473123172449886687161457327389299872 1424201691977355590243605134031641656775780348

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 135 32373 5928708 1073319729 194265136915 35161840887114 6364291051081959 1151936658605318145 208500535067692922724 37738596846963668465293

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
 The endomorphism algebra of this simple isogeny class is 4.0.5395052.1.
All geometric endomorphisms are defined over $\F_{181}$.

## 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.bv_bja $2$ (not in LMFDB)