# Properties

 Label 2.107.abh_sf Base Field $\F_{107}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{107}$ Dimension: $2$ L-polynomial: $1 - 33 x + 473 x^{2} - 3531 x^{3} + 11449 x^{4}$ Frobenius angles: $\pm0.0734344692256$, $\pm0.286479328979$ Angle rank: $2$ (numerical) Number field: 4.0.16508493.1 Galois group: $D_{4}$ Jacobians: 18

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 18 curves, and hence is principally polarizable:

• $y^2=53x^6+86x^5+48x^4+55x^3+17x^2+65x+106$
• $y^2=8x^6+2x^5+89x^4+67x^3+80x^2+79x+59$
• $y^2=24x^6+93x^5+31x^4+15x^3+67x^2+39x+74$
• $y^2=72x^6+70x^5+92x^4+x^3+52x^2+56x+21$
• $y^2=95x^6+58x^5+48x^4+35x^3+12x^2+61x+70$
• $y^2=82x^6+45x^5+65x^4+55x^3+31x^2+39x+63$
• $y^2=32x^6+72x^5+102x^4+100x^3+6x^2+83x+40$
• $y^2=49x^6+103x^5+30x^4+43x^3+x^2+59x+1$
• $y^2=71x^6+85x^5+35x^4+x^3+74x^2+38x+56$
• $y^2=21x^6+13x^5+95x^4+78x^3+59x^2+3x+54$
• $y^2=84x^6+32x^5+63x^4+45x^3+56x^2+57x+8$
• $y^2=89x^6+21x^5+86x^4+2x^3+83x^2+48x+5$
• $y^2=22x^6+x^5+26x^4+44x^3+5x^2+40x+19$
• $y^2=91x^6+93x^5+66x^4+19x^3+100x^2+49x+73$
• $y^2=6x^6+18x^5+48x^4+96x^3+9x^2+48x+90$
• $y^2=30x^6+70x^5+104x^4+88x^3+11x^2+78x+92$
• $y^2=81x^6+18x^5+6x^4+25x^3+59x^2+5x+87$
• $y^2=90x^6+89x^5+72x^4+69x^3+85x^2+106x+45$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8359 129455833 1501093229233 17182741714048989 196714489624683441424 2252188573128331854084601 25785337612377586246946406997 295216373338673653712394499875093 3379932279361068138793439957062525819 38696844633594811277819732599430364268288

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 75 11307 1225341 131086315 14025471240 1500728342271 160578123425151 17181861709977955 1838459214393836229 196715135773350779862

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The endomorphism algebra of this simple isogeny class is 4.0.16508493.1.
All geometric endomorphisms are defined over $\F_{107}$.

## 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 2.107.bh_sf $2$ (not in LMFDB)