# Properties

 Label 2.107.abk_uq 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: $1 - 36 x + 536 x^{2} - 3852 x^{3} + 11449 x^{4}$ Frobenius angles: $\pm0.112288198128$, $\pm0.203926913540$ Angle rank: $2$ (numerical) Number field: 4.0.499968.5 Galois group: $D_{4}$ Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=21x^6+69x^5+63x^4+80x^3+69x^2+22x+51$
• $y^2=105x^6+12x^5+19x^4+80x^3+75x^2+91x+61$
• $y^2=65x^6+76x^5+67x^4+78x^3+83x^2+41x+68$
• $y^2=46x^6+91x^5+62x^4+35x^3+72x^2+19x+4$
• $y^2=12x^6+41x^5+66x^4+34x^3+71x^2+68x+98$
• $y^2=106x^6+103x^5+60x^4+72x^3+89x^2+61x+98$
• $y^2=85x^6+49x^5+89x^4+54x^3+103x^2+19x+46$
• $y^2=66x^6+63x^5+43x^4+46x^3+94x^2+61x+97$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8098 128547652 1500335061106 17183896870412304 196719088775649102178 2252196304333003958997508 25785345605309342835597008242 295216377325724308359297598636032 3379932276382061774436797736346897762 38696844624497629336653736475067518616772

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 72 11226 1224720 131095126 14025799152 1500733493898 160578173201112 17181861942027934 1838459212773454152 196715135727105319866

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The endomorphism algebra of this simple isogeny class is 4.0.499968.5.
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.bk_uq $2$ (not in LMFDB)