# Properties

 Label 2.107.abk_up Base Field $\F_{107}$ Dimension $2$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{107}$ Dimension: $2$ L-polynomial: $1 - 36 x + 535 x^{2} - 3852 x^{3} + 11449 x^{4}$ Frobenius angles: $\pm0.0971505065705$, $\pm0.211972914317$ Angle rank: $2$ (numerical) Number field: 4.0.909072.1 Galois group: $D_{4}$ Jacobians: 14

This isogeny class is simple and geometrically simple.

## Newton polygon

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

## Point counts

This isogeny class contains the Jacobians of 14 curves, and hence is principally polarizable:

• $y^2=103x^6+45x^5+18x^4+39x^3+23x^2+103x+70$
• $y^2=3x^6+53x^5+103x^4+16x^3+80x^2+104x+84$
• $y^2=54x^6+33x^5+98x^4+63x^3+29x^2+54x+66$
• $y^2=21x^6+19x^5+66x^4+94x^3+41x^2+22x+72$
• $y^2=72x^6+37x^5+72x^4+99x^3+44x^2+100x+28$
• $y^2=75x^6+42x^5+24x^4+95x^3+26x^2+67x+13$
• $y^2=51x^6+96x^5+77x^4+102x^3+52x^2+10x+36$
• $y^2=43x^6+105x^5+49x^4+81x^3+75x^2+51x+35$
• $y^2=94x^6+37x^5+38x^4+26x^3+11x^2+80x+60$
• $y^2=10x^6+11x^5+57x^4+85x^3+21x^2+10x+33$
• $y^2=74x^6+4x^5+39x^4+83x^3+91x^2+86x+70$
• $y^2=72x^6+61x^5+93x^4+94x^3+71x^2+71x+55$
• $y^2=50x^6+36x^5+59x^4+4x^3+100x^2+82x+43$
• $y^2=15x^6+68x^5+87x^4+38x^3+82x^2+94x+60$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8097 128523681 1500202346436 17183498036437161 196718250597527385177 2252194951447240426413072 25785343890130374557862630081 295216375702769177574699681727113 3379932275557036443351934193108703972 38696844625225466572825488851103846106641

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 72 11224 1224612 131092084 14025739392 1500732592414 160578162519840 17181861847570468 1838459212324695036 196715135730805275304

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The endomorphism algebra of this simple isogeny class is 4.0.909072.1.
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.bk_up $2$ (not in LMFDB)