# Properties

 Label 2.107.abl_vh 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: $1 - 37 x + 553 x^{2} - 3959 x^{3} + 11449 x^{4}$ Frobenius angles: $\pm0.0615358508181$, $\pm0.201040771877$ Angle rank: $2$ (numerical) Number field: 4.0.398333.1 Galois group: $D_{4}$ Jacobians: 7

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 7 curves, and hence is principally polarizable:

• $y^2=58x^6+33x^5+63x^4+62x^3+93x^2+27x+103$
• $y^2=86x^6+6x^5+59x^4+x^3+88x^2+105x+32$
• $y^2=98x^6+45x^5+18x^4+62x^3+73x^2+26x+45$
• $y^2=18x^6+9x^5+103x^4+52x^3+83x^2+19x+24$
• $y^2=69x^6+25x^5+71x^4+61x^3+65x^2+18x+66$
• $y^2=89x^5+61x^4+93x^3+69x^2+18x+23$
• $y^2=101x^6+55x^5+2x^4+60x^3+3x^2+10x+9$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8007 128103993 1499326371657 17182164941185149 196716570086744379312 2252193052085463061046601 25785341792303193226682451741 295216373243904014130285016943253 3379932272453669978168176281550580283 38696844621302986076004493509980387205888

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 71 11187 1223897 131081915 14025619576 1500731326791 160578149455627 17181861704462275 1838459210636669297 196715135710865373462

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The endomorphism algebra of this simple isogeny class is 4.0.398333.1.
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.bl_vh $2$ (not in LMFDB)