# Properties

 Label 2.107.abm_wc 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: $( 1 - 20 x + 107 x^{2} )( 1 - 18 x + 107 x^{2} )$ Frobenius angles: $\pm0.0823304377774$, $\pm0.164078095836$ Angle rank: $2$ (numerical) Jacobians: 12

This isogeny class is not 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 12 curves, and hence is principally polarizable:

• $y^2=72x^6+67x^5+32x^4+34x^3+32x^2+67x+72$
• $y^2=44x^6+20x^5+42x^4+71x^3+86x^2+5x+48$
• $y^2=26x^6+17x^5+81x^4+21x^3+99x^2+32x+78$
• $y^2=38x^6+61x^5+95x^4+x^3+95x^2+61x+38$
• $y^2=35x^6+48x^5+59x^4+59x^3+59x^2+48x+35$
• $y^2=67x^6+50x^5+100x^4+26x^3+100x^2+50x+67$
• $y^2=71x^6+15x^5+80x^4+61x^3+60x^2+82x+45$
• $y^2=18x^6+10x^5+99x^4+75x^3+11x^2+49x+74$
• $y^2=8x^6+17x^5+91x^4+99x^3+91x^2+17x+8$
• $y^2=18x^6+48x^5+62x^4+92x^3+33x^2+100x+26$
• $y^2=14x^6+60x^5+25x^4+87x^3+41x^2+15x+25$
• $y^2=58x^6+9x^5+85x^4+41x^3+85x^2+9x+58$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 7920 127733760 1498731165360 17181743962521600 196717032583030119600 2252195192001181081374720 25785346102879704258090547440 295216379510735944567070392320000 3379932279521031740822863585562375280 38696844627189568061060577746087110348800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 70 11154 1223410 131078702 14025652550 1500732752706 160578176299730 17181862069197598 1838459214480845830 196715135740789771314

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.au $\times$ 1.107.as and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ac_afq $2$ (not in LMFDB) 2.107.c_afq $2$ (not in LMFDB) 2.107.bm_wc $2$ (not in LMFDB)