# Properties

 Label 2.107.abh_sg 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: $( 1 - 20 x + 107 x^{2} )( 1 - 13 x + 107 x^{2} )$ Frobenius angles: $\pm0.0823304377774$, $\pm0.283718842690$ Angle rank: $2$ (numerical) Jacobians: 28

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 28 curves, and hence is principally polarizable:

• $y^2=63x^6+88x^5+39x^4+53x^3+14x^2+75x+66$
• $y^2=95x^6+50x^5+58x^4+36x^3+56x^2+5x+15$
• $y^2=70x^6+38x^5+85x^4+85x^3+101x^2+97x+55$
• $y^2=2x^6+79x^5+52x^4+66x^3+68x^2+71x+2$
• $y^2=100x^6+7x^5+47x^4+92x^3+104x^2+98x+58$
• $y^2=55x^6+16x^5+85x^4+46x^3+43x^2+26x+3$
• $y^2=80x^6+55x^5+40x^4+61x^3+65x^2+85x+38$
• $y^2=29x^6+46x^5+70x^4+102x^3+58x^2+92x+78$
• $y^2=57x^6+21x^5+76x^4+25x^3+92x^2+15x+37$
• $y^2=22x^6+45x^5+18x^4+22x^2+58x+96$
• $y^2=8x^6+45x^5+53x^4+104x^3+6x^2+66x+14$
• $y^2=73x^6+44x^5+39x^4+8x^3+48x^2+69x+11$
• $y^2=76x^6+91x^5+11x^4+16x^3+95x^2+25x+97$
• $y^2=78x^6+55x^5+97x^4+70x^3+49x^2+83x+57$
• $y^2=68x^6+84x^5+23x^4+105x^3+104x^2+74x+5$
• $y^2=82x^6+104x^5+10x^4+20x^3+70x^2+52x+103$
• $y^2=66x^6+82x^5+51x^4+8x^3+85x^2+7x+4$
• $y^2=26x^6+26x^5+88x^4+29x^3+8x^2+90x+93$
• $y^2=96x^6+23x^5+18x^4+24x^3+60x^2+65x+101$
• $y^2=10x^6+52x^5+32x^4+34x^3+3x^2+52x+98$
• $y^2=67x^6+40x^5+60x^4+8x^2+21x+105$
• $y^2=18x^6+57x^5+84x^4+29x^3+18x^2+44x+90$
• $y^2=7x^6+9x^5+71x^4+26x^3+73x^2+95x+12$
• $y^2=93x^6+101x^5+4x^4+77x^3+52x^2+56x+78$
• $y^2=77x^6+64x^5+54x^4+52x^3+2x^2+63x+27$
• $y^2=97x^6+26x^5+78x^4+36x^3+54x^2+38x+58$
• $y^2=63x^6+101x^5+70x^4+54x^2+58x+17$
• $y^2=43x^6+92x^5+49x^4+105x^3+22x^2+21x+8$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8360 129479680 1501214797280 17183064471654400 196715065863966207800 2252189336661777183784960 25785338402618496274362773720 295216374028255948558807418880000 3379932279990000202030150478293583840 38696844634363134316318619765673968358400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 75 11309 1225440 131088777 14025512325 1500728851046 160578128346375 17181861750112273 1838459214735933600 196715135777256544589

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.au $\times$ 1.107.an 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.ah_abu $2$ (not in LMFDB) 2.107.h_abu $2$ (not in LMFDB) 2.107.bh_sg $2$ (not in LMFDB)