# Properties

 Label 2.107.abi_ti 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: $( 1 - 18 x + 107 x^{2} )( 1 - 16 x + 107 x^{2} )$ Frobenius angles: $\pm0.164078095836$, $\pm0.218559897265$ Angle rank: $2$ (numerical) Jacobians: 36

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 36 curves, and hence is principally polarizable:

• $y^2=57x^6+27x^5+5x^4+19x^3+5x^2+27x+57$
• $y^2=34x^6+73x^5+91x^4+6x^3+91x^2+73x+34$
• $y^2=77x^6+97x^5+99x^4+74x^3+99x^2+97x+77$
• $y^2=53x^6+67x^5+51x^4+18x^3+88x^2+65x+57$
• $y^2=65x^6+105x^5+77x^4+69x^3+93x^2+30x+80$
• $y^2=45x^6+65x^5+63x^4+38x^3+94x^2+82x+80$
• $y^2=32x^6+51x^5+2x^4+62x^3+2x^2+51x+32$
• $y^2=15x^6+37x^5+78x^4+54x^3+78x^2+37x+15$
• $y^2=93x^6+48x^5+55x^4+99x^3+15x^2+92x+17$
• $y^2=6x^6+2x^5+59x^4+81x^3+73x^2+95x+28$
• $y^2=80x^6+4x^5+99x^4+64x^3+89x^2+47x+82$
• $y^2=50x^6+99x^4+43x^3+99x^2+50$
• $y^2=20x^6+10x^5+36x^4+93x^3+9x^2+14x+7$
• $y^2=64x^6+92x^5+102x^4+23x^3+89x^2+41x+85$
• $y^2=29x^6+42x^5+79x^4+27x^3+79x^2+42x+29$
• $y^2=60x^6+39x^5+62x^4+67x^3+62x^2+39x+60$
• $y^2=42x^6+92x^5+64x^4+50x^3+64x^2+92x+42$
• $y^2=39x^6+42x^5+63x^4+104x^3+63x^2+42x+39$
• $y^2=82x^6+31x^5+77x^4+56x^3+58x^2+55x+80$
• $y^2=91x^6+34x^5+30x^4+59x^3+30x^2+34x+91$
• and 16 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8280 129366720 1501940639160 17186047922534400 196721124782456201400 2252197315237945134870720 25785344754554266479018444120 295216374187747829868481150156800 3379932271138279167265762589786835480 38696844617893742292389533620173911185600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 74 11298 1226030 131111534 14025944314 1500734167506 160578167903038 17181861759394846 1838459209921183850 196715135693534506818

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.as $\times$ 1.107.aq 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_acw $2$ (not in LMFDB) 2.107.c_acw $2$ (not in LMFDB) 2.107.bi_ti $2$ (not in LMFDB)