Properties

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

Invariants

 Base field: $\F_{107}$ Dimension: $2$ L-polynomial: $( 1 - 20 x + 107 x^{2} )( 1 - 19 x + 107 x^{2} )$ Frobenius angles: $\pm0.0823304377774$, $\pm0.129482033963$ Angle rank: $2$ (numerical) Jacobians: 0

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 is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 7832 127316992 1497867399776 17180497637822464 196715709548079020552 2252194329555486174724096 25785346363271793039272617064 295216381485538107227006493081600 3379932283484423550166948459493915744 38696844632866934567326724037485030167552

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 69 11117 1222704 131069193 14025558219 1500732178022 160578177921321 17181862184132881 1838459216636668368 196715135769650623757

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.au $\times$ 1.107.at 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.ab_agk $2$ (not in LMFDB) 2.107.b_agk $2$ (not in LMFDB) 2.107.bn_ww $2$ (not in LMFDB)