Properties

Label 2.107.abi_tj
Base Field $\F_{107}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{107}$
Dimension:  $2$
L-polynomial:  $( 1 - 17 x + 107 x^{2} )^{2}$
Frobenius angles:  $\pm0.193011390838$, $\pm0.193011390838$
Angle rank:  $1$ (numerical)
Jacobians:  21

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 21 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8281 129390625 1502065945744 17186390634765625 196721739951669013081 2252198054565040036000000 25785345172578550339972705969 295216373612665823448502353515625 3379932268973325549429141508622202256 38696844614090589496713891203503312890625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 74 11300 1226132 131114148 14025988174 1500734660150 160578170506282 17181861725924548 1838459208743592524 196715135674201206500

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
The isogeny class factors as 1.107.ar 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-139}) \)$)$
All geometric endomorphisms are defined over $\F_{107}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.107.a_acx$2$(not in LMFDB)
2.107.bi_tj$2$(not in LMFDB)
2.107.r_ha$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.107.a_acx$2$(not in LMFDB)
2.107.bi_tj$2$(not in LMFDB)
2.107.r_ha$3$(not in LMFDB)
2.107.a_cx$4$(not in LMFDB)
2.107.ar_ha$6$(not in LMFDB)