Properties

Label 3.13.aq_es_avi
Base Field $\F_{13}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
L-polynomial:  $( 1 - 6 x + 13 x^{2} )( 1 - 10 x + 49 x^{2} - 130 x^{3} + 169 x^{4} )$
Frobenius angles:  $\pm0.151058869957$, $\pm0.187167041811$, $\pm0.334339837461$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 632 4537760 11092755296 23720595868800 51385281922411832 112545827109430561280 247130953553319137008856 542851068350390788895040000 1192553650942543655591798074592 2619988859435131899903417554224800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 158 2296 29074 372738 4830692 62765386 815806306 10604680408 137858134878

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The isogeny class factors as 1.13.ag $\times$ 2.13.ak_bx 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 $\F_{13}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.ae_c_bi$2$(not in LMFDB)
3.13.e_c_abi$2$(not in LMFDB)
3.13.q_es_vi$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.13.ae_c_bi$2$(not in LMFDB)
3.13.e_c_abi$2$(not in LMFDB)
3.13.q_es_vi$2$(not in LMFDB)
3.13.ao_dy_aro$4$(not in LMFDB)
3.13.ag_w_acm$4$(not in LMFDB)
3.13.g_w_cm$4$(not in LMFDB)
3.13.o_dy_ro$4$(not in LMFDB)