Properties

Label 2.181.abx_bkz
Base field $\F_{181}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 961 x^{2} - 8869 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0989332971490$, $\pm0.164773451880$
Angle rank:  $2$ (numerical)
Number field:  \(\Q(\zeta_{5})\)
Galois group:  $C_4$
Jacobians:  $11$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $24805$ $1057710005$ $35144116439905$ $1151947736663190005$ $37738739669628951250000$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $133$ $32283$ $5926753$ $1073293443$ $194264980098$ $35161843616283$ $6364291159308733$ $1151936660686152003$ $208500535094782804993$ $37738596847170094900198$

Jacobians and polarizations

This isogeny class contains the Jacobians of 11 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{181}$.

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is \(\Q(\zeta_{5})\).

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

TwistExtension degreeCommon base change
2.181.bx_bkz$2$(not in LMFDB)
2.181.ae_bu$5$(not in LMFDB)
2.181.l_ach$5$(not in LMFDB)

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.181.bx_bkz$2$(not in LMFDB)
2.181.ae_bu$5$(not in LMFDB)
2.181.l_ach$5$(not in LMFDB)
2.181.l_nx$5$(not in LMFDB)
2.181.bf_th$5$(not in LMFDB)
2.181.abf_th$10$(not in LMFDB)
2.181.al_ach$10$(not in LMFDB)
2.181.al_nx$10$(not in LMFDB)
2.181.e_bu$10$(not in LMFDB)