Properties

Label 2.49.az_js
Base Field $\F_{7^{2}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{7^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 7 x )^{2}( 1 - 11 x + 49 x^{2} )$
Frobenius angles:  $0$, $0$, $\pm0.212295615010$
Angle rank:  $1$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

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

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
$A(\F_{q^r})$ 1404 5481216 13794266304 33229872000000 79792089206639004 191580099210202300416 459985468327682400887004 1104427067459638133952000000 2651730588152789271029629850304 6366805674073169973346283287862016

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 25 2281 117250 5764273 282474625 13841205406 678221497825 33232912311073 1628413439654050 79792265209337881

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
The isogeny class factors as 1.49.ao $\times$ 1.49.al 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 $\F_{7^{2}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.49.ad_ace$2$(not in LMFDB)
2.49.d_ace$2$(not in LMFDB)
2.49.z_js$2$(not in LMFDB)
2.49.aq_ew$3$(not in LMFDB)
2.49.ab_adg$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.49.ad_ace$2$(not in LMFDB)
2.49.d_ace$2$(not in LMFDB)
2.49.z_js$2$(not in LMFDB)
2.49.aq_ew$3$(not in LMFDB)
2.49.ab_adg$3$(not in LMFDB)
2.49.al_du$4$(not in LMFDB)
2.49.l_du$4$(not in LMFDB)
2.49.abb_ku$6$(not in LMFDB)
2.49.am_cs$6$(not in LMFDB)
2.49.b_adg$6$(not in LMFDB)
2.49.m_cs$6$(not in LMFDB)
2.49.q_ew$6$(not in LMFDB)
2.49.bb_ku$6$(not in LMFDB)
2.49.an_du$12$(not in LMFDB)
2.49.ac_du$12$(not in LMFDB)
2.49.c_du$12$(not in LMFDB)
2.49.n_du$12$(not in LMFDB)