Properties

Label 2.49.aba_kh
Base Field $\F_{7^{2}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{7^{2}}$
Dimension:  $2$
L-polynomial:  $( 1 - 13 x + 49 x^{2} )^{2}$
Frobenius angles:  $\pm0.121037718324$, $\pm0.121037718324$
Angle rank:  $1$ (numerical)
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1369 5433561 13774308496 33230186580969 79798428896628649 191585480762348015616 459988518428635068448489 1104428436772447798142978889 2651731098423960721055865252496 6366805832081790770045470407222201

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 24 2260 117078 5764324 282497064 13841594206 678225995016 33232953514564 1628413753008822 79792267189587700

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
The isogeny class factors as 1.49.an 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$
All geometric endomorphisms are defined over $\F_{7^{2}}$.

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{7^{2}}$.

SubfieldPrimitive Model
$\F_{7}$2.7.a_an

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.49.a_act$2$(not in LMFDB)
2.49.ba_kh$2$(not in LMFDB)
2.49.al_cu$3$(not in LMFDB)
2.49.ac_abt$3$(not in LMFDB)
2.49.e_dy$3$(not in LMFDB)
2.49.n_eq$3$(not in LMFDB)
2.49.w_il$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.49.a_act$2$(not in LMFDB)
2.49.ba_kh$2$(not in LMFDB)
2.49.al_cu$3$(not in LMFDB)
2.49.ac_abt$3$(not in LMFDB)
2.49.e_dy$3$(not in LMFDB)
2.49.n_eq$3$(not in LMFDB)
2.49.w_il$3$(not in LMFDB)
2.49.a_ct$4$(not in LMFDB)
2.49.ay_jh$6$(not in LMFDB)
2.49.aw_il$6$(not in LMFDB)
2.49.ap_eu$6$(not in LMFDB)
2.49.an_eq$6$(not in LMFDB)
2.49.aj_cy$6$(not in LMFDB)
2.49.ae_dy$6$(not in LMFDB)
2.49.a_ax$6$(not in LMFDB)
2.49.a_dq$6$(not in LMFDB)
2.49.c_abt$6$(not in LMFDB)
2.49.j_cy$6$(not in LMFDB)
2.49.l_cu$6$(not in LMFDB)
2.49.p_eu$6$(not in LMFDB)
2.49.y_jh$6$(not in LMFDB)
2.49.a_adq$12$(not in LMFDB)
2.49.a_x$12$(not in LMFDB)