Properties

Label 2.73.abg_pm
Base Field $\F_{73}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $( 1 - 16 x + 73 x^{2} )^{2}$
Frobenius angles:  $\pm0.114200251220$, $\pm0.114200251220$
Angle rank:  $1$ (numerical)
Jacobians:  5

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 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3364 27248400 150874757476 806378250240000 4297709354163860644 22902177458926012899600 122045132702291258612766436 650377968072158198843965440000 3465863778468454047928798219506724 18469587804284548868292951655184010000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 42 5110 387834 28395358 2073111882 151335081430 11047409260314 806460201328318 58871587675106922 4297625837184282550

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.aq 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-1}) \)$)$
All geometric endomorphisms are defined over $\F_{73}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.a_aeg$2$(not in LMFDB)
2.73.bg_pm$2$(not in LMFDB)
2.73.q_hb$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.a_aeg$2$(not in LMFDB)
2.73.bg_pm$2$(not in LMFDB)
2.73.q_hb$3$(not in LMFDB)
2.73.aw_ji$4$(not in LMFDB)
2.73.am_ha$4$(not in LMFDB)
2.73.ak_by$4$(not in LMFDB)
2.73.a_eg$4$(not in LMFDB)
2.73.k_by$4$(not in LMFDB)
2.73.m_ha$4$(not in LMFDB)
2.73.w_ji$4$(not in LMFDB)
2.73.aq_hb$6$(not in LMFDB)
2.73.a_ads$8$(not in LMFDB)
2.73.a_ds$8$(not in LMFDB)
2.73.ag_abl$12$(not in LMFDB)
2.73.g_abl$12$(not in LMFDB)