# Properties

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

## 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:

• $y^2=5x^6+5x^3+47$
• $y^2=62x^6+63x^4+63x^2+62$
• $y^2=40x^6+12x^5+39x^4+70x^3+21x^2+70x+62$
• $y^2=5x^6+5x^3+33$
• $y^2=35x^6+48x^5+10x^4+21x^3+31x^2+70x+32$

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

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)