# Properties

 Label 2.73.abb_me 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: $( 1 - 17 x + 73 x^{2} )( 1 - 10 x + 73 x^{2} )$ Frobenius angles: $\pm0.0323195869136$, $\pm0.301013746420$ Angle rank: $1$ (numerical) Jacobians: 8

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 8 curves, and hence is principally polarizable:

• $y^2=x^6+5x^3+34$
• $y^2=43x^6+23x^5+43x^4+28x^3+19x^2+x+31$
• $y^2=66x^6+18x^5+13x^4+49x^3+6x^2+72x+40$
• $y^2=66x^6+4x^5+23x^4+44x^3+58x^2+26x+28$
• $y^2=39x^6+65x^5+72x^4+41x^3+63x^2+32x+22$
• $y^2=52x^6+38x^5+26x^4+44x^3+43x^2+36x+37$
• $y^2=6x^6+57x^5+16x^4+32x^3+34x^2+64x+53$
• $y^2=28x^6+27x^5+36x^4+59x^3+x^2+38x+33$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3648 27885312 151333588224 806424595651584 4297457859193040448 22901854924751191474176 122044889062668807734223936 650377835271794272485149798400 3465863721549107233992470829655296 18469587780548589667554266878749226752

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 47 5233 389018 28396993 2072990567 151332950158 11047387206287 806460036657601 58871586708267914 4297625831661242593

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.ar $\times$ 1.73.ak and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
Endomorphism algebra over $\overline{\F}_{73}$
 The base change of $A$ to $\F_{73^{6}}$ is 1.151334226289.abkhxa 2 and its endomorphism algebra is $\mathrm{M}_{2}($$$\Q(\sqrt{-3})$$$)$
All geometric endomorphisms are defined over $\F_{73^{6}}$.
Remainder of endomorphism lattice by field
• Endomorphism algebra over $\F_{73^{2}}$  The base change of $A$ to $\F_{73^{2}}$ is 1.5329.afn $\times$ 1.5329.bu. The endomorphism algebra for each factor is:
• Endomorphism algebra over $\F_{73^{3}}$  The base change of $A$ to $\F_{73^{3}}$ is 1.389017.abtu $\times$ 1.389017.btu. The endomorphism algebra for each factor is:

## 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.ah_ay $2$ (not in LMFDB) 2.73.h_ay $2$ (not in LMFDB) 2.73.bb_me $2$ (not in LMFDB) 2.73.ay_kf $3$ (not in LMFDB) 2.73.ad_cy $3$ (not in LMFDB) 2.73.a_afn $3$ (not in LMFDB) 2.73.a_bu $3$ (not in LMFDB) 2.73.a_dt $3$ (not in LMFDB) 2.73.d_cy $3$ (not in LMFDB) 2.73.y_kf $3$ (not in LMFDB) 2.73.bb_me $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.ah_ay $2$ (not in LMFDB) 2.73.h_ay $2$ (not in LMFDB) 2.73.bb_me $2$ (not in LMFDB) 2.73.ay_kf $3$ (not in LMFDB) 2.73.ad_cy $3$ (not in LMFDB) 2.73.a_afn $3$ (not in LMFDB) 2.73.a_bu $3$ (not in LMFDB) 2.73.a_dt $3$ (not in LMFDB) 2.73.d_cy $3$ (not in LMFDB) 2.73.y_kf $3$ (not in LMFDB) 2.73.bb_me $3$ (not in LMFDB) 2.73.abi_qt $6$ (not in LMFDB) 2.73.au_jm $6$ (not in LMFDB) 2.73.ar_ii $6$ (not in LMFDB) 2.73.ao_hn $6$ (not in LMFDB) 2.73.ak_bb $6$ (not in LMFDB) 2.73.k_bb $6$ (not in LMFDB) 2.73.o_hn $6$ (not in LMFDB) 2.73.r_ii $6$ (not in LMFDB) 2.73.u_jm $6$ (not in LMFDB) 2.73.bi_qt $6$ (not in LMFDB) 2.73.a_adt $12$ (not in LMFDB) 2.73.a_abu $12$ (not in LMFDB) 2.73.a_fn $12$ (not in LMFDB)