# Properties

 Label 2.73.abb_mk 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: $( 1 - 16 x + 73 x^{2} )( 1 - 11 x + 73 x^{2} )$ Frobenius angles: $\pm0.114200251220$, $\pm0.277387524567$ Angle rank: $2$ (numerical) Jacobians: 25

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 25 curves, and hence is principally polarizable:

• $y^2=70x^6+56x^5+68x^4+23x^3+66x^2+62x+5$
• $y^2=36x^6+32x^5+10x^4+52x^3+20x^2+49x+59$
• $y^2=39x^6+20x^5+57x^4+64x^3+46x^2+43x+34$
• $y^2=10x^6+68x^5+32x^4+68x^3+24x^2+69x+51$
• $y^2=57x^6+39x^5+70x^4+x^3+19x^2+17x+37$
• $y^2=39x^6+34x^5+72x^4+62x^3+14x^2+6x+19$
• $y^2=41x^6+23x^5+64x^4+24x^3+66x^2+18x+9$
• $y^2=17x^6+25x^5+2x^4+33x^3+9x^2+41x+34$
• $y^2=47x^6+6x^5+35x^4+49x^3+40x^2+59x+51$
• $y^2=21x^6+17x^5+67x^4+27x^3+29x^2+69x+59$
• $y^2=39x^6+6x^5+46x^4+52x^3+64x^2+22x+42$
• $y^2=3x^6+42x^5+43x^4+6x^3+22x^2+2x+11$
• $y^2=36x^6+16x^5+36x^4+3x^3+45x^2+15x+29$
• $y^2=55x^6+55x^5+45x^4+64x^3+5x^2+56x+7$
• $y^2=64x^6+7x^5+x^4+x^3+33x^2+29x+71$
• $y^2=10x^6+13x^5+15x^4+61x^3+17x^2+6x+9$
• $y^2=28x^6+29x^5+47x^4+13x^3+38x^2+12x+61$
• $y^2=52x^6+19x^5+x^3+61x^2+8x+22$
• $y^2=37x^6+49x^5+2x^4+30x^3+58x^2+39x+52$
• $y^2=51x^6+53x^5+58x^4+6x^3+13x^2+4x+10$
• $y^2=56x^6+51x^5+5x^4+5x^3+51x^2+7x+33$
• $y^2=57x^6+20x^5+58x^4+65x^3+69x^2+39x+56$
• $y^2=43x^6+57x^5+17x^4+42x^3+64x^2+66x+34$
• $y^2=34x^6+67x^5+56x^4+27x^3+19x^2+61x+13$
• $y^2=68x^6+59x^5+51x^4+21x^3+62x^2+25x+57$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3654 27953100 151523428896 806704103520000 4297733246546141094 22902054632694247046400 122045001160908380902872966 650377888569925802158965120000 3465863749693557010910075592093984 18469587801718243842065602839755527500

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 47 5245 389504 28406833 2073123407 151334269810 11047397353319 806460102746593 58871587186332992 4297625836587137725

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.aq $\times$ 1.73.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 $\F_{73}$.

## 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.af_abe $2$ (not in LMFDB) 2.73.f_abe $2$ (not in LMFDB) 2.73.bb_mk $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.af_abe $2$ (not in LMFDB) 2.73.f_abe $2$ (not in LMFDB) 2.73.bb_mk $2$ (not in LMFDB) 2.73.ar_ie $4$ (not in LMFDB) 2.73.af_dc $4$ (not in LMFDB) 2.73.f_dc $4$ (not in LMFDB) 2.73.r_ie $4$ (not in LMFDB)