# Properties

 Label 2.73.aba_ln 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: $( 1 - 17 x + 73 x^{2} )( 1 - 9 x + 73 x^{2} )$ Frobenius angles: $\pm0.0323195869136$, $\pm0.323434683416$ Angle rank: $2$ (numerical) Jacobians: 12

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 12 curves, and hence is principally polarizable:

• $y^2=26x^6+48x^5+66x^4+31x^3+x^2+48x+14$
• $y^2=15x^6+20x^5+23x^4+41x^3+25x^2+5x+62$
• $y^2=17x^6+5x^5+54x^4+58x^3+35x^2+41x+53$
• $y^2=29x^6+48x^5+8x^4+19x^3+4x^2+12x+31$
• $y^2=16x^6+55x^5+61x^4+29x^3+67x^2+32x+2$
• $y^2=16x^6+66x^5+44x^4+37x^3+34x^2+9x+28$
• $y^2=33x^6+53x^5+50x^4+28x^3+45x^2+18x+42$
• $y^2=40x^6+54x^5+67x^4+69x^3+57x^2+54x+10$
• $y^2=40x^6+2x^5+66x^4+17x^3+66x^2+26x+59$
• $y^2=17x^6+27x^5+30x^4+72x^3+60x^2+27x+42$
• $y^2=8x^6+11x^5+65x^4+17x^3+5x^2+63x+60$
• $y^2=18x^6+55x^5+16x^4+6x^3+40x^2+37x+39$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3705 27983865 151353755280 806364724408425 4297392935156060025 22901835786500290314240 122044908795268953619620105 650377860741637437378296097225 3465863731558385829217058050596240 18469587775942803177444934033898856825

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 48 5252 389070 28394884 2072959248 151332823694 11047388992464 806460068239876 58871586878286750 4297625830589537732

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.ar $\times$ 1.73.aj 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.ai_ah $2$ (not in LMFDB) 2.73.i_ah $2$ (not in LMFDB) 2.73.ba_ln $2$ (not in LMFDB) 2.73.ac_df $3$ (not in LMFDB) 2.73.b_ce $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.ai_ah $2$ (not in LMFDB) 2.73.i_ah $2$ (not in LMFDB) 2.73.ba_ln $2$ (not in LMFDB) 2.73.ac_df $3$ (not in LMFDB) 2.73.b_ce $3$ (not in LMFDB) 2.73.at_jc $6$ (not in LMFDB) 2.73.aq_ib $6$ (not in LMFDB) 2.73.ab_ce $6$ (not in LMFDB) 2.73.c_df $6$ (not in LMFDB) 2.73.q_ib $6$ (not in LMFDB) 2.73.t_jc $6$ (not in LMFDB)