# Properties

 Label 2.73.aba_lu 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: $( 1 - 16 x + 73 x^{2} )( 1 - 10 x + 73 x^{2} )$ Frobenius angles: $\pm0.114200251220$, $\pm0.301013746420$ Angle rank: $2$ (numerical) Jacobians: 66

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 66 curves, and hence is principally polarizable:

• $y^2=5x^6+25x^5+4x^4+66x^3+15x^2+14x+38$
• $y^2=13x^6+52x^5+53x^4+10x^3+x^2+29x+58$
• $y^2=44x^6+6x^5+44x^4+20x^3+66x^2+50x+39$
• $y^2=44x^6+63x^5+53x^4+14x^3+24x^2+7x+14$
• $y^2=17x^6+17x^5+58x^4+45x^3+21x^2+45x+10$
• $y^2=50x^6+5x^5+19x^4+43x^3+19x^2+5x+50$
• $y^2=5x^6+3x^5+67x^4+70x^3+3x^2+72x+7$
• $y^2=29x^6+53x^5+46x^4+70x^3+44x^2+7x+6$
• $y^2=50x^6+27x^5+3x^4+27x^3+27x^2+63x+68$
• $y^2=70x^6+3x^5+x^4+28x^3+x^2+62x+30$
• $y^2=25x^6+61x^5+28x^4+60x^3+6x^2+11x+39$
• $y^2=43x^6+18x^5+56x^4+64x^3+40x^2+12x+51$
• $y^2=13x^6+44x^5+7x^4+50x^3+66x^2+35x+66$
• $y^2=44x^6+58x^5+33x^4+23x^3+54x^2+54x+26$
• $y^2=17x^6+61x^5+28x^4+29x^3+47x^2+12x+21$
• $y^2=5x^6+12x^5+54x^4+72x^3+50x^2+14x+49$
• $y^2=6x^6+37x^5+65x^4+49x^3+31x^2+31x+31$
• $y^2=60x^6+33x^5+70x^4+22x^3+23x^2+66x+29$
• $y^2=43x^6+53x^5+71x^4+11x^3+15x^2+30x+58$
• $y^2=40x^6+53x^5+6x^4+60x^3+11x^2+6x+7$
• and 46 more

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3712 28062720 151566932608 806661763891200 4297664587820870272 22902016191270812144640 122045004050655148160499328 650377910905101662103797760000 3465863767456453371048559807829632 18469587806019406883725623126076953600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 48 5266 389616 28405342 2073090288 151334015794 11047397614896 806460130441918 58871587488055728 4297625837587960786

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.aq $\times$ 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:
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.ag_ao $2$ (not in LMFDB) 2.73.g_ao $2$ (not in LMFDB) 2.73.ba_lu $2$ (not in LMFDB) 2.73.ax_jy $3$ (not in LMFDB) 2.73.b_aew $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.ag_ao $2$ (not in LMFDB) 2.73.g_ao $2$ (not in LMFDB) 2.73.ba_lu $2$ (not in LMFDB) 2.73.ax_jy $3$ (not in LMFDB) 2.73.b_aew $3$ (not in LMFDB) 2.73.aq_hy $4$ (not in LMFDB) 2.73.ae_di $4$ (not in LMFDB) 2.73.e_di $4$ (not in LMFDB) 2.73.q_hy $4$ (not in LMFDB) 2.73.abh_qc $6$ (not in LMFDB) 2.73.aj_bi $6$ (not in LMFDB) 2.73.ab_aew $6$ (not in LMFDB) 2.73.j_bi $6$ (not in LMFDB) 2.73.x_jy $6$ (not in LMFDB) 2.73.bh_qc $6$ (not in LMFDB) 2.73.ax_jo $12$ (not in LMFDB) 2.73.an_hg $12$ (not in LMFDB) 2.73.al_bs $12$ (not in LMFDB) 2.73.ab_ea $12$ (not in LMFDB) 2.73.b_ea $12$ (not in LMFDB) 2.73.l_bs $12$ (not in LMFDB) 2.73.n_hg $12$ (not in LMFDB) 2.73.x_jo $12$ (not in LMFDB)