# Properties

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

# Learn more about

## Invariants

 Base field: $\F_{73}$ Dimension: $2$ L-polynomial: $( 1 - 16 x + 73 x^{2} )( 1 - 13 x + 73 x^{2} )$ Frobenius angles: $\pm0.114200251220$, $\pm0.224822766824$ Angle rank: $2$ (numerical) Jacobians: 6

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 6 curves, and hence is principally polarizable:

• $y^2=33x^6+68x^5+9x^4+62x^3+62x^2+11x+37$
• $y^2=63x^6+23x^5+72x^4+35x^3+17x^2+52x+59$
• $y^2=5x^6+9x^5+27x^4+7x^3+19x^2+60x+15$
• $y^2=10x^6+12x^5+45x^4+39x^3+64x^2+36x+20$
• $y^2=4x^6+41x^5+19x^4+44x^3+35x^2+20x+34$
• $y^2=51x^6+56x^5+48x^4+18x^3+32x^2+71x+30$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 3538 27702540 151357182568 806706829612800 4297842204101706898 22902166557382887440640 122045056505728396588624114 650377887008980252465363737600 3465863721517396143177775493349352 18469587775540279050114349873794770700

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 45 5197 389076 28406929 2073175965 151335009394 11047402363077 806460100811041 58871586707729268 4297625830495875757

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
 The isogeny class factors as 1.73.aq $\times$ 1.73.an 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.ad_ack $2$ (not in LMFDB) 2.73.d_ack $2$ (not in LMFDB) 2.73.bd_nq $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.73.ad_ack $2$ (not in LMFDB) 2.73.d_ack $2$ (not in LMFDB) 2.73.bd_nq $2$ (not in LMFDB) 2.73.at_iq $4$ (not in LMFDB) 2.73.ah_cq $4$ (not in LMFDB) 2.73.h_cq $4$ (not in LMFDB) 2.73.t_iq $4$ (not in LMFDB)