Properties

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

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Invariants

Base field:  $\F_{73}$
Dimension:  $2$
L-polynomial:  $( 1 - 15 x + 73 x^{2} )^{2}$
Frobenius angles:  $\pm0.159004799845$, $\pm0.159004799845$
Angle rank:  $1$ (numerical)
Jacobians:  3

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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 3481 27573001 151264989184 806711038270281 4297927782030847561 22902281082118094258176 122045151751927088792045689 650377939958111008646793455625 3465863733830378504390387402838016 18469587762187585757436775934904884521

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 44 5172 388838 28407076 2073217244 151335766158 11047410984668 806460166467268 58871586916879094 4297625827388882772

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{73}$
The isogeny class factors as 1.73.ap 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-67}) \)$)$
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.
TwistExtension DegreeCommon base change
2.73.a_adb$2$(not in LMFDB)
2.73.be_oh$2$(not in LMFDB)
2.73.p_fw$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.73.a_adb$2$(not in LMFDB)
2.73.be_oh$2$(not in LMFDB)
2.73.p_fw$3$(not in LMFDB)
2.73.a_db$4$(not in LMFDB)
2.73.ap_fw$6$(not in LMFDB)