Properties

Label 2.137.abt_bea
Base Field $\F_{137}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{137}$
Dimension:  $2$
L-polynomial:  $( 1 - 23 x + 137 x^{2} )( 1 - 22 x + 137 x^{2} )$
Frobenius angles:  $\pm0.0596181899068$, $\pm0.111017258455$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13340 343638400 6600757502720 124085936228800000 2329185132493164832700 43716645329268458883481600 820517701637845826515029336380 15400296298025874010242193708800000 289048159951931795261687853947266108160 5425144911483129864790165269668556834160000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 93 18305 2567034 352241313 48261539733 6611856590990 905824336906029 124097930578186753 17001416414763915498 2329194047682915403025

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The isogeny class factors as 1.137.ax $\times$ 1.137.aw 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 $\F_{137}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.ab_aiy$2$(not in LMFDB)
2.137.b_aiy$2$(not in LMFDB)
2.137.bt_bea$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.ab_aiy$2$(not in LMFDB)
2.137.b_aiy$2$(not in LMFDB)
2.137.bt_bea$2$(not in LMFDB)
2.137.abf_rq$4$(not in LMFDB)
2.137.ap_dm$4$(not in LMFDB)
2.137.p_dm$4$(not in LMFDB)
2.137.bf_rq$4$(not in LMFDB)