Properties

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

Invariants

 Base field: $\F_{137}$ Dimension: $2$ L-polynomial: $( 1 - 21 x + 137 x^{2} )( 1 - 20 x + 137 x^{2} )$ Frobenius angles: $\pm0.145687313345$, $\pm0.173950867407$ 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 13806 346834332 6610806999576 124108960975107264 2329227446771918894526 43716708140160737615821056 820517770630961286601551450318 15400296327343956532405455897158400 289048159845361029115448847493354303704 5425144911081455888390209822391595943773852

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 97 18477 2570944 352306673 48262416497 6611866090722 905824413072137 124097930814436321 17001416408495569168 2329194047510463486957

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
 The isogeny class factors as 1.137.av $\times$ 1.137.au 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 is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.137.ab_afq $2$ (not in LMFDB) 2.137.b_afq $2$ (not in LMFDB) 2.137.bp_bas $2$ (not in LMFDB)