Properties

 Label 1.13.c Base Field $\F_{13}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{13}$ Dimension: $1$ L-polynomial: $1 + 2 x + 13 x^{2}$ Frobenius angles: $\pm0.589456187511$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3})$$ Galois group: $C_2$ Jacobians: 4

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $1$ Slopes: $[0, 1]$

Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 16 192 2128 28416 372496 4826304 62733904 815766528 10604617744 137857789632

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 16 192 2128 28416 372496 4826304 62733904 815766528 10604617744 137857789632

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-3})$$.
All geometric endomorphisms are defined over $\F_{13}$.

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 1.13.ac $2$ 1.169.w 1.13.ah $3$ (not in LMFDB) 1.13.f $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.13.ac $2$ 1.169.w 1.13.ah $3$ (not in LMFDB) 1.13.f $3$ (not in LMFDB) 1.13.af $6$ (not in LMFDB) 1.13.h $6$ (not in LMFDB)