Properties

 Label 1.313.aba Base Field $\F_{313}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{313}$ Dimension: $1$ L-polynomial: $1 - 26 x + 313 x^{2}$ Frobenius angles: $\pm0.237274388652$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1})$$ Galois group: $C_2$ Jacobians: 18

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 18 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 288 97920 30671136 9598118400 3004153401888 940299125074560 294313621062360096 92120163538764441600 28833611193027570009888 9024920303512106293545600

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 288 97920 30671136 9598118400 3004153401888 940299125074560 294313621062360096 92120163538764441600 28833611193027570009888 9024920303512106293545600

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{313}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1})$$.
All geometric endomorphisms are defined over $\F_{313}$.

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 1.313.ba $2$ (not in LMFDB) 1.313.ay $4$ (not in LMFDB) 1.313.y $4$ (not in LMFDB)