# Properties

 Label 2.49.abc_li Base Field $\F_{7^{2}}$ Dimension $2$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{7^{2}}$ Dimension: $2$ L-polynomial: $( 1 - 7 x )^{4}$ Frobenius angles: $0$, $0$, $0$, $0$ Angle rank: $0$ (numerical) Jacobians: 1

This isogeny class is not simple.

## Newton polygon

This isogeny class is supersingular. $p$-rank: $0$ Slopes: $[1/2, 1/2, 1/2, 1/2]$

## Point counts

This isogeny class contains the Jacobians of 1 curves, and hence is principally polarizable:

• $y^2=ax^5+6ax$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 1296 5308416 13680577296 33177600000000 79773277746356496 191574717809222025216 459984302365352962983696 1104426907919194521600000000 2651730583010213788123328871696 6366805670751667301725999443542016

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 22 2206 116278 5755198 282408022 13840816606 678219778678 33232907510398 1628413436496022 79792265167711006

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
 The isogeny class factors as 1.49.ao 2 and its endomorphism algebra is $\mathrm{M}_{2}(B)$, where $B$ is the quaternion algebra over $$\Q$$ ramified at $7$ and $\infty$.
All geometric endomorphisms are defined over $\F_{7^{2}}$.

## Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{7^{2}}$.

 Subfield Primitive Model $\F_{7}$ 2.7.a_ao

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.49.a_adu $2$ (not in LMFDB) 2.49.bc_li $2$ (not in LMFDB) 2.49.o_fr $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.49.a_adu $2$ (not in LMFDB) 2.49.bc_li $2$ (not in LMFDB) 2.49.o_fr $3$ (not in LMFDB) 2.49.ao_du $4$ (not in LMFDB) 2.49.a_du $4$ (not in LMFDB) 2.49.o_du $4$ (not in LMFDB) 2.49.h_bx $5$ (not in LMFDB) 2.49.ao_fr $6$ (not in LMFDB) 2.49.a_a $8$ (not in LMFDB) 2.49.ah_bx $10$ (not in LMFDB) 2.49.a_abx $12$ (not in LMFDB)