Invariants
| Base field: | $\F_{211}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 50 x + 1035 x^{2} - 10550 x^{3} + 44521 x^{4}$ |
| Frobenius angles: | $\pm0.0641278114367$, $\pm0.234211395958$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.1850256.1 |
| Galois group: | $D_{4}$ |
| Jacobians: | $30$ |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $34957$ | $1963080249$ | $88232788535632$ | $3928848286621443081$ | $174914168295458492424277$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $162$ | $44092$ | $9392532$ | $1982145076$ | $418227622302$ | $88245938488102$ | $18619893103088922$ | $3928797474896079268$ | $828976267899835877292$ | $174913992535369071473452$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 30 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=93x^6+39x^5+113x^4+132x^3+140x^2+165x+67$
- $y^2=138x^6+147x^5+196x^4+99x^3+29x^2+141x+72$
- $y^2=118x^6+34x^5+152x^4+177x^3+56x^2+184x+145$
- $y^2=197x^6+185x^5+116x^4+150x^3+25x^2+163x+89$
- $y^2=77x^6+139x^5+81x^4+68x^3+139x^2+58x+97$
- $y^2=88x^6+100x^5+132x^4+25x^3+173x^2+156x+131$
- $y^2=8x^6+34x^5+148x^4+98x^3+119x^2+81x+148$
- $y^2=36x^6+17x^5+107x^4+167x^3+43x^2+92x+141$
- $y^2=8x^6+27x^5+49x^4+169x^3+80x^2+52x+196$
- $y^2=x^6+167x^5+79x^4+137x^3+78x^2+11x+41$
- $y^2=80x^6+112x^5+106x^4+93x^3+205x^2+65x+187$
- $y^2=10x^6+155x^5+106x^4+159x^3+80x^2+62x+55$
- $y^2=207x^6+71x^5+163x^4+203x^3+118x^2+60x+3$
- $y^2=148x^6+98x^5+89x^4+55x^3+9x^2+123x+199$
- $y^2=80x^6+33x^5+18x^4+22x^3+139x^2+145x+193$
- $y^2=26x^6+197x^5+50x^4+185x^3+100x^2+70x+73$
- $y^2=55x^6+124x^5+137x^4+85x^3+186x^2+49x+46$
- $y^2=87x^6+158x^5+19x^4+98x^3+174x^2+103x+42$
- $y^2=26x^6+169x^5+149x^4+173x^3+99x^2+161x+173$
- $y^2=79x^6+48x^5+141x^4+123x^3+6x^2+139x+98$
- $y^2=137x^6+87x^5+85x^4+121x^3+99x^2+152x+205$
- $y^2=41x^6+7x^5+191x^4+148x^3+100x^2+5x+140$
- $y^2=53x^6+172x^5+195x^4+192x^3+120x^2+178x+156$
- $y^2=129x^6+129x^5+73x^4+156x^3+149x^2+174x+55$
- $y^2=176x^6+122x^5+46x^4+60x^3+60x^2+92x+206$
- $y^2=130x^6+50x^5+128x^4+200x^3+74x^2+103x+201$
- $y^2=202x^6+69x^5+73x^4+99x^3+116x^2+104x+38$
- $y^2=156x^6+106x^5+100x^4+6x^3+132x^2+12x+198$
- $y^2=18x^6+138x^5+158x^4+115x^3+143x^2+97x+82$
- $y^2=94x^6+126x^5+59x^4+204x^3+16x^2+66x+156$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{211}$.
Endomorphism algebra over $\F_{211}$| The endomorphism algebra of this simple isogeny class is 4.0.1850256.1. |
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 |
|---|---|---|
| 2.211.by_bnv | $2$ | (not in LMFDB) |