Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 50 x + 1002 x^{2} - 9550 x^{3} + 36481 x^{4}$ |
Frobenius angles: | $\pm0.0545220769588$, $\pm0.191978923746$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.136400.1 |
Galois group: | $D_{4}$ |
Jacobians: | $24$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $27884$ | $1312890256$ | $48527892101564$ | $1771194511720582400$ | $64615134540443980747804$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $142$ | $35986$ | $6964522$ | $1330861278$ | $254195241702$ | $48551231450386$ | $9273284238841282$ | $1771197284823098238$ | $338298681534362064862$ | $64615048177458151442706$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=76x^6+178x^5+65x^4+98x^3+102x^2+66x+159$
- $y^2=165x^6+91x^5+25x^4+42x^3+3x^2+97x+84$
- $y^2=47x^6+29x^5+153x^4+156x^3+100x^2+187x+186$
- $y^2=134x^6+132x^5+168x^4+120x^3+187x^2+22x+117$
- $y^2=45x^6+133x^5+9x^4+82x^3+190x^2+122x+33$
- $y^2=102x^6+x^5+132x^4+50x^3+114x^2+23x+7$
- $y^2=178x^6+125x^5+97x^4+150x^3+17x^2+24x+126$
- $y^2=112x^6+165x^5+151x^4+7x^3+144x^2+143x+79$
- $y^2=186x^6+54x^5+116x^4+26x^3+83x^2+115x+73$
- $y^2=31x^6+141x^5+145x^4+101x^3+153x^2+62x+98$
- $y^2=83x^6+138x^5+25x^4+161x^3+24x^2+182x+92$
- $y^2=168x^6+14x^5+124x^4+56x^3+68x^2+71x+83$
- $y^2=175x^6+64x^5+137x^4+51x^3+71x^2+20x+50$
- $y^2=8x^6+164x^5+37x^4+93x^3+146x^2+181x+132$
- $y^2=119x^6+160x^5+149x^4+17x^3+147x^2+93x+73$
- $y^2=151x^6+127x^5+117x^4+87x^3+116x^2+185x+47$
- $y^2=87x^6+4x^5+120x^4+131x^3+107x^2+150x+148$
- $y^2=142x^6+149x^5+134x^4+138x^3+89x^2+162x+60$
- $y^2=64x^6+171x^5+170x^4+57x^3+188x^2+180x+22$
- $y^2=29x^6+115x^5+18x^4+65x^3+87x^2+56x+119$
- $y^2=17x^6+64x^5+56x^4+25x^3+73x^2+184x+73$
- $y^2=137x^6+177x^5+129x^4+138x^3+36x^2+161x+113$
- $y^2=83x^6+76x^5+133x^4+145x^3+58x^2+165x+53$
- $y^2=65x^6+44x^5+53x^4+58x^3+156x^2+116x+41$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{191}$.
Endomorphism algebra over $\F_{191}$The endomorphism algebra of this simple isogeny class is 4.0.136400.1. |
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 |
---|---|---|
2.191.by_bmo | $2$ | (not in LMFDB) |