Invariants
Base field: | $\F_{191}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 26 x + 191 x^{2} )( 1 - 22 x + 191 x^{2} )$ |
$1 - 48 x + 954 x^{2} - 9168 x^{3} + 36481 x^{4}$ | |
Frobenius angles: | $\pm0.110219473395$, $\pm0.206981219725$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $32$ |
This isogeny class is not 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $28220$ | $1316519440$ | $48546218097020$ | $1771262611568296960$ | $64615343927199401685500$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $144$ | $36086$ | $6967152$ | $1330912446$ | $254196065424$ | $48551243138678$ | $9273284393960304$ | $1771197286880617726$ | $338298681562924658832$ | $64615048177864704875126$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 32 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=131x^6+86x^5+87x^4+92x^3+187x^2+177x+176$
- $y^2=38x^6+27x^5+189x^4+55x^3+165x^2+135x+85$
- $y^2=190x^6+41x^5+7x^4+81x^3+113x^2+36x+92$
- $y^2=93x^6+101x^5+36x^4+122x^3+60x^2+157x+140$
- $y^2=35x^6+127x^5+78x^4+113x^3+15x^2+105x+91$
- $y^2=92x^6+66x^5+106x^4+154x^3+106x^2+66x+92$
- $y^2=24x^6+112x^5+187x^4+167x^3+21x^2+6x+170$
- $y^2=176x^6+151x^5+164x^4+79x^3+164x^2+151x+176$
- $y^2=124x^6+45x^5+48x^4+57x^3+104x^2+48x+50$
- $y^2=116x^6+171x^5+39x^4+40x^3+172x^2+131x+139$
- $y^2=155x^6+124x^5+77x^4+150x^3+136x^2+188x+105$
- $y^2=188x^6+181x^5+178x^4+86x^3+x^2+179x+50$
- $y^2=149x^6+112x^5+190x^4+27x^3+190x^2+112x+149$
- $y^2=4x^6+172x^5+98x^4+83x^3+136x^2+163x+1$
- $y^2=49x^6+132x^5+11x^4+149x^3+14x^2+64x+117$
- $y^2=93x^6+102x^5+59x^4+58x^3+163x^2+185x+36$
- $y^2=162x^6+51x^5+155x^4+17x^3+45x^2+164x+145$
- $y^2=7x^6+116x^5+58x^4+155x^3+142x^2+33x+124$
- $y^2=171x^6+168x^5+86x^4+69x^3+86x^2+168x+171$
- $y^2=45x^6+6x^5+169x^4+54x^3+126x^2+132x+142$
- and 12 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{191}$.
Endomorphism algebra over $\F_{191}$The isogeny class factors as 1.191.aba $\times$ 1.191.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ae_ahi | $2$ | (not in LMFDB) |
2.191.e_ahi | $2$ | (not in LMFDB) |
2.191.bw_bks | $2$ | (not in LMFDB) |