Invariants
Base field: | $\F_{157}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 793 x^{2} - 6908 x^{3} + 24649 x^{4}$ |
Frobenius angles: | $\pm0.0818462939099$, $\pm0.210771717314$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.241025.1 |
Galois group: | $D_{4}$ |
Jacobians: | $40$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $18491$ | $599015945$ | $14971307380304$ | $369156122495218025$ | $9099101406401262983331$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $114$ | $24300$ | $3868662$ | $607591188$ | $95389427674$ | $14976076830150$ | $2351243307048162$ | $369145194470331108$ | $57955795543891117614$ | $9099059901020026901500$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 40 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=65x^6+25x^5+90x^4+126x^3+66x^2+112x+50$
- $y^2=130x^6+106x^5+81x^4+108x^3+44x^2+116x+81$
- $y^2=15x^6+97x^5+78x^4+38x^3+120x^2+25x+97$
- $y^2=132x^6+25x^5+70x^4+124x^3+100x^2+20x+111$
- $y^2=106x^6+111x^5+142x^4+63x^3+140x^2+9x+100$
- $y^2=147x^6+44x^5+40x^4+96x^3+155x^2+34x+131$
- $y^2=66x^6+132x^5+142x^4+94x^3+85x^2+52x+114$
- $y^2=90x^6+28x^5+44x^4+61x^3+85x^2+27x+144$
- $y^2=66x^6+84x^5+146x^4+3x^3+117x^2+23x+103$
- $y^2=129x^6+45x^5+26x^4+86x^3+100x^2+103x+21$
- $y^2=60x^6+98x^5+59x^4+19x^3+137x^2+135x+114$
- $y^2=103x^6+38x^5+16x^4+51x^3+133x^2+8x+26$
- $y^2=56x^6+125x^5+73x^4+20x^3+11x^2+113x+59$
- $y^2=96x^6+84x^5+15x^4+14x^3+97x^2+65x+31$
- $y^2=43x^6+13x^5+102x^4+8x^3+22x^2+54x+7$
- $y^2=63x^6+16x^5+33x^4+148x^3+81x^2+64x+137$
- $y^2=83x^6+30x^5+28x^4+21x^3+136x^2+51x+89$
- $y^2=100x^6+41x^5+15x^4+64x^3+145x^2+94x+63$
- $y^2=26x^6+122x^5+52x^4+42x^3+41x^2+125x+61$
- $y^2=88x^6+127x^5+131x^4+12x^3+75x^2+75$
- and 20 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{157}$.
Endomorphism algebra over $\F_{157}$The endomorphism algebra of this simple isogeny class is 4.0.241025.1. |
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 |
---|---|---|
2.157.bs_ben | $2$ | (not in LMFDB) |