# Properties

 Label 2.97.bc_om Base field $\F_{97}$ Dimension $2$ $p$-rank $2$ Ordinary yes Supersingular no Simple yes Geometrically simple yes Primitive yes Principally polarizable yes Contains a Jacobian yes

# Related objects

## Invariants

 Base field: $\F_{97}$ Dimension: $2$ L-polynomial: $1 + 28 x + 376 x^{2} + 2716 x^{3} + 9409 x^{4}$ Frobenius angles: $\pm0.674361963755$, $\pm0.856942942614$ Angle rank: $2$ (numerical) Number field: 4.0.64940288.1 Galois group: $D_{4}$ Jacobians: $56$ Isomorphism classes: 56

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $12530$ $88236260$ $831618618530$ $7838776984010000$ $73742040248119207650$

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $126$ $9378$ $911190$ $88544454$ $8587296886$ $832971846306$ $80798277983262$ $7837433810920446$ $760231055872321950$ $73742412705107798818$

## Jacobians and polarizations

This isogeny class contains the Jacobians of 56 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=35x^6+3x^5+85x^4+46x^3+8x^2+64x+50$
• $y^2=94x^6+69x^5+71x^4+8x^3+40x^2+47x+65$
• $y^2=87x^6+80x^5+67x^4+55x^3+11x^2+11x+80$
• $y^2=4x^6+83x^5+26x^4+91x^3+83x^2+19x+4$
• $y^2=60x^6+61x^5+58x^4+46x^3+82x^2+31x+66$
• $y^2=80x^6+33x^5+71x^4+89x^3+42x^2+67x+85$
• $y^2=19x^6+15x^5+70x^4+4x^3+59x^2+87x+52$
• $y^2=44x^6+71x^5+54x^4+60x^3+84x^2+59x+58$
• $y^2=54x^6+91x^5+92x^4+75x^3+49x^2+26x+19$
• $y^2=2x^6+62x^5+33x^4+81x^3+86x^2+70x+93$
• $y^2=45x^6+x^4+51x^3+9x^2+6x+44$
• $y^2=11x^6+13x^5+2x^4+49x^3+91x^2+33x+1$
• $y^2=47x^6+35x^5+23x^4+58x^3+77x^2+71x+14$
• $y^2=60x^6+19x^5+25x^4+87x^3+32x^2+92x$
• $y^2=95x^6+50x^5+3x^4+60x^3+38x^2+46x+52$
• $y^2=85x^6+43x^5+76x^4+63x^3+54x^2+40x+92$
• $y^2=54x^6+67x^5+61x^4+64x^3+81x^2+60x+37$
• $y^2=64x^6+27x^5+73x^4+53x^3+24x^2+72x+64$
• $y^2=91x^6+7x^5+77x^4+32x^3+31x^2+49x+94$
• $y^2=16x^6+50x^5+3x^3+5x^2+11x+36$
• and 36 more

## Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{97}$.

Endomorphism algebra over $\F_{97}$
 The endomorphism algebra of this simple isogeny class is 4.0.64940288.1.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.97.abc_om$2$(not in LMFDB)