Properties

 Label 2.199.aby_bnh Base Field $\F_{199}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{199}$ Dimension: $2$ L-polynomial: $1 - 50 x + 1021 x^{2} - 9950 x^{3} + 39601 x^{4}$ Frobenius angles: $\pm0.114292864932$, $\pm0.184902183990$ Angle rank: $2$ (numerical) Number field: 4.0.1507904.2 Galois group: $D_{4}$ Jacobians: 15

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 15 curves, and hence is principally polarizable:

• $y^2=149x^6+76x^5+106x^4+150x^3+97x^2+77x+83$
• $y^2=97x^6+195x^5+180x^4+88x^3+61x^2+180x+114$
• $y^2=131x^6+152x^5+2x^4+93x^3+153x^2+193x+78$
• $y^2=66x^6+110x^5+28x^4+197x^3+46x^2+171x+80$
• $y^2=92x^6+26x^5+78x^4+135x^3+19x^2+144x+95$
• $y^2=120x^6+147x^5+171x^4+57x^3+198x^2+74x+169$
• $y^2=77x^6+17x^5+61x^4+70x^3+107x^2+93x+91$
• $y^2=101x^6+111x^5+184x^4+x^3+149x^2+186x+179$
• $y^2=189x^6+119x^5+31x^4+173x^3+101x^2+193x+78$
• $y^2=48x^6+142x^5+33x^4+8x^3+57x^2+55x+152$
• $y^2=180x^6+159x^5+160x^4+27x^3+188x^2+105x+170$
• $y^2=150x^6+66x^5+64x^4+189x^3+87x^2+138x+150$
• $y^2=62x^6+191x^5+152x^4+164x^3+166x^2+159x+152$
• $y^2=123x^6+67x^5+98x^4+127x^3+64x^2+76x+119$
• $y^2=83x^6+183x^5+7x^4+183x^3+173x^2+46x+88$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 30623 1550228129 62090456785700 2459442447020867369 97394093908836770643903 3856888478039613492952490000 152736586642867908080321713574543 6048521422016991492879187817559596489 239527496529775289137496726063818816571300 9485528389645059306974297553112494885572573409

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 150 39144 7878900 1568282724 312080935750 62103864122598 12358664592937050 2459374194781352964 489415464141321686700 97393677359702072427304

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
 The endomorphism algebra of this simple isogeny class is 4.0.1507904.2.
All geometric endomorphisms are defined over $\F_{199}$.

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 2.199.by_bnh $2$ (not in LMFDB)