# Properties

 Label 2.61.abd_mt Base Field $\F_{61}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{61}$ Dimension: $2$ L-polynomial: $1 - 29 x + 331 x^{2} - 1769 x^{3} + 3721 x^{4}$ Frobenius angles: $\pm0.00565540645541$, $\pm0.172515385279$ Angle rank: $2$ (numerical) Number field: $$\Q(\zeta_{5})$$ Galois group: $C_4$ Jacobians: 1

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 1 curves, and hence is principally polarizable:

• $y^2=16x^5+60$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 2255 13194005 51316721555 191662462946405 713338599476250000 2654348964974812242005 9876830332246605354975755 36751690553827489342421332805 136753049927269747265285817799655 508858107650663515605158797620000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 33 3543 226083 13842603 844591198 51520374183 3142742135643 191707295768883 11694145843711353 713342908902617398

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\zeta_{5})$$.
All geometric endomorphisms are defined over $\F_{61}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.61.bd_mt $2$ (not in LMFDB) 2.61.b_abd $5$ (not in LMFDB) 2.61.b_dn $5$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.61.bd_mt $2$ (not in LMFDB) 2.61.b_abd $5$ (not in LMFDB) 2.61.b_dn $5$ (not in LMFDB) 2.61.l_bz $5$ (not in LMFDB) 2.61.q_gk $5$ (not in LMFDB) 2.61.aq_gk $10$ (not in LMFDB) 2.61.al_bz $10$ (not in LMFDB) 2.61.ab_abd $10$ (not in LMFDB) 2.61.ab_dn $10$ (not in LMFDB)