todo.txt

/*
-Dieudonne Module of p-divisible group (this should be trivially the same)
-Location in Isogeny Graph (highlighted in graph)

Properties/Invariants:
-Dimension
-Isogeny Class
-dimension
-p-rank
-base field

Non-isogeny invariants:
-A[p]; p-torsion subgroup (these will all be the same for ordinary abelian varieties)
-a-number
-A(FF_{q^r}) group structure for r=1,2,3,...,g 
-Hasse-Witt Matrix
-Slope Filtration on Crystalline Cohomology 
-Neron Sevari group --- this is isomorphic to the group of polarizations. This group is Pic/Pic^0. 
-Picard Number, the rank of the Neron-Sevari group. 

Related Objects:
-Dual Abelian Variety (highlighted in graph)
-Frobenius Isogeny, Vershiebung
-Frobenius Twist $A^{(p)}$, Vershiebung
-weak-neighbors (neighbors in WEMbar(I:I)), smallest degree isogenies to elements in the same weak equivalence class with same endomorphism algebra
-non-weak neighbors
-Lattice of Canonical Lift (we need to link to http://beta.lmfdb.org/Variety/Abelian/Fq/)

-Simple Factors/is simple?
-Order, Number Field, Endomorphism Ring
-rational torsion group 

Location in Isogeny Graph
-Determinant/Norm of endomorphism ring
-Smallest Degree Polarization?


****************************
Improvements to Isogeny Classes:
-Cardinality of Isogeny Class
-Isogeny Graph (experiment to find the best way to display)
-Display Isomorphism Classes of Abelian Varieties with non-Gorenstein endomorphism algebras
-Neron Sevari group: 
-Picard Number: this is easy for powers of simples, rho(A^n) = e(A)*n(n+1)/2

*****************************

TODO EXAMPLES:
-Example with interesting endomorphism algebra
-Isogeny Graph Example


label: "2.9.ab_d"
polynomial: ["1","-1","3","-9","81"]
angle_numbers (doubles): [0.23756..., 0.69210...]
number_field: "4.0.213413.1"
p-rank: 1
slopes: ["0","1/2","1/2","1"]
A_counts: ["75", "7125"]
C_counts: ["9", "87"]
known_jacobian (0,1,-1): 1
decomposition: ["9.2.-1._3"]
pricipally_polarizable (0,1,-1): 1
Brauer Invariants: inv_v( End(A_{FFbar_q})_{QQ} )=(v(\pi)/v(q))*[QQ(pi)_{v}: QQ(pi): v\vert p place of QQ(\pi)], these are stored as elements of QQ.
Primitive models: 
cardinality_of_isogeny_class
neron_severi_group
picard_number
*/