= Group III Final Presentation =

== Agenda ==

1. Congruences of newforms with newforms arising from elliptic curves

2. (Ir)reducibility testing and Serre levels

3. S_4 number fields arising from elliptic curves

4. Period lattices

[[http://nt.sagenb.org/home/pub/14/ | computing splitting field of modular mod p reps]]

5. Elliptic curves whose Galois representations are surjective mod 4 (resp. 8) but not mod 2 (resp. 4)

[[attachment:s4fieldellipticcurve.csv]]

[[attachment:compileddata.csv]]

[[attachment:freakshow.csv]]

[[attachment:newfndata.csv]]

[[attachment:exceptionalfields.csv]]

[[attachment:serre.pdf]]

[[attachment:BenPresentation.sws]]

http://wiki.sagemath.org/GaganSekhon.