Add cyclic isogeny invariants, search options, and tests for AV/Fq Issue #6696

[hgu2699]

This PR adds support for viewing and searching the cyclicity of the group of points for isogeny classes of abelian varieties over finite fields.

Main changes

• lmfdb/abvar/fq/isog_class.py

  • Extend AbvarFq_isoclass to include:
    • is_cyclic (whether the group of points is cyclic)
    • noncyclic_primes (primes where the isotypic components are non-cyclic)
  • Expose this information on the AV/Fq isogeny class page via properties(), under:
    • “Cyclic group of points”
    • “Non-cyclic primes”

• lmfdb/abvar/fq/main.py

  • (If applicable in your branch) add/adjust search options and columns so that the new invariants can be queried and, where relevant, shown in the browse/search results.

• lmfdb/abvar/fq/test_av.py

  • Update test_cyclic_group_of_points_display so it checks for the new “Cyclic group of points” text and passes with the updated display.

• lmfdb/abvar/fq/test_browse_page.py

  • (If you modified it) add/adjust tests to ensure the new search options and columns behave as expected.

Testing

All tests in the AV/Fq module pass locally:

sage -python -m pytest lmfdb/abvar/fq

[roed314]

Good start! Let me know if you have any questions about these suggestions.

[roed314]

Better; now we mostly just need the knowls.

[roed314]

I'm happy with this PR now. @AndrewVSutherland, if you agree with my changes to the knowls (https://beta.lmfdb.org/knowledge/show/av.fq.cyclic_group_points and https://beta.lmfdb.org/knowledge/show/av.fq.noncyclic_primes), feel free to merge this.