Curve Research from the CLI

Rank bounds

sage -python -m rank42.cli rank-bounds \
  --db rank42.db \
  --curve-id 123 \
  --engine auto \
  --timeout 300

See rank-bounds.

Classical descent attack

sage -python -m rank42.attack \
  --db rank42.db \
  --id 123 \
  --timeout 900

Exact-rank certification attempt

sage -python -m rank42.certify_curve \
  --db rank42.db \
  --id 123 \
  --timeout 120

It only records exact rank when the rigorous evidence closes.

Advanced upper-bound attack

sage -python -m rank42.advanced_upper_bound \
  --db rank42.db \
  --curve-id 123 \
  --backend simon_strong \
  --timeout 900

Available backends are simon_strong and sage_proof_rank.

This is for hard cases. A timeout remains inconclusive.

Independence

sage -python -m rank42.independence_check \
  --db rank42.db \
  --curve-id 123 \
  --timeout 120

Restrict the attempt to selected Point Ledger rows by repeating --point-id.

Strategies:

standard
saturation
trial-saturation

Hard-case independence

sage -python -m rank42.hard_case_escalator \
  --db rank42.db \
  --curve-id 123 \
  --certificate-timeout 600

Mordell-Weil relation attack

sage -python -m rank42.mw_relation_attack \
  --db rank42.db \
  --curve-id 123 \
  --timeout 180

Saturation

sage -python -m rank42.cli saturate \
  --db rank42.db \
  --curve-id 123 \
  --max-prime 100 \
  --timeout 900

See saturate.

Height lattice

sage -python -m rank42.lattice \
  --db rank42.db \
  --curve-id 123 \
  --source stored-generators \
  --precision 256

List saved lattices:

sage -python -m rank42.lattice --db rank42.db --list

Quartics workbench

Run a pointed search from a saved quartic search:

sage -python -m rank42.quartic_workbench_runner \
  --db rank42.db \
  --mode pointed \
  --search-id 17 \
  --height 100000 \
  --timeout 60

Search a stored covering:

sage -python -m rank42.quartic_workbench_runner \
  --db rank42.db \
  --mode covering \
  --covering-id 8 \
  --height 100000

Plan covering-local searches for a curve:

sage -python -m rank42.quartic_workbench_runner \
  --db rank42.db \
  --mode covering-local \
  --curve-id 123