Add Szpiro ratio for elliptic curves over number fields

[roed-math]

Adds the classical Szpiro ratio $\sigma = \log|N(\mathfrak{D}_{\mathrm{min}})|/\log N(\mathfrak{N})$ (Hindry) to the ECNF section: curve homepage display, search box, results column and sort order. All uses are guarded by a check that the szpiro_ratio column exists in ec_nfcurves, so this is safe to deploy before the data upload.

That check is a startup-time compatibility guard, not a live one: it, the result columns, the search array and the sort choices are all built when lmfdb.ecnf.main is imported, so adding the column does not make the feature appear in a running web worker (and neither does db.refresh_tables()). The migration therefore ends with a restart. The full order (generate and verify the file, create the ec.szpiro_ratio knowl, add the column, upload, create the index backing the new range search and sort, restart every web worker, smoke test display/search/sort) is written out in the generator's docstring.

Includes scripts/ecnf/generate_szpiro_ratio.py, which computes the ratio for all 767518 curves from stored invariants in ~3 minutes (NULL for the 712 curves with everywhere good reduction, where the ratio is undefined), cross-checks two independent formulas on every non-minimal-model row plus exactly --sample-check minimal-model rows, and can re-verify random rows from scratch in Sage; values were additionally checked against base changes of Q-curves with known ratios. Being a one-time production migration it fails closed: every integrity problem raises with the offending label and exits nonzero, and rows are streamed to a temporary file that replaces the output path only once the row counts match and all cross-checks and the requested --verify have passed. Addresses LMFDB#6292.

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[roed-math]

Pushed 1ab4984 with the review follow-up. The classical definition and the frontend design are unchanged; what changed is the deployment contract, the index, the tests and the generator's failure behaviour. The PR description has been corrected too.

1. Activation contract. HAVE_SZPIRO_RATIO is now documented as a startup-time compatibility guard: it, ecnf_columns, ECNFSearchArray.sorts and the search boxes are all built when lmfdb.ecnf.main is imported, so adding the column does not activate the feature in a running worker, and db.refresh_tables() does not either. The generator docstring carries the migration order: generate and verify the file, create the ec.szpiro_ratio knowl, add the column, upload and check the row counts, create the index, restart every web worker, smoke test display/search/sort. The description no longer promises automatic activation.

2. Index. Deployment step 5 creates ec_nfcurves_szpiro_ratio_sort, a btree on exactly the sort tuple registered for "Szpiro ratio" in ECNFSearchArray.sorts, through create_index so that it is recorded in meta_indexes and rebuilt by later reloads. It is created after update_from_file, since that merges into a new table and rebuilds every index during the swap, and is followed by list_indexes(verbose=True) plus two analyze(..., explain_only=True) checks (a ratio-ordered LIMIT 50 and a narrow range query). Note that none of the other ECNF float sorts (reg, sha, class_size, class_deg) has an index today, so this one is new ground rather than a restoration.

3. Tests. The old positive search proved nothing, since the same curve comes back when the constraint is ignored. With the column present, test_szpiro_ratio now asserts the displayed value 1.0 in the curve-page row, that szpiro_ratio=0.5-1.5 contains the full curve url /EllipticCurve/2.2.5.1/31.1/a/1 while the disjoint szpiro_ratio=1.1-1.5 does not, that sort_order=szpiro_ratio returns 200 and un-hides the column (its <th class="col-szpiro_ratio"> loses display:none), and that the everywhere-good-reduction curve 3.3.1369.1-1.1-a1 shows no ratio row. Without the column the compatibility branch only claims that the pages load and offer no ratio, and says so in a comment. A new test_szpiro_ratio_generator covers the generator helpers and runs whatever the schema is: szpiro_ratio(31, 31) == 1.0, szpiro_ratio(1, 1) is None, invalid Nnorm == 1 with Dnorm != 1 raising, a synthetic non-minimal row agreeing under both formulas, and missing local_data for a listed non_min_p raising with the label and the prime in the message.

One thing worth knowing for the test: the curve-page assertion matches the label text, not the knowl markup, because KNOWL() renders a bare label until ec.szpiro_ratio exists and an anchor afterwards. That is also why the knowl is step 2 of the migration.

4. Fail closed. Every data-integrity assert in generate, min_disc_norm_from_normdisc, szpiro_ratio and verify is now an explicit ValueError/RuntimeError naming the curve and the values (Dnorm > 0, Nnorm > 0, Nnorm == 1 => Dnorm == 1, every non_min_p prime present in local_data, divisibility by normp**12, agreement of the two formulas, the verification tolerance and the expected \N). The two partition counts must add up to count() before anything is written, and the rows written must equal min(limit, minimal) + min(limit, nonminimal); the warning-only completion path is gone. Rows stream into a temporary file next to the output path, and --verify runs against that temporary file, so the requested output is only replaced after every check has passed; on any failure the temporary file is deleted and any pre-existing output is left alone.

5. --sample-check N. Positions are now drawn once with random.sample over the minimal rows actually processed, so exactly min(N, processed_minimal) rows are cross-checked (the old Bernoulli frequency came from the full table count, so a small --limit usually checked none). The count is reported and enforced. --limit, --sample-check and --verify must be nonnegative, --verify above the generated row count gives a clear error naming the actual count, and a new --seed makes the sampling reproducible.

Verified

• sage -python -m pytest lmfdb/ecnf/test_ecnf.py -k szpiro -> 2 passed; pyflakes, pylint -e W0129,W0108 and ruff --select=E722 clean.
• Curve-page markup and the everywhere-good-reduction omission checked against a simulated column-present row (the page depends only on the attribute, not on the flag), including a negative control that the value regex does not match a wrong value.
• --limit 1000 --sample-check 100 --verify 20 wrote exactly 2000 rows with exactly 100 cross-checks; the file is mode 0644 with no temporary left behind.
• Injecting a mismatch between the two formulas partway through: exits nonzero with 2.0.68.1-66.1-a2: local_data gives Norm(D_min) = ... but normdisc gives ..., the pre-existing output is byte-identical afterwards and no temporary file survives. --verify 10 on a 4-row file and negative flags also exit nonzero without creating the output.
• A full run against devmirror (--verify 25 --seed 7, ~3 min) exits 0 having written exactly 767518 rows, that is db.ec_nfcurves.count(), with exactly 712 \N rows, matching count({"conductor_norm": 1}), and exactly 1000 cross-checks. Its output has the same 767518 label|value pairs as the file generated before this rewrite (only the physical row order differs, sort=[]), so the hardening changed no values.

Not yet possible here: devmirror has no szpiro_ratio column, so the column-present branch of test_szpiro_ratio still skips over the real path. It has to be rerun against the data once the column is added, as the review asks, before the workers are restarted.

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