New (since December 2020) schema for ECQ:

    Before this there was one table ec_curves with an "extra" table
    (see below for the schema) and ec_padic.

New tables (since December 2020): 8 tables, the first of which will be
the main search table, with ec_padic unchanged.

ec_curvedata
ec_localdata
ec_classdata
ec_mwbsd
ec_galrep
ec_2adic
ec_torsion_growth [only has data for conductors up to 400000]
ec_iwasawa        [only has data for conductors up to 150000]
ec_padic          [only has data for conductors up to 130000]

NB (1) All curves have an 'lmfdb_label' (e.g. '11.a1'), with
'lmfdb_iso' the isogeny class label (e.g. '11.a'), 'lmfdb_number' the
number of the curve in its isogeny class (e.g. 1), 'iso_nlabel'
(numerical converson of the letter part of the label).  Curves of
conductor <500000 also have "Cremona label" columns 'Clabel'
(e.g. '11a1') and 'Ciso' (e.g.'11a').

(2) The 'conductor' column is in all tables though apparently
redundant in all but ec_curvedata.  This is fo ease of housekeeping
operations such as deleteing/backup of curves by conductor range.

schemas:

ec_curvedata: one row per curve, contains all columns used in search

{'id': 'bigint',
 'Clabel': 'text',
 'lmfdb_label': 'text',
 'Ciso': 'text',
 'lmfdb_iso': 'text',
 'regulator': 'numeric',
 'ainvs': 'numeric[]',
 'jinv': 'numeric[]',
 'min_quad_twist_ainvs': 'numeric[]',
 'iso_nlabel': 'smallint',
 'Cnumber': 'smallint',
 'lmfdb_number': 'smallint',
 'cm': 'smallint',
 'num_bad_primes': 'smallint',
 'optimality': 'smallint',
 'manin_constant': 'smallint',
 'torsion': 'smallint',
 'rank': 'smallint',
 'analytic_rank': 'smallint',
 'signD': 'smallint',
 'class_deg': 'smallint',
 'class_size': 'smallint',
 'min_quad_twist_disc': 'smallint',
 'faltings_index': 'smallint',
 'faltings_ratio': 'smallint',
 'isogeny_degrees': 'smallint[]',
 'nonmax_primes': 'smallint[]',
 'torsion_structure': 'smallint[]',
 'torsion_primes': 'smallint[]',
 'sha_primes': 'smallint[]',
 'conductor': 'integer',
 'nonmax_rad': 'integer',
 'num_int_pts': 'integer',
 'sha': 'integer',
 'bad_primes': 'integer[]',
 'degree': 'bigint',
 'semistable': 'boolean',
 'potential_good_reduction': 'boolean'}

NB (1) no 'equation' column: constructed on the fly from ainvs.
(2) we store the ainvs of the minimal quadratic twist and look up its
label on the fly.

ec_localdata: one row per (curve, bad prime)

{'id': 'bigint',
 'lmfdb_label': 'text',
 'tamagawa_number': 'smallint',
 'kodaira_symbol': 'smallint',
 'reduction_type': 'smallint',
 'root_number': 'smallint',
 'conductor_valuation': 'smallint',
 'discriminant_valuation': 'smallint',
 'j_denominator_valuation': 'smallint',
 'prime': 'integer',
 'conductor': 'integer'}

NB kodaira_symbol uses the pari numerical encoding.  Sage has (thanks
to David Roe) a suitable class to use to convert these to text via
latex(KodairaSymbol(n)), and K._pari_code() converts a Sage Kodaira
Symbol object K to its pari code.

ec_mwbsd: one row per curve

{'id': 'bigint',
 'lmfdb_label': 'text',
 'special_value': 'numeric',
 'real_period': 'numeric',
 'area': 'numeric',
 'sha_an': 'numeric',
 'tamagawa_product': 'integer',
 'ngens': 'smallint',
 'rank_bounds': 'smallint[]',
 'torsion_generators': 'numeric[]',
 'xcoord_integral_points': 'numeric[]',
 'gens': 'numeric[]',
 'heights': 'numeric[]',
 'conductor': 'integer'}

ec_classdata: one row per isogeny class

{'id': 'bigint',
 'lmfdb_iso': 'text',
 'trace_hash': 'bigint',
 'class_size': 'smallint',
 'class_deg': 'smallint',
 'isogeny_matrix': 'smallint[]',
 'aplist': 'smallint[]',
 'anlist': 'smallint[]',
 'conductor': 'integer'}

ec_2adic: one row per curve (Rouse data)

{'id': 'bigint',
 'lmfdb_label': 'text',
 'twoadic_label': 'text',
 'twoadic_index': 'smallint',
 'twoadic_log_level': 'smallint',
 'twoadic_gens': 'smallint[]',
 'conductor': 'integer'}

ec_galrep: one row per (curve, nonmaximal prime) (Sutherland data)

{'id': 'bigint',
 'lmfdb_label': 'text',
 'image': 'text',
 'prime': 'smallint',
 'conductor': 'integer'}

ec_torsion_growth: one row per (curve, extension field) (Gonzalez-Jimenez--Najman data)

[No data for conductors over 400000]

{'id': 'bigint',
 'lmfdb_label': 'text',
 'degree': 'smallint',
 'field': 'numeric[]',
 'torsion': 'smallint[]',
 'conductor': 'integer'}

ec_iwasawa: one row per curve (Pollack data)

[No data for conductors over 4150000]

{'id': 'bigint',
 'lmfdb_label': 'text',
 'iwp0': 'smallint',
 'iwdata': 'jsonb',
 'conductor': 'integer'}

NB Type jsonb is only used for ec_iwasawa.iwdata, which is a dict with
keys a variable number of primes.

ec_padic: one row per (curve, prime p) for p<100.

{'id': 'bigint',
 'lmfdb_iso': 'text',
 'p': 'smallint',
 'prec': 'smallint',
 'unit': 'numeric',
 'val': 'smallint'}

See make_tables.py for commands used to create these tables, and also
the commands for creating indexes for them.

======================= Old schemas =============================

Search table columns (* indicates "used for searching Nov 2020"):

*'label'
*'lmfdb_label'
*'iso'
*'lmfdb_iso'
 'iso_nlabel'
*'number'
 'lmfdb_number'
*'ainvs'
*'jinv'
*'conductor'
*'torsion'
*'rank'
*'sha'
*'torsion_structure'
*'cm'
*'isogeny_degrees'
*'nonmax_primes'
 'nonmax_rad'
 'trace_hash'
*'bad_primes'
 'class_size'
 'num_bad_primes'
*'semistable'
 'optimality'
 'manin_constant'
*'num_int_pts'
*'regulator'
*'isodeg'
 'torsion_growth'

Extra table columns:

 'equation'
 'signD'
 'torsion_generators'
 'xcoord_integral_points'
 'gens'
 'heights'
 'tamagawa_product'
 'special_value'
 'real_period'
 'degree'
 'modp_images'
 '2adic_label'
 '2adic_index'
 '2adic_log_level'
 '2adic_gens'
 'isogeny_matrix'
 'class_deg'
 'sha_an'
 'sha_primes'
 'torsion_primes'
 'tor_degs'
 'tor_fields'
 'tor_gro'
 'local_data'
 'min_quad_twist'
 'aplist'
 'anlist'
 'iwdata'
 'iwp0'