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AndrewVSutherland
GitHub Repository: AndrewVSutherland/lmfdb
 Path: blob/main/scripts/belyi/find_friends.py
1127 views
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from lmfdb import db

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from lmfdb.ecnf.WebEllipticCurve import parse_ainvs

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from lmfdb.belyi.main import hyperelliptic_polys_to_ainvs, curve_string_parser

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from sage.all import EllipticCurve

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import re

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from lmfdb.genus2_curves.main import genus2_lookup_equation as genus2_lookup_equation_polys

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def base_field_label(rec):

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    if rec['base_field'] == [-1, 1]:

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        rec['base_field_label'] = '1.1.1.1'

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    else:

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        field_rec = db.nf_fields.lucky({'coeffs':rec['base_field']})

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        if field_rec:

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            rec['base_field_label'] = field_rec['label']

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    return rec

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def genus2_lookup_equation(rec):

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    f,h = curve_string_parser(rec)

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    lab, _ = genus2_lookup_equation_polys(str([f,h]))

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    if lab:

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        return lab

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def genus1_lookup_equation_QQ(rec):

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    assert rec['g'] == 1

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    f,h = curve_string_parser(rec)

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    ainvs = hyperelliptic_polys_to_ainvs(f,h)

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    E = EllipticCurve(ainvs)

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    j = E.j_invariant()

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    for r in db.ec_curvedata.search({"jinv":[j.numerator(), j.denominator()]}):

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        ainvs2 = r['ainvs']

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        E2 = EllipticCurve(ainvs2)

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        if E.is_isomorphic(E2):

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            return r['lmfdb_label']

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    #print("Curve not found in database")

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    return None

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def NFelt(a):

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    r""" Returns an NFelt string encoding the element a (in a number field

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    K).  This consists of d strings representing the rational

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    coefficients of a (with respect to the power basis), separated by

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    commas, with no spaces.

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    For example the element (3+4*w)/2 in Q(w) gives '3/2,2'.

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    """

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    return ",".join(str(c) for c in list(a))

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def genus1_lookup_equation_nf(rec):

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    assert rec['g'] == 1

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    # make base field

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    nf_matches = list(db.nf_fields.search({'coeffs':rec['base_field']}))

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    if len(nf_matches) == 0:

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        return None

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    else:

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        nf_rec = nf_matches[0]

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        # make curve

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        f,h = curve_string_parser(rec)

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        ainvs = hyperelliptic_polys_to_ainvs(f,h)

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        E = EllipticCurve(ainvs)

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        K = E.base_field()

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        j = E.j_invariant()

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        j_str = NFelt(j)

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        j_matches = list(db.ec_nfcurves.search({"field_label":nf_rec['label'], "jinv":j_str}))

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        for r in j_matches:

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            ainvs2 = parse_ainvs(K, r['ainvs'])

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            E2 = EllipticCurve(ainvs2)

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            assert E.base_field() == E2.base_field()

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            if E.is_isomorphic(E2):

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                return r['label']

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    #print("Curve not found in database")

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    return None

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# This code might not find base changes.

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def genus1_lookup_equation(rec):

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    if rec['base_field'] == [-1, 1]: # if defined over QQ

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        return genus1_lookup_equation_QQ(rec)

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    else:

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        return genus1_lookup_equation_nf(rec)

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def find_curve_label(rec):

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    if rec['g'] == 1:

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        #print("Searched for curve for %s") % rec['label']

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        return genus1_lookup_equation(rec)

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    elif rec['g'] == 2:

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        if rec['base_field'] == [-1, 1]: # currently LMFDB only has g2 curves over QQ

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            #print("Searched for curve for %s") % rec['label']

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            return genus2_lookup_equation(rec)

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def find_curve_url(rec):

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    label = find_curve_label(rec)

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    if label:

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        curve_url = ''

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        if rec['g'] == 1:

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            curve_url += 'EllipticCurve'

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            if rec['base_field'] == [-1, 1]: # over QQ

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                curve_url += '/Q'

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                label_spl = label.split(".")

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                curve_url += '/%s' % label_spl[0] # conductor

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                curve_url += '/%s/%s' % re.match(r"(\D+)(\d+)", label_spl[1]).groups() # isog class and isomorphism index

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            else: # over number field

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                label_spl = label.split("-")

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                curve_url += "/%s/%s" % (label_spl[0], label_spl[1]) # field, conductor

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                curve_url += '/%s/%s' % re.match(r"(\D+)(\d+)", label_spl[2]).groups() # isog class and isomorphism index

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        if rec['g'] == 2:

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            curve_url += 'Genus2Curve'

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            if rec['base_field'] == [-1, 1]:

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                curve_url += '/Q'

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                curve_url += '/%s' % label.replace(".","/")

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        return curve_url

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def initialize_friends(rec):

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    rec[u'friends'] = []

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    return rec

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def assign_curve_friends(rec):

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    curve_url = find_curve_url(rec)

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    if curve_url:

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        rec['friends'].append(curve_url)

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    return rec

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def assign_curve_label(rec):

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    label = find_curve_label(rec)

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    if label:

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        rec['curve_label'] = label

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    return rec

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