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# file copied from lmfdb codebase (lmfdb/lmfdb/utils/trace_hash.py)
# Sage translation of the Magma function TraceHash(), just for elliptic curves /Q and /NF
from sage.all import GF, ZZ, QQ, pari, prime_range
TH_C = [326490430436040986,559705121321738418,1027143540648291608,1614463795034667624,455689193399227776,
812966537786397194,2073755909783565705,1309198521558998535,486216762465058766,1847926951704044964,
2093254198748441889,566490051061970630,150232564538834691,1356728749119613735,987635478950895264,
1799657824218406718,1921416341351658148,1827423174086145070,1750068052304413179,1335382038239683171,
1126485543032891129,2189612557070775619,1588425437950725921,1906114970148501816,1748768066189739575,
1105553649419536683,41823880976068680,2246893936121305098,680675478232219153,1096492737570930588,
1064058600983463886,2124681778445686677,1153253523204927664,1624949962307564146,884760591894578064,
722684359584774534,469294503455959899,1078657853083538250,497558833647780143,430880240537243608,
1008306263808672160,871262219757043849,1895004365215350114,553114791335573273,928282405904509326,
1298199971472090520,1361509731647030069,426420832006230709,750020119738494463,892950654076632414,
1225464410814600612,1911848480297925904,842847261377168671,836690411740782547,36595684701041066,
57074465600036538,35391454785304773,1027606372000412697,858149375821293895,1216392374703443454,
59308853655414224,1030486962058546718,382910609159726501,768789926722341438,762735381378628682,
1005758989771948074,1657009501638647508,1783661361016004740,796798233969021059,1658520847567437422,
502975179223457818,2063998821801160708,2126598223478603304,817551008849328795,1793074162393397615,
1287596263315727892,1629305847068896729,2282065591485919335,1280388906297308209,173159035165825250,
1203194438340773505,2146825320332825798,847076010454532974,2132606604399767971,865350797130078274,
421223214903942949,2202859852828864983,1627572340776304831,1301036100621122535,2151172683210770621,
555918022010940381,1195820575245311406,2060813966122583132,824196499832939747,1252314214858834971,
380498114208176064,621869463771460120,1487674193901485781,1569074147090699661,1723498454689514459,
1489838779667276265,607626788325788389,93543108859195056,1874271115035734974,1456016012787031897,
619764822731213939,1812449603590865741,808484663842074461,2009697952400734786,1525933978789885248,
343887624789001682,1182376379945660137,1982314473921546769,1109549848371395693,1037594154159590924,
1071053104849367160,1322181949714913233,1516660949039528341,960526604699918173,1729904691101240134,
261117919934717464,2271784899875479358,756802274277310875,1289220444092802136,474369139841197116,
1716815258254385285,103716246685267192,543779117105835462,1645057139707767457,895800586311529398,
1255427590538696616,152478208398822237,59235267842928844,1502771737122401274,1149578551939377903,
1470772656511184950,1546086255370076952,1723497785943073942,778240149963762596,240870114509877266,
394305328258085500,2102620516550230799,1039820873553197464,979798654654721830,880027557663442629,
1676981816531131145,1802107305139241263,1972433293052973713,2107405063590590043,1798917982073452520,
1369268024301602286,867033797562981667,1038357135783187942,758476292223849603,1948092882600628075,
2207529277533454374,1821419918118374849,1231889908299259230,566310110224392380,1609356725483962542,
280378617804444931,1072662998681271815,116308709127642766,1193169610307430309,866966243748392804,
166237193327216135,1077013023941018041,404884253921467160,786088301434511589,1383535122407493085,
2280658829488325172,101154688442168806,186007322364504054,132651484623670765,2214024743056683473,
2082072212962344576,1527055902872993253,914904768868572390,828477094595207304,1020679050708770534,
482636846586846145,1930865547754160712,1593671129282272719,1493198467868909485,729902645271416500,
275540268357558312,164114802119030362,788447619988896953,1762740703670330645,660855577878083177,
1651988416921493024,740652833177384429,1112201596451006206,415698847934834932,1211582319647132127,
1146510220721650373,1849436445614060470,2087092872652683432,2118502348483502728,1356524772912098481,
1199384942357517449,172551026757446140,578031956729941707,523340081847222890,1076777027268874489,
504399020033657060,1278551106709414382,2159465951497451565,1178157191616537256,204263226455195995,
1056341819781968292,183521353142147658,2188450004032853736,815413180157425263,1872285744226329343,
959184959959358956,473007083155872003,655761716995053547,1131460430873190185,2139124645518872072,
511733859594496686,15198510254334311,1224323599606986326,717867206610437778,2091512354759023324,
372342232752868676,1361511712413436237,1389190973283340505,394349220142131124,2079377585202309849,
353365880305796299,2032166139485738617,1890917131797951728,242865361432353437,1418792507475867019,
2119099350463010017,1014188227490285243,479492624224518275,1303029569429482669,517247294593876834,
1554557044656123283,750281115903727536,2167122262389919937,760554688782332821,2023636030598854916,
1790146557619247357,386163722563943194,1515274606763521578,2204179368292080266,964158696771121369,
303439105863023359,8182230548124380,1750434984088519049,1725590414598766182,1265114980378421064,
1015227773830014864,229929992560423398,764214183816115409,538352539450824188,1941773060895353999,
1068434172733967371,1355790773646160387,459324502245141234,609129328626229402,1241119177010491262,
1783576433920437207,1523680846139002895,882824005398680507,413096479776864968,522865969927243974,
1858351603281690756,1968585526421383793,2178118415854385403,2071714574011626742,2075065799199309684,
2276241901353008033,303400925906664587,1426227202230524239,1930606302598963877,249953308414640146,
611228839507773914,1672745442514341102,467604306000306674,1474554813214382459,1601661712875312382,
614840167992924737,1228071177654928913,527816710270111610,2217787042387174521,639805394326521740,
222549283662427192,1360905187147121266,2218130040969485290,1295851844663939225,563784543912533038,
1995338666855533310,1570565903061390324,1421390998286027062,1394318358097125191,1259069656723159936,
782274544912671248,727119931274242152,461373271832281770,431218333850664873,1192819027123234430,
2078764559709872649,185598300798682005,753027393642717163,39457098005678485,1334017905593361063,
2208208003949042369,995759906937041788,1045940157364976040,194824647782216037,550631184874398695,
1360200364068800381,1357865448826768161,1831861326200370539,942093021910086667,1640270910790040055,
186615109286328085,1330440696074470319,499018273810238035,502274974614414055,1207335215870481547,
2013999866627689866,1419916425046140717,191559056573160841,1328802988676857752,1405960078185023606,
227507798797399340,1637526486952132401,1076968863810265335,944510191997220613,1301386330701215932,
285779824044017183,1429750858521890899,1618865668058420542,841779507635076338,2271885690336656780,
1950830875641497149,2020789551919109899,975546679421148460,1197104163269028491,1270315990156796392,
748604252817308486,816129261753596233,384118410847738091,2113266006559319391,1338854039375748358,
1361143499198430117,633423014922436774,1290791779633361737,81273616335831288,734007502359373790,
1803343551649794557,178160046107106100,1669700173018758407,1829836142710185153,1253431308749847288,
70019619094993502,939065521645602191,571602252457140250,26887212485499413,984459396949257361,
852773633209386873,2289526104158020696,756333221468239349,478223842701987702,2004947225028724200,
526770890233938212,1661268713623636486,1595033927594418161,1532663022957125952,364955822302609296,
603258635519191127,371859597962583054,94282227629658712,2160611809915747887,27000232625437140,
22687777651226933,734430233276692626,1127699960534747774,346857527391478939,399588948728484631,
1369575405845760568,2217803687757289581,2206814713288610370,130141496340768529,861110681132541840,
230850531138610791,1780590839341524422,1923534983071749673,1055631719355441015,1222514615506258219,
937915311769343786,852868812961957254,718656592041199719,2250542267067365785,2169537354592688250,
1568074419444165342,853778925104674827,105031681250262217,1204393036537417656,592755100672600484,
1509207668054427766,1409630039748867615,433329873945170157,168130078420452894,701434349299435396,
1736119639406860361,1801042332324036889,82826810621030003,581092394588713697,1513323039712657034,
2086339870071049553,512802587457892537,1294754943443095033,1486581673100914879,930909063370627411,
2280060915913643774,219424962331973086,118156503193461485,743557822870685069,1997655344719642813,
393161419260218815,1086985962035808335,2119375969747368461,1650489163325525904,1967094695603069467,
916149623124228391,1122737829960120900,144869810337397940,2261458899736343261,1226838560319847571,
897743852062682980,45750188043851908,1858576614171946931,1568041120172266851,289541060457747472,
1539585379217609033,866887122666596526,6060188892447452,1707684831658632807,1062812350167057257,
887626467969935688,1968363468003847982,2169897168216456361,217716763626832970,413611451367326769,
336255814660537144,1464084696245397914,1902174501258288151,1440415903059217441,302153101507069755,
1558366710940453537,717776382684618355,1206381076465295510,1308718247292688437,555835170043458452,
1029518900794643490,1034197980057311552,131258234416495689,260799345029896943]
TH_P = prime_range(2**12,2**13)
TH_F = GF(2**61-1)
def TraceHash_from_ap(aplist):
r"""Return the trace hash of this list of ap, indexed by the primes in TH_P
"""
return ZZ(sum([TH_F(a*c) for a,c in zip(aplist,TH_C)]))
TH_P_cache = {}
def TraceHash(E):
r"""Return the trace hash of this elliptic curve defined over either
QQ or a number field.
"""
K = E.base_field()
if K == QQ:
E_pari = pari(E.a_invariants()).ellinit()
return TraceHash_from_ap([E_pari.ellap(p) for p in TH_P])
if not K in TH_P_cache:
TH_P_cache[K] = dict([(p,[P for P in K.primes_above(p) if P.norm()==p]) for p in TH_P])
def ap(p):
return sum([E.reduction(P).trace_of_frobenius() for P in TH_P_cache[K][p]], 0)
return TraceHash_from_ap([ap(p) for p in TH_P])
# Dictionary to hold the trace hashes of isogeny classes by label. We
# store the trace hash for every curve but isogenous curves have the
# same hash. (So do Galois conjugates, but we do not take advantage
# of that).
TH_dict = {}
def TraceHashClass(iso, E):
r"""Return the trace hash of this elliptic curve defined over either QQ
or a number field, given also the label of its isogeny class.
Hash values are cached.
For curves over number fields the iso label should include the
field label.
"""
global TH_dict
if iso in TH_dict:
return TH_dict[iso]
else:
th = TH_dict[iso] = TraceHash(E)
return th
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