{
  "id": 3926,
  "curve_key": "146916916751443969826750919522847077396439550966756655103994761:-1776539600987629472046548398099618178957415160810230897546095463977562846250823137398693112741",
  "ainvs": [
    "1",
    "0",
    "1",
    "-3060769098988416038057310823392647445759157311807430314666558",
    "2056180093735682259313134720022451161553574068119780985146772214538736327458765049092635556"
  ],
  "rank_lower_bound": 31,
  "torsion": [],
  "naive_height": 429.4349184434194,
  "faltings_height": 33.59228667821944,
  "conductor": "26805408071927774799000455910266014028467217724488358819512397292588705717588554252370176594825217067259912163411527308486793136304454846114493997910510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "41",
    "2930575238817476392722758093181379206639338654038667330971921189700570769472466042611145949111797282084965077593189111899932748482559363371253"
  ],
  "discriminant": "8707784688317903469801008592719134688634564893993366198571104851944217598127623681717550731607834103941625253079933837488757911498174666462966371232859307753338413448391395263437500",
  "regulator": "312866461744761389256203585318223255273.0065029677953105389314357565479161933806214749511381129991379",
  "points": [
    [
      "959895193053390503080494552770",
      "51076510829890759010238771695744165907123117"
    ],
    [
      "961143046047263581206819507395",
      "47362609385782252224815071292587219749111867"
    ],
    [
      "961157875895423381897179257347",
      "47317289886551648498457276949124970229080699"
    ],
    [
      "965016200981224294408527464126",
      "34142521659039925746309567279325483519716249"
    ],
    [
      "-8525147081466740407622124260",
      "1443008309364570346804819276445516157326587367"
    ],
    [
      "1056500901058800972779339122790",
      "41652276211642290511294305010086156002743992"
    ],
    [
      "1059154457054719506406804040255",
      "50209334596377208425814565521636066379074767"
    ],
    [
      "389758449449514609230281747325",
      "960431322024792606884665065429749441107405167"
    ],
    [
      "395602470908929205073513976760",
      "952493875153227209501834598944145696688736292"
    ],
    [
      "420330957806428603404211554815",
      "918644309650172524775373393591513735004436367"
    ],
    [
      "594198019214853126740017138790",
      "668783534971266158173991415984508377960379617"
    ],
    [
      "705855114313245065449977334640",
      "497392986695628863724602443476979471702827867"
    ],
    [
      "767008003877184987151772307695",
      "399721760375551822378750824049569991046873937"
    ],
    [
      "805792247012558294722678119677",
      "336211113396061611312500584667261510074047699"
    ],
    [
      "865921357387472602412613640940",
      "234690727255895580024195714116792999766384567"
    ],
    [
      "884410491717315874684426941890",
      "202419575270847257113456997868775269111699117"
    ],
    [
      "909690206853996795841155712172",
      "156939675688581406898748630802300213986255324"
    ],
    [
      "924664938503422759377086835485",
      "128792851387264325023264417691143712140645347"
    ],
    [
      "1127282688073030787674458806726",
      "195808274653023805768791460682104036800536184"
    ],
    [
      "1143684159352565591776389727355",
      "227115015000894332877500699358659052317097267"
    ],
    [
      "1271130162334009718905954417175",
      "468402131066459942627667046378845276816784167"
    ],
    [
      "1347095883729304334110898869640",
      "614460345750094416039450464327203305312186867"
    ],
    [
      "225557896375529208128735708795",
      "1173573610923045472972310858961564787449217617"
    ],
    [
      "1969385374036399013329254507890",
      "1914827805192497557014616939938782303073082992"
    ],
    [
      "-1037486474957583701270618818600",
      "2028536129153356696724044765686238057093145667"
    ],
    [
      "-1660933580209057099389841008610",
      "1599342430312300402062470978203742542490821992"
    ],
    [
      "-6830191222013220535090254210565/4",
      "12142775180346736682164097735643169347905452311/8"
    ],
    [
      "56507077430347299094932096514985/64",
      "104981092062921401579854198886731511930021361279/512"
    ],
    [
      "1489042519034866858323405638150015/1681",
      "13780933185694892244332692057049955255686841620007/68921"
    ],
    [
      "2750305590109547174887715573455885/9409",
      "994132947831202686258242925102684040135137564757991/912673"
    ],
    [
      "48269515570754580848970477422304683600/45738169",
      "11599824786226297766143192312562981963567101751027423649/309327236947"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "(Amusing coincidence: the ln(N) of this curve matches the primary laser-cooling transition of the BaF molecule in THz to 8 significant figures. This number has been burned into my head since undergrad.)\r\n\r\nSpecialization at T = 229817/49160 of the rank-17 fibration of X1152 given by:\r\ny^2 + (Lx+B)y = x(x+D)(x+E),\r\nwhere\r\nB = pE + qD + pq(L-p-q),\r\nL = 194222T^2 - 546468T + 628841,\r\np = 9255T^2 - 65810T + 19856,\r\nq = 561868T^2 - 824209T + 405,\r\nD = 69(50861980T^4 - 423923797T^3 + 327033605T^2 + 272380918T + 2084880),\r\nE = 23(36050220T^4 - 167366909T^3 - 3016081708T^2 + 7157890125T - 3824049600).",
  "created_at": "2026-10-05 01:17:31",
  "updated_at": "2026-10-05 01:17:31"
}