{
  "id": 627,
  "curve_key": "4229226248998434731759210602087842304406760748297441:-275191172429167580141925910212827645257429648870004209547284968477929860207825",
  "ainvs": [
    "1",
    "0",
    "0",
    "-88108880187467390244983554210163381341807515589530",
    "318508301422647662201303129477995684907149943554616095388335083180311039076"
  ],
  "rank_lower_bound": 27,
  "torsion": [],
  "naive_height": 356.62269600633846,
  "faltings_height": 27.471207011728698,
  "conductor": "255417940288246678150583574922944179897578074304448055056272816920964172850303531273517623698377800620421130739930868904355190006",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "37",
    "41",
    "71",
    "1327",
    "338177617721711",
    "613548173194227342170437609",
    "1201184027477738426918374049",
    "642839906786788643584327182240675424261680581201"
  ],
  "discriminant": "-49039776566510582000950184566169350233516872079338741934263021194957711940191240379209795043386946144496881210372526345874210490545126624645563629568",
  "regulator": "346949950424240469110872242008017.60665602071833961253630511512531717909442967316444143473663",
  "points": [
    [
      "16097469004602767700993593172/1369",
      "1526544981653909181574751583621953108322654/50653"
    ],
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      "1300695039941017398789753933300/241081",
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    ],
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    ],
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      "313130609052607174642358136/49",
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    ],
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      "134366986997567550298430553012/11881",
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    ],
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      "1717272949456986562673046",
      "13124998594452988457350634269692059808"
    ],
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      "1843000044654584108586613716/361",
      "9077202959349721082092485072419037787122/6859"
    ],
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      "253299457743765685169080184916/11881",
      "116771833896779800165700792736341148815073582/1295029"
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      "56138997367459476846142404",
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      "5452841945970221154042860",
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      "-10178799591593170191049860",
      "-12678574947413182303741548998689025994"
    ],
    [
      "-9057430759630493983458077544/1849",
      "1999675453304493874673558507062555580792022/79507"
    ],
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      "8107127088446819893202401598196/58081",
      "-23032538075944868796363196672219086668545331082/13997521"
    ],
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      "31258487745492027671221682116/5625",
      "295038224588108438106686422771546295567986/421875"
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      "751697945714151138619291556589337887682039628526413857707462/1582080373886805535515625"
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      "62527860767159315631662360458611579188/17850379950841",
      "-548289979121304338492694941399088864302583027353346893726/75417337631284650611"
    ],
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      "34995349130732752278795520632/6241",
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      "7997019417386492445897114",
      "11194990712094137994397028205254263050"
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    [
      "-46509375571534300147302025685256/5583769",
      "287420731011448645944066716381475134573376965526/13194446147"
    ],
    [
      "255160329768396550483765140/49",
      "325321446680351308698455454558100942842/343"
    ],
    [
      "-4071315001410756096990861021855094290/420563923081",
      "-4433551628100104466419164380644025890724809798938014024/272739489193336229"
    ],
    [
      "54551696116160854783526750484/30625",
      "69302677367794867614239236659893541149437002/5359375"
    ],
    [
      "-19085448473370657258424929/4",
      "-200843555221823854187831481188699674215/8"
    ],
    [
      "344808198803564498979884333209884/66178225",
      "504973492092274943810597319437283140211273845082/538359860375"
    ],
    [
      "-48498631454963984784801577356/10609",
      "27334758747942388295509476609892072710268602/1092727"
    ],
    [
      "-1037321004694596017733372",
      "-20218538522161063305165176216692656042"
    ]
  ],
  "submitter": "Roy van Rijn",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Roy van Rijn",
      "at": "2026-09-07 08:41:31"
    }
  ],
  "commentary": "This curve was found prospectively as the specialization t = -1867/270 of an elliptic K3 family with generic Mordell–Weil rank 16.\r\n\r\nWe found 27 independent rational points on the specialized curve, proving rank at least 27 over Q; the exact rank is not currently known. The submitted equation is a globally minimal integral Weierstrass model. In this presentation, the specialization has 11 independent directions beyond the 16 generic sections.",
  "created_at": "2026-09-07 08:26:36",
  "updated_at": "2026-09-07 08:41:31"
}