{
  "id": 615,
  "curve_key": "1143389493067935138189593004828932947049297905062635041:-249889572047616033948130883630349663373979401516777294544432524215302167232234161",
  "ainvs": [
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  "rank_lower_bound": 28,
  "torsion": [],
  "naive_height": 373.4207763368499,
  "faltings_height": 29.184050570628795,
  "conductor": "18953687733083223999142325594019759588962896426225863549465819845748137281442267116736751293352927963809555082278665495077084083130",
  "bad_primes": [
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    "7",
    "13",
    "23",
    "29",
    "53",
    "149",
    "709",
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    "13304039783244056077097891497661130559978681974428774803618115435894522011"
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  "discriminant": "828908268243177215456565575627703375854124622299768004485259797664586721143980604759965393068114386891877176310319576170645244768536922035101806458011136000000",
  "regulator": "3437203961467798821467356243105651.378640706816933147798919920761466972317073052903314084629222",
  "points": [
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      "175432673043709857090433260",
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      "674229398502747521805257980",
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      "-957080630140784241879551915/16",
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      "-4240823599287528328955222498420/73441",
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      "-17534970601907936945204184507600998689999101033190/14119845713"
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      "-15264580204302596976695452156310/208849",
      "122220791573316886978481779773756329364817800910/95443993"
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      "-114726904727435974317444020",
      "1229643749163318226208295726725497504570"
    ],
    [
      "-44670849989955536764240640",
      "1124353650814011390207580120146637036570"
    ],
    [
      "387322555556950788554546860",
      "7012033448176869629710810628849506876570"
    ],
    [
      "54592963988074244793983770660/361",
      "2615500704314580418278697646347231097713630/6859"
    ],
    [
      "71123865449354547162902713540/289",
      "-15008870381287561165766277392088564965222590/4913"
    ],
    [
      "-22117119174178643716673162716340/908209",
      "800256785973697720376543609620171672814963907530/865523177"
    ],
    [
      "253696302094708560140194780",
      "3251826621433321072474151610647517494650"
    ]
  ],
  "submitter": "Mundoamundo",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-09-11 20:49:20"
    }
  ],
  "commentary": "Fiber t = -1707/3023 of a rank-17 elliptic fibration of Elkies' K3 surface (arXiv:2608.25406). Found by a Mestre-Nagao sieve over t = a/b re-scored at 2^20, then an iterated 2-covering point search (fake 2-descent over 3000 cosets of the growing known lattice at level 0, minimal reduced quartic models, ratpoints). Basis LLL-reduced with respect to the canonical height. The 28 points are certified independent by the F2-rank of their images under the 2-descent map at the good primes.",
  "created_at": "2026-09-06 22:22:55",
  "updated_at": "2026-09-11 20:49:20"
}