{
  "id": 4641,
  "curve_key": "65514988912291299226790470223031214824588801:-582563895758312096185188717104865200714495343043393417616947923201",
  "ainvs": [
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    "-1",
    "1",
    "-1364895602339402067224801462979816975512267",
    "674263768238787148362828164994178832825249884443746595004234459"
  ],
  "rank_lower_bound": 27,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 302.86059946067587,
  "faltings_height": 23.205601444533563,
  "conductor": "17984475627235815753345124804186459602778915872970873955731747764282717775024241574505607568113683745180806871490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "47",
    "193",
    "12601",
    "1356589602179057",
    "184097786862976000802134949924953839102217146822749721562620206256708540975846273985109"
  ],
  "discriminant": "-33666872076214494848150880501968974223437450830006001925300081405222289423034574378110357110037076876694712228902828939264000000",
  "regulator": "5268355214405083157346327513367.6953596682517183592751934914686310362475278430115751286803609",
  "points": [
    [
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      "8775056219712781792629006403466"
    ],
    [
      "613484532985643090317",
      "8234954362028494967157427851116"
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    [
      "-7491713974162816456037/9",
      "-948323791585196944450365342915898/27"
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    [
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      "-70015960005845869826907005181094"
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      "-45144965395912205453778376135184"
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    [
      "-1197400530395043346253",
      "-24326855254458216766634034105214"
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      "704254364636640582667",
      "7894433813096068630599278141066"
    ],
    [
      "-873406544584884024533",
      "-34642516533610960512831583876534"
    ],
    [
      "99396606774961782001063/289",
      "76981401419835517363976679071203258/4913"
    ],
    [
      "6151723573022987052877/16",
      "-919290225363486510014001974652301/64"
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      "195929796884381499580067",
      "-86724744908777715377546599501978934"
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      "-1215714419422673395733",
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    [
      "-215989741022803609253",
      "-30967579107267506266635933628534"
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    [
      "204538494944149477867",
      "20090971793694572947200323453066"
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      "591019335175840905067",
      "-8604034440674338552723593926134"
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      "-26719276674644551467440509314934"
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    [
      "782646476402550246859",
      "-9242931929997855989526299221078"
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    [
      "1390524463911052206667",
      "-38275359434975073619388719247734"
    ],
    [
      "970077594787037733787",
      "16220393629534573705784918851466"
    ],
    [
      "-873315814117256885333",
      "34643725707150051528798455544266"
    ],
    [
      "1624363303696761433183/9",
      "-562352441184418480772318613700918/27"
    ],
    [
      "741530154667481917367",
      "8360350509639402647031239455066"
    ],
    [
      "2997956902511075618521387/961",
      "4874867341059090182490200328658430006/29791"
    ],
    [
      "-762783167570703197344517/1849",
      "-2716216068246326847313114077940545538/79507"
    ],
    [
      "6612639060452455571947",
      "-529905217189876776128504652796534"
    ],
    [
      "89343978771954738561667",
      "-26703058422829673271900730856102734"
    ],
    [
      "-606569625741356006933",
      "35763037002380422750228728221066"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -3364/729 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -34563528913036557884400T^8 - 363066894139066649206560T^7 - 1253243958943048847118720T^6 + 1217803890141503318620800T^5 - 1229632829129776891166640T^4 + 889782194202589151280720T^3 + 747172710296992900801080T^2 - 433583331227756476888680T - 198981396396273976948827,\nA6 = 2529174685018796943057183053750400T^12 + 38255811556046455632742522418874240T^11 + 209255178696584738819667007675000896T^10 + 459298877624289867341928240423086400T^9 + 710742840439999694736111158271090960T^8 - 2594464885975235791000216537446763680T^7 + 507169769440286090575053053081870400T^6 + 1519561014747819598698469788704128704T^5 - 146641249872692903802186384657680160T^4 - 569600267540526989066094026512214160T^3 - 74471423161824441814957627679250840T^2 + 111793067512606356283231367322794040T + 33201984796393433668897397905886454.\nIt is a 2-neighbour of another fibration built here: its Mordell-Weil lattice (rank 17, no reducible fibres) is a root-free Kneser 2-neighbour of that fibration's, realised by the pencil |O + P - F| for a section P of height 12. Constructed and searched by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-19 13:55:13",
  "updated_at": "2026-10-19 13:55:13"
}