{
  "id": 4195,
  "curve_key": "3731635529235373295637820496706060929370844081:-198471001713640252132469826871933377188333202764517473644674720394729",
  "ainvs": [
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    "229711807538935477005166932197499449222673317168718072399630398297"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 314.79952740591426,
  "faltings_height": 24.220062231985803,
  "conductor": "17325221244070607551070058908530094913795847478774914858418853013110279303837924712209042392405987310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "23",
    "29",
    "47",
    "89",
    "97",
    "131",
    "151",
    "1412925975016666469",
    "6940835705861581881638584274637257599061774294349159013941539345039"
  ],
  "discriminant": "7275852592599506101656665672248212335423785976825992875037322571408096305496452743497226283696950701970890849361293632851276800000000",
  "regulator": "2225189286992116014832603022.17738555743130338322300032086932342840850986022207284814544838",
  "points": [
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      "1272752397372164609804",
      "-364453978907399589552182469996157"
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    [
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      "171494612927335271000690936/529",
      "-2245000802781024319440251558183529265139/12167"
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      "-39453563981891178372289/4",
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      "23987972283284391626626/9",
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      "-934323034933946603861205109584311/8"
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      "102099058520888265292634",
      "32505308850024145410942607446704483"
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      "9073349328014908163834",
      "520862109567537980611238079294083"
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      "-3947080101982733191078",
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      "-1672605523347054591676281262027117"
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    [
      "12303374056979448415589954/1681",
      "15834476378932958432905462004511704443/68921"
    ],
    [
      "36156031093056632950634",
      "-6684619432132374745670951367711517"
    ],
    [
      "-7810403604386799399916",
      "600381530855229170982486139575833"
    ],
    [
      "-7617821571743397514366",
      "616334505337782008310385438718483"
    ],
    [
      "17419068227395171971657194/5041",
      "-17291740276198240984130465357330789387/357911"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 5403/1139 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4247232044073407555787T^8 + 31562440352380138911048T^7 - 1079699554459262036768544T^6 + 808673010384011405337504T^5 - 370492253920133220842280T^4 - 583074314969616668304144T^3 + 1749298418924942437857936T^2 + 6981774061823935535232T - 733152591313571732712192,\nA6 = 99353320243156880097765275026566T^12 - 1192047168420920079142624551372696T^11 + 51816962014333011197785218484470384T^10 - 160733095313938224161654547702105120T^9 + 1161258380951665950605765814917343480T^8 - 500375410396179478662655437513305328T^7 - 2173656091315178125605895871772822192T^6 + 963181788398399075637606795285979968T^5 + 1772421005485324185894755005716179280T^4 - 460279153080260982936199267860712320T^3 - 927109903404780261014801473928185344T^2 + 58145438007481575316035550439430144T + 241998303936746269490887631501697024.\nIt is a 2-neighbour of the fibration given in curve#3900: 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": "2026-10-12 04:31:10",
  "updated_at": "2026-10-12 04:31:10"
}