{
  "id": 5946,
  "curve_key": "9236564491514398519075877569921:-17824605633854556809383124373584690877620731969",
  "ainvs": [
    "1",
    "0",
    "0",
    "-192428426906549969147414116040",
    "20630330594739054345528225812484852157180992"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 213.9021683941784,
  "faltings_height": 15.862691163039221,
  "conductor": "8175487638384495547299219987208353872382860538427185834956068280010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "31",
    "37",
    "41",
    "83",
    "767230134297205154212370595195642386798106318173328683657"
  ],
  "discriminant": "272160207592899028326171446939115737655951062062692327494632776026368271939784288768000000",
  "regulator": "10287945003808443477.374612963821775454966226805138952380383746079586256730931188",
  "points": [
    [
      "637320453899344",
      "12524252084785143521848"
    ],
    [
      "3047389574993944",
      "-166535471757151894339592"
    ],
    [
      "369612719545408",
      "21136319252212774456"
    ],
    [
      "966094205764624",
      "27137036755369189768888"
    ],
    [
      "2241793115998504",
      "-104190608359176595161632"
    ],
    [
      "80644055424784",
      "2374149819116439302968"
    ],
    [
      "-108862640160276",
      "-6347318902363546079412"
    ],
    [
      "378400768830208",
      "-1413290842831914663224"
    ],
    [
      "308763868114267624/6241",
      "-1652329784425775241095610488/493039"
    ],
    [
      "386198138274064",
      "-1978862814078826803272"
    ],
    [
      "-481868684522192",
      "1211154158430784125496"
    ],
    [
      "-473733177233726",
      "2339526141691892989588"
    ],
    [
      "531133949801824",
      "-8261942265049454588312"
    ],
    [
      "404378980810192",
      "2990204601633033772600"
    ],
    [
      "386207285946424",
      "1979451800775004087288"
    ],
    [
      "2013942713576974",
      "88326507875070775797838"
    ],
    [
      "773300642403424",
      "18282624117157149535288"
    ],
    [
      "114213159864304",
      "-377282624948344417832"
    ],
    [
      "-270874391392496",
      "7271823445979984237368"
    ],
    [
      "115094586152194",
      "86551828641608064148"
    ],
    [
      "62534920713424",
      "-2973446559444839848712"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 35/6 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -28627871103769984370352T^8 + 250727503810391437739328T^7 - 288854657346414564166464T^6 - 1046563569239575640345856T^5 - 2237723908977579748622280T^4 - 2929539083122814891913864T^3 - 75441235775660299609524T^2 + 875991646929384189258912T - 320782968880211172761712,\nA6 = 1174522160214039703024876049652096T^12 - 16131442871155893431215736050050816T^11 + 93303642018533859944970389927921664T^10 - 231262072230896017869661906694261760T^9 - 366595866204221333220660871885856160T^8 + 1809536503795113401754131369092034592T^7 + 3099112034539070371703903967203738928T^6 + 554652868729364853437329955292672288T^5 - 394633275566228428167096479633610540T^4 + 857804045527423469286999564571793520T^3 + 199633165297674561155987038442283696T^2 - 284106783901779659207593408557902976T + 70103120599376154084348899681491584.\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": "2026-10-26 05:05:27",
  "updated_at": "2026-10-26 05:05:27"
}