{
  "id": 4201,
  "curve_key": "1184552537606383528702642426237700923125788917681:-1288107776937493274485331718577778282756701857893655302404180535704402921",
  "ainvs": [
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    "1490865482566543141765428173320569297663667597141222159551847045163225"
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  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 332.0803486847849,
  "faltings_height": 25.441852358741095,
  "conductor": "22304343890526450064144705503043731669398709375695492452300742909568725455497738810473799887632978110",
  "bad_primes": [
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    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "53",
    "109",
    "173",
    "101879",
    "104094700537",
    "179223765898916789751764060783309600874223337494008677165715327850089829"
  ],
  "discriminant": "1678633134172064369840906248841182960042419955994408007191716970466236153637086837214614706007412336065984601844110479915278055918080000000",
  "regulator": "1457829711754532561521663348.36028392005093788127981553030549607463079261404615890058645543",
  "points": [
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      "-81033071976229982404870",
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    [
      "377148530211402206186543/4",
      "11998500651117331948619637727049233/8"
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      "17244885916868513519059370",
      "71609811609476054410162539034982497715"
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    [
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    [
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      "-81309857290213722687099191804454263405/4913"
    ],
    [
      "837979193854080106775380355/6724",
      "10329131332982582749730068614860085431795/551368"
    ],
    [
      "-174071002408074764300830",
      "22630620910394871940839717766640915"
    ],
    [
      "2208255138066509836498346/25",
      "-57161475697816069419775885448640521/125"
    ],
    [
      "-108046582327291443091330",
      "53813711516634163910898811143793415"
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    [
      "84267799518260828805170",
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  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -11584/4313 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -154503213541262535600T^8 + 4159635009352858651680T^7 - 21187086453270000393696T^6 - 687438318305734637863392T^5 - 4576470188855512350897360T^4 - 19322004287067422371639920T^3 - 39029689014386535692132184T^2 + 4186478995367154403195512T - 1679949255743694529867467,\nA6 = 747141710909816776767093360000T^12 - 29305404314392232038648503024000T^11 + 301598848438544320323778700280000T^10 + 2292679730804159433657382244285760T^9 - 4484131884783219751251582549192624T^8 + 544733850758018343321283421195576736T^7 + 7256453148985237089497289163544883552T^6 + 31881087967205708307154627785355135968T^5 + 53417637701365905114499013007709555776T^4 + 36362990355034819792007607408188452080T^3 + 65566855132366254216911881386291117144T^2 - 854195394262226327944905852404523432T + 424114741036883895390965869842474630.\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": "2026-10-13 01:17:56",
  "updated_at": "2026-10-13 01:17:56"
}