{
  "id": 4189,
  "curve_key": "13633778949837668944879735200443155481601:-1555231807701017442143316683765448156169974923691939014182401",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-284037061454951436351661150009232405867",
    "1800036814468770187736885056758932484284645523256867145659"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 277.2401072592643,
  "faltings_height": 21.00600578076895,
  "conductor": "1995026868259792220925033067480146082178558945648195128203283132535465250851319644490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "29",
    "41",
    "47",
    "79",
    "97",
    "191",
    "23539",
    "587813",
    "54727019917837527982984475073613251020888263874071025419"
  ],
  "discriminant": "66840208365375964394195629531099444292324786075131242827274711064622671996299031584236653908332104679478389760000000",
  "regulator": "194768232689864400108037.63917393864080176301348664817520202139802040096169537524027373",
  "points": [
    [
      "739375616386560907",
      "39880207323649106504237657066"
    ],
    [
      "7175505684049815467",
      "11462061512134208429219737066"
    ],
    [
      "-14001956220734132933",
      "55063244512771185094524127466"
    ],
    [
      "7296583605441639227",
      "10770688233052076256849529066"
    ],
    [
      "36734395430000143867",
      "-202326668943544915264203501334"
    ],
    [
      "16480896968989497707",
      "-39942357544231653218721958934"
    ],
    [
      "-5960865438087764213",
      "-57283003956330218781849818134"
    ],
    [
      "33787571509488499267",
      "175428063690675284698353588266"
    ],
    [
      "11654208617855361367",
      "-8525901811850660550559830034"
    ],
    [
      "7565044735185435307",
      "-9177717898871917930282230934"
    ],
    [
      "6210115805430936607",
      "16602115188813173596185472826"
    ],
    [
      "5130192334071846067",
      "21860762602596020925640231466"
    ],
    [
      "-13104337328516266933",
      "57199908706875114395596479466"
    ],
    [
      "7894627535024397067",
      "7050092579043924784603327466"
    ],
    [
      "-17805293882106793183",
      "34822618083520051042982174966"
    ],
    [
      "6660780018389380987",
      "-14270267476489008809383640854"
    ],
    [
      "-16384786512853617413",
      "-45334793504372164514929436134"
    ],
    [
      "23362999825881513643/4",
      "-147577951144037864056558329647/8"
    ],
    [
      "11372551563708637867",
      "6377996301639873811611554666"
    ],
    [
      "684666720697474263251/25",
      "-15084149873907708438435486015166/125"
    ],
    [
      "13036184404683243067",
      "17682587679204656176644319466"
    ],
    [
      "3059579455966809067",
      "30978115833897753076952767466"
    ],
    [
      "11426173338393025567",
      "6808232022635594427242737466"
    ],
    [
      "1638566529432925478683267/121801",
      "864509232660199220092548665915546834/42508549"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -609/8 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -159593418515992752T^8 + 66594122607180400704T^7 - 9577916877180584429856T^6 + 378921666915696440595168T^5 - 8319401481873790592668080T^4 + 116272680309493432400708928T^3 - 728840755857976029224439616T^2 - 494050735965340585862790156T - 1390993922871848594371288527,\nA6 = 40790046358717726655041920T^12 - 19761746514541051225237666560T^11 + 3565895854811577447633633290880T^10 - 339557681946125505951450862243200T^9 + 23467317247680868700633154198453120T^8 - 886973909798626440691615033339785600T^7 + 17462193623232977878169289412672255680T^6 - 168744348646923648755279986373234058480T^5 + 648041970284178877886227382317646179620T^4 - 1598469487562293877807341226375296120200T^3 + 21038628236849997090209222042624669117476T^2 + 9643147208228838672635695562458112132532T + 18608807243853177902952156937051966196946.\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 01:16:57",
  "updated_at": "2026-10-12 01:16:57"
}