{
  "id": 5864,
  "curve_key": "10295476902960638104416225:-32027457041491196223100104925752947025",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-214489102145013293842005",
    "37068816020298062348568782172711597"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 172.7812406850285,
  "faltings_height": 12.314172003375928,
  "conductor": "82059570064912862085402111004891520533731609059359314653050",
  "bad_primes": [
    "2",
    "5",
    "17",
    "61",
    "881",
    "28211",
    "11014621",
    "36597105443",
    "4529773564243",
    "34873320307748327"
  ],
  "discriminant": "37922489255181650380811241125451729875478892671335015593243271495680000",
  "regulator": "155364176304152835.7702887321408077271382180487798041671512719632196956247978",
  "points": [
    [
      "345382701983",
      "-64718178910817104"
    ],
    [
      "-433857458721",
      "220137737275494320"
    ],
    [
      "207458848159",
      "-38730083639810640"
    ],
    [
      "937817684639",
      "812852335210348720"
    ],
    [
      "182966156219",
      "-62846387281449100"
    ],
    [
      "-169194867277",
      "-261755041650992420"
    ],
    [
      "565574534719",
      "310921160830820400"
    ],
    [
      "190045682335",
      "56302985143304368"
    ],
    [
      "304696691999",
      "1661050417851440"
    ],
    [
      "227804459735",
      "5396666397721496"
    ],
    [
      "326797455519",
      "-43303428896178000"
    ],
    [
      "210982699679",
      "-34741243996926800"
    ],
    [
      "339614791839",
      "58272511177253040"
    ],
    [
      "140550260059",
      "98482413254867280"
    ],
    [
      "339950854015",
      "-58651863940914864"
    ],
    [
      "-351251532001",
      "262815428467968560"
    ],
    [
      "134835861189",
      "-102953478407173930"
    ],
    [
      "1347252261279",
      "1481039563405734320"
    ],
    [
      "2542806068255",
      "3991627410913073456"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -9/8 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -1294316468457527272747T^8 - 61482963914543295234088T^7 - 943435684374763790645824T^6 - 2688743270213054211837664T^5 - 3856670928366631764978280T^4 - 999902363213138391166096T^3 + 2961913384000561526356496T^2 + 1046903749166543421058688T - 943686476906321498328832,\nA6 = 32662063813788609918746258888614T^12 + 1796450107115792990741776388684984T^11 + 35062265377401817193324124680756816T^10 + 316874613294458685885325494699025760T^9 + 1878352364777031985219759926555560760T^8 + 3544464889310281997809284624918208080T^7 + 1303911666228891105042353858020750800T^6 - 1471880942788787576791593483327263040T^5 + 252670343673375657835921804367034960T^4 + 730639334234102885410704041977318400T^3 - 1097948334966447155670068911813786880T^2 - 383111400250142557306211553242163200T + 375132589068583102936074200430223360.\nIt is a 2-neighbour of the fibration given in curve#4187 (itself a 2-neighbour of the fibration 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": "2026-10-25 16:01:15",
  "updated_at": "2026-10-25 16:01:15"
}