{
  "id": 6080,
  "curve_key": "1241329047858176608790462601:-42902808278536784463304424768600220101925",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-25861021830378679349801304",
    "49656028100164780606504382596458075444"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 187.1579403877914,
  "faltings_height": 13.490343022120243,
  "conductor": "1865148669019383984630594692507645716597728614358098766797012149359846",
  "bad_primes": [
    "2",
    "3",
    "11",
    "17",
    "23",
    "1462367",
    "371865419899",
    "14767537397857653509657412883442196847010574953"
  ],
  "discriminant": "41730467021203231434095968792416948749305693667382458904760524021371621154492",
  "regulator": "37777017932299208353.1401485267202703538103811377942561963732304415173181640074",
  "points": [
    [
      "2491465276041",
      "830486455722264564"
    ],
    [
      "3265605917590",
      "170697080699440958"
    ],
    [
      "-4806276119409",
      "-7932517178617115961"
    ],
    [
      "-1667015914856",
      "-9387982039544213982"
    ],
    [
      "3273049346646",
      "-274448020500001026"
    ],
    [
      "1295809328662",
      "-4280292282487586260"
    ],
    [
      "372576046792",
      "6330288052496344458"
    ],
    [
      "10394845251459/4",
      "192070195361295165/8"
    ],
    [
      "20211727101",
      "7009517836447341240"
    ],
    [
      "2578889011176",
      "338612174656367934"
    ],
    [
      "2067095399418",
      "2243051896872322572"
    ],
    [
      "-4083345804687",
      "9336542473208688147"
    ],
    [
      "169153916760931/49",
      "422886035315748902409/343"
    ],
    [
      "38806255531477/9",
      "115539761265396169225/27"
    ],
    [
      "20167336931016",
      "-87923824771751035986"
    ],
    [
      "-5060115703902",
      "-7138112576221904670"
    ],
    [
      "6212565747432",
      "11347805076976893630"
    ],
    [
      "4771822065873",
      "-5908266584970763428"
    ],
    [
      "-5338737666642",
      "5962879365856942422"
    ],
    [
      "-5800313971898",
      "-2124705689556846580"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 7/1 of a rank-17 fibration of X1092 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -179953294423718847382027T^8 - 2422012411772909548445296T^7 - 8684786346925804611549268T^6 - 4573475462542070744244864T^5 - 8326574805923000528641650T^4 + 35444345428350105767505072T^3 + 17731786323723333634379340T^2 - 19763869255646989140411552T - 10177374299919296571719307,\nA6 = 29433046587806298151568576053541446T^12 + 603520435264734361699466145077660112T^11 + 4382581162253179659711002005983168540T^10 + 11396517244561787350481309183444475360T^9 - 10659015250764560811790628626096653654T^8 - 80586644259246975736139435374429063488T^7 + 42318930188195229744508377014871751368T^6 + 137262458200367432785871414671050119040T^5 - 23161725646205355538786516956002840214T^4 - 116199202372193956963687253523228736080T^3 - 14693145837274105663456587481964821764T^2 + 37328369442971825728801730381692902624T + 12558368421895894107424021098828811206.\nIt is a 2-neighbour of the fibration given in curve#728: 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": "2026-10-29 00:41:03",
  "updated_at": "2026-10-29 00:41:03"
}