{
  "id": 5951,
  "curve_key": "3255793989803761601113684641:-507948305149436719061495498277715874104689",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-67829041454245033356535097",
    "587903130960013159877835202783473247321"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 192.0623966153027,
  "faltings_height": 14.057660178032734,
  "conductor": "440297493976087960023517249003388483860934280796363033238162130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "59",
    "61",
    "101",
    "131",
    "757",
    "810437274950053",
    "1407236009254311962801458292956547"
  ],
  "discriminant": "-129339948580540223883805132685641265847288132727977394277936725059028342291200000",
  "regulator": "3104291246236475914.46050056286455979131184120754876379543525224586258595308779",
  "points": [
    [
      "3421672812631",
      "19896599965867717004"
    ],
    [
      "981901286911",
      "22852754014549406444"
    ],
    [
      "-1353619908521",
      "26023790790491771276"
    ],
    [
      "13314543554311",
      "45223368656385969644"
    ],
    [
      "4216011643831",
      "19413232372419989564"
    ],
    [
      "-10920557628089",
      "5124837497109141644"
    ],
    [
      "54951078551311",
      "-403475004119509136956"
    ],
    [
      "4321105097791",
      "-19377570875782608916"
    ],
    [
      "1400551558111",
      "-22263250815783674956"
    ],
    [
      "-6826266231289",
      "-27070875444965179156"
    ],
    [
      "16587918710911",
      "63459241716863505644"
    ],
    [
      "4884727022881",
      "19316547252292530254"
    ],
    [
      "11946491172811",
      "-38504177103395124856"
    ],
    [
      "-3215687435602121/529",
      "338845955679819447332788/12167"
    ],
    [
      "36535843640911",
      "216518423620702560644"
    ],
    [
      "13236756614171",
      "-44825240431543227796"
    ],
    [
      "5533251500311",
      "19544787828678357644"
    ],
    [
      "18784476912571",
      "77084335415598678104"
    ],
    [
      "-767404417781/4",
      "-196107585385480684823/8"
    ],
    [
      "4044366117679",
      "-19486688120987261524"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 8/11 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -48409603383664787003467T^8 - 394068766077940965499368T^7 - 868178038487744679634824T^6 + 75232746619435737072176T^5 - 1595443198591218244734480T^4 + 2109751284798891015753984T^3 + 698088862800109333591616T^2 - 451094270783465286539232T - 253592240870068502573232,\nA6 = 4040236832859543331678148357555974T^12 + 49819909994079550561071236517492344T^11 + 234267578460325937004132088864988136T^10 + 398279879863645004081067873151110480T^9 - 481849875819898361648289850645703040T^8 - 2228123003432291609437160968553906112T^7 + 1566656402007985551644615301279128448T^6 + 1326858671203210206487814863820521632T^5 - 86078958551730838909970610055003440T^4 - 798762607809093749675638617207229120T^3 - 133072535405990991623348292517512896T^2 + 130627123922202571126617921344467584T + 49036442300194391139017017822237056.\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 07:22:26",
  "updated_at": "2026-10-26 07:22:26"
}