{
  "id": 4640,
  "curve_key": "39874605937436380184130239147646937921:-251559550386920988848657601573805196916816232400683456225",
  "ainvs": [
    "1",
    "0",
    "0",
    "-830720957029924587169379982242644540",
    "291156887021899292579682514661632669722940826017607696"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 259.73640907918525,
  "faltings_height": 19.415459454629765,
  "conductor": "29059786682435112110130040375597681105691029237985002427121492680864975748630737397754638",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "23",
    "379",
    "136999",
    "73127333383811939",
    "4082787399006094054822683523",
    "149272165591023108979543678416653"
  ],
  "discriminant": "68163181528330024722196160644746065547503759067289529338336187640174381096708114484338193528317564108275712",
  "regulator": "12112408874014264920740345.917576481388700879346335118153721439379592750648907006914422",
  "points": [
    [
      "541443564844677752",
      "9928749675785360147451524"
    ],
    [
      "-765018799279764448",
      "-692057731941087470143141156"
    ],
    [
      "25453279823258171264/25",
      "88455473177341094514816870028/125"
    ],
    [
      "5199995129446287752",
      "-11686702568233738491529377676"
    ],
    [
      "639522460907662136",
      "146457549682523800041182276"
    ],
    [
      "-821861528782742248",
      "647118904349879314688821124"
    ],
    [
      "-143279751022245256",
      "-638154351502053334270646524"
    ],
    [
      "546602846743772816",
      "-19837675216545015210416404"
    ],
    [
      "67412927998489751120/121",
      "47380664181052243347426956356/1331"
    ],
    [
      "120679563640204656572/289",
      "642087091771463862943361793232/4913"
    ],
    [
      "10537906119091974632/49",
      "120025112383148843409028439132/343"
    ],
    [
      "3159049832488367596/9",
      "-5586771013699389255090631040/27"
    ],
    [
      "4280878840504713080",
      "8670986094792399301847675396"
    ],
    [
      "543408794439138218",
      "-14166525495467214761040826"
    ],
    [
      "469020803544754898",
      "68606950934600252896750814"
    ],
    [
      "-804187761894364630",
      "662668732345795018233552326"
    ],
    [
      "-49774381093759258408/49",
      "-101078555986167524910298871236/343"
    ],
    [
      "12109624330970752424/25",
      "6147667979027567627849931508/125"
    ],
    [
      "-665583167105333896",
      "-741091624027873951728718204"
    ],
    [
      "498312758088089204",
      "30608326452837316131217496"
    ],
    [
      "708691750410445880",
      "-241594651204758533680114876"
    ],
    [
      "19623521958056152952",
      "-86837011808883967936473461116"
    ],
    [
      "-791696598225603448",
      "672765542854673726394156404"
    ],
    [
      "426445019936363498",
      "-120213903071386712953274362"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 653/80 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -5295620710700377671600T^8 - 94037966474871021583680T^7 - 590731768793188987891776T^6 - 316565515830122546981184T^5 - 762681779746720476850440T^4 + 1987613918828860347667800T^3 + 1569564836467837283726676T^2 - 3214905333565214256563376T - 2212765344524109268510452,\nA6 = 149936157543712438778032606320000T^12 + 4003077612324280274862537287520000T^11 + 40256463697048454693428799356032000T^10 + 181374780086403872414844938171109120T^9 + 402662249843699366956864710038784096T^8 - 758031533540911762791576885234671328T^7 - 399143032260021392125750735091011632T^6 + 2151897782383821345209559268211414304T^5 + 557784900106071266465324558195950116T^4 - 3137783098558594528537444090769421600T^3 - 420721733859426366310009677118678488T^2 + 2767709433062054442394845582008506272T + 1268413949854822572813035476740281796.\nIt is a 2-neighbour of another fibration built here: 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": "2026-10-19 11:22:48",
  "updated_at": "2026-10-19 11:22:48"
}