{
  "id": 4219,
  "curve_key": "95668385792590472765886281557842943807713841:-928406718890037677484787827929231607177621125262657534131048616361",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1993091370678968182622630865788394662660705",
    "1074544813530136200792412413600165186884805897963334224207566025"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 303.8083854079121,
  "faltings_height": 23.172017994928616,
  "conductor": "734643589999131929201004058305667710915325726599822550780582597629519219231224255521423999590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "31",
    "61",
    "97",
    "1804377679093114436633352127",
    "189040081051771170380233813120652878800344527779412927"
  ],
  "discriminant": "7905167260073296847962111912157683330393727730919115999472489596859694727963723173690587085168657407408922402173672038400000000",
  "regulator": "21397380928977207070892410.21251332988081709401098785835724218548322895475468470199779126",
  "points": [
    [
      "-615540265478228695190",
      "45476926738379105426501930187595"
    ],
    [
      "884094723459331240810",
      "1868808117971729687160764427595"
    ],
    [
      "1243738065294975958122",
      "22794301657523004785716711489611"
    ],
    [
      "-1476975046347220786490",
      "-28219426086718210404292878774605"
    ],
    [
      "17844255438221190828810",
      "-2376432550143095409906944665632405"
    ],
    [
      "1603693399204012504810",
      "44751180680604391111082662587595"
    ],
    [
      "-874788002862411910550",
      "-46353448319712522602910107025845"
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    [
      "884958435665961621610",
      "1948912235872318329793087486795"
    ],
    [
      "874928224092729732340",
      "699963115366265036561991818395"
    ],
    [
      "433989584204248668010",
      "17067645906482394528840916683595"
    ],
    [
      "734373801597633177010",
      "2630988788333666568031660769395"
    ],
    [
      "697404222704450287210",
      "-4873685996940537032175211220405"
    ],
    [
      "519368699042614354810",
      "13397464364429295174860879037595"
    ],
    [
      "683341248522050325930",
      "-5627882334237520480640440236405"
    ],
    [
      "2566010740165475610730",
      "113383952118687306401891879019595"
    ],
    [
      "2942855294239065738611994010/151321",
      "159234774843691012994318467982467089865055/58863869"
    ],
    [
      "1997580829239504904810",
      "-71163113701695495060940954292405"
    ],
    [
      "-1628743254481649911190",
      "203369776477379903641191243595"
    ],
    [
      "1185982901485175037802",
      "-19465950574345146765194175242933"
    ],
    [
      "-7833256448529655190",
      "33017521541060448096556407627595"
    ],
    [
      "900709487408168953510",
      "3173944005460458114568170785395"
    ],
    [
      "753405630304596664810",
      "765956919215445987602538267595"
    ],
    [
      "2161948743504920128810",
      "82888963184294589780231384003595"
    ],
    [
      "49081030975868767088039290/56169",
      "5222954897192390864553297979249446535/13312053"
    ],
    [
      "-424368597200876779190",
      "-42940961923552783648415794172405"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 499/1004 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -10490924381115083744475T^8 - 198606534222460688122680T^7 - 1065417976804438457255016T^6 + 1639325103621379811930736T^5 - 2065857830370934339051440T^4 + 1624515338975555277541440T^3 + 627292956712495652706816T^2 - 579571543143419272734816T - 175069545700351062329712,\nA6 = 377475523351270352670804404613750T^12 + 8093831427752091624508772362041000T^11 + 59608190005431403688311326659353800T^10 + 258877237945365511005499173975059280T^9 + 1166329210851912140109373033476192096T^8 - 3290737074386209591354797503931856128T^7 + 1076110014915408676877000781319873728T^6 + 1655411108858774108267005356846449184T^5 - 323687792595432052178005121163318384T^4 - 745457216313233319000016951349121600T^3 + 632802115601259765911745996693312T^2 + 143229663791151165669809219876399232T + 28115415195462890182082065162444416.\nIt is a 2-neighbour of another fibration built here (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": "2026-10-14 07:58:43",
  "updated_at": "2026-10-14 07:58:43"
}