{
  "id": 5859,
  "curve_key": "75452984753417323508667156561:-21530675811461867080833864090965035536756441",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1571937182362860906430565762",
    "24919763670673850253779229709399102475649"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 199.5561052118516,
  "faltings_height": 14.55456302762506,
  "conductor": "240750722295132188495050670286129904011703471421749110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "23",
    "29",
    "37",
    "47",
    "59",
    "67",
    "3343",
    "7547",
    "54239602231351",
    "3523386339502485821"
  ],
  "discriminant": "-19678600299203855218749700882890645386627959479695628258490429977990803765760000000",
  "regulator": "8747590570371059.5445479404871500784425231236854866007940064103710625979126",
  "points": [
    [
      "25298997607337",
      "-36656265416181615129"
    ],
    [
      "3878566915457",
      "137409046144178668671"
    ],
    [
      "41880234408257",
      "-180395896966375800129"
    ],
    [
      "-31066696248543",
      "209215118610206135871"
    ],
    [
      "19101704317457",
      "43160398581605705871"
    ],
    [
      "322749720083057",
      "-5756524355732835160929"
    ],
    [
      "24067967320257",
      "-32065747446212112129"
    ],
    [
      "127269419043407",
      "1373428961109832871121"
    ],
    [
      "-44581741807743",
      "-79948936878094048129"
    ],
    [
      "3921434299374377/361",
      "-655243240101040334828811/6859"
    ],
    [
      "10871249300057",
      "-95475924238963117929"
    ],
    [
      "299429692058953/9",
      "2624377406624745734117/27"
    ],
    [
      "8640142182257",
      "109466918992644965871"
    ],
    [
      "-41375726220111",
      "138298978964104319007"
    ],
    [
      "40424081060993",
      "-165628804905763907457"
    ],
    [
      "10331005910657",
      "-98907519216353040129"
    ],
    [
      "25701673004417",
      "-38681487098386723329"
    ],
    [
      "9700681117757",
      "102877434853590302871"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 10/3 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -52648197173377472411667T^8 - 502136288453868619765932T^7 - 1375723089516896204761224T^6 - 113586999512798824277616T^5 + 115484330308006964556720T^4 + 1146633583580186797214496T^3 + 875307711060207742486176T^2 - 552420246310353167485248T - 379684178449627628010672,\nA6 = 4604058775563334978457275228090926T^12 + 65897015586211952847350301356878644T^11 + 353596781702159377755551694850071564T^10 + 792468362119369014579444750140997960T^9 + 225448975378970803493231159228247540T^8 - 2087772451361914308664322072224378224T^7 - 550444434966430640467599977153927136T^6 + 2077986353393758716550697478306369984T^5 + 497054571856074095600647080235134720T^4 - 1050047839109210694723463620193948800T^3 - 326801521813959825897823057885147776T^2 + 226384397181047822018105284978542336T + 93697525934370302137180629038948736.\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": "2026-10-25 15:13:46",
  "updated_at": "2026-10-25 15:13:46"
}