{
  "id": 4190,
  "curve_key": "200113341594596916684704103910313213936721:-89272378481020298773474402669701458654948838502435420849559769",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-4169027949887435764264668831464858623682",
    "103324512130810530988859852669996695347256952511610914713281"
  ],
  "rank_lower_bound": 26,
  "torsion": [],
  "naive_height": 285.29910762231145,
  "faltings_height": 21.586734346212527,
  "conductor": "34095396583563628150779759927351282847188652317457175606079208548621263015281621315321866798319264290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "219108004521326573811321636960036519807137409661700248095104482672201420315414313445934495201589"
  ],
  "discriminant": "25492558413978830582805881090534313419836148855039646459275152906235514735546453673290015135449774521166822252544000000",
  "regulator": "10944798641777078125716155629.6778311094694256496234578874497567105836202929354092421571516",
  "points": [
    [
      "38898666444758816641",
      "3563687595412192784915023679"
    ],
    [
      "-10488295476422635759",
      "-381964332198825882629558826721"
    ],
    [
      "44748894234164403841",
      "-79832012934379391031687510721"
    ],
    [
      "39082673948184958225",
      "-9208342323815267821459522273"
    ],
    [
      "-26317644147354070559",
      "-441379000107090317560372583521"
    ],
    [
      "5309563614594197031889/529",
      "-3041535569141708336932952320403207/12167"
    ],
    [
      "33032343783405200641",
      "40675771489826702441463679679"
    ],
    [
      "-54773439009567388799",
      "-409083235341753093423590996161"
    ],
    [
      "30584674567866615841",
      "-66526206968858669200578201121"
    ],
    [
      "39574729690036550853601/625",
      "4770486496761725377263249430436951/15625"
    ],
    [
      "-17224341916186487039",
      "-412338686596758624774204490561"
    ],
    [
      "39856756869875559041",
      "-21805297908414229733326729921"
    ],
    [
      "-5109897596476104389",
      "-352837630108427477051290413001"
    ],
    [
      "44076213462497314561",
      "72089952358653091235755314239"
    ],
    [
      "-13017472925119427519",
      "-394193924233001726347731631681"
    ],
    [
      "-73503477045242835275",
      "-112431459428540213055082712473"
    ],
    [
      "29826227195300877601",
      "-74240576674138569910612457761"
    ],
    [
      "39933943847335728961",
      "-22852524406785289975830086401"
    ],
    [
      "40937124626534006641",
      "-35509166094292035386652346321"
    ],
    [
      "520237735315530503041",
      "11778598300158063755601678722879"
    ],
    [
      "-12053907688218379199",
      "389648812775922685279675261439"
    ],
    [
      "41231632789549386241",
      "39043803693929523743456825279"
    ],
    [
      "18244399543114976561",
      "-182581206441222818952791849761"
    ],
    [
      "41314663304900466641",
      "-40032272917678252234676926321"
    ],
    [
      "114073442349056698369",
      "-1054589189272992782788084077121"
    ],
    [
      "86125544733623322463369/9",
      "-25274822382685945185277073103371867/27"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -373/1268 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -73932522356183031905227T^8 + 649309903876882877687472T^7 - 1685916835628140824312084T^6 + 645581139407117375333216T^5 - 406054368862523371209330T^4 - 858600221311968331297296T^3 + 1074013049265607843957676T^2 + 189439686366819237655008T - 279637802575984309948587,\nA6 = 7677120880090165783883135437481350T^12 - 104661205483741457154365858257793680T^11 + 560585458424820914639770163531974620T^10 - 1380712030244078852090340039520473600T^9 + 959024595422485011830600330788665450T^8 + 2176075475403505129770137846307997920T^7 - 1812178037587130500705886817575824920T^6 - 1469296539009918506803974573439080480T^5 + 1256479376113039680818470745801469450T^4 + 491406111407235947158204600615297520T^3 - 440604154329209614719459225390266084T^2 - 63212663150279697924996150457217184T + 62214320185228162206822083588855334.\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": "2026-10-12 02:25:24",
  "updated_at": "2026-10-12 02:25:24"
}