{
  "id": 5966,
  "curve_key": "4188906423444013490212363986763294800:-8588741701922313407776804810960913804451257835233649600",
  "ainvs": [
    "0",
    "0",
    "0",
    "-87268883821750281046090916390901975",
    "9940673266113788666408338901575131718114881753742650"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 252.98009452576906,
  "faltings_height": 18.876814609304898,
  "conductor": "2314167259789826544946546589393075654953902813678227588751359933456947430542982916600",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "113",
    "131",
    "1663",
    "25541251",
    "16390347970059334554573498893",
    "285190068998030142196440106061713"
  ],
  "discriminant": "-152781718279024499091239295278486132762610091935151062601391863096716125136679737072290785960688298720000",
  "regulator": "684350007777956656417981.62606386084524543908926817983805758377593066606672098825608070",
  "points": [
    [
      "179318780814049119",
      "7599946537097772589214028"
    ],
    [
      "183193278900883165",
      "10076009139988022124409670"
    ],
    [
      "153673281407938899",
      "12603389677440732789887268"
    ],
    [
      "160897650082059315",
      "-8040022129210241539949580"
    ],
    [
      "167546078479842655",
      "4734481865616832715820980"
    ],
    [
      "-41318906409012626",
      "116086115976245066460740932"
    ],
    [
      "133987598751982725",
      "-25557016814674915789263330"
    ],
    [
      "-574041448203354615/4",
      "1117397958089326028869625235/8"
    ],
    [
      "159449435772634705",
      "8919696112746160657372730"
    ],
    [
      "171857110695469806",
      "4321094742122587586961804"
    ],
    [
      "356665193758997925",
      "-155519454613622889943528830"
    ],
    [
      "174672656661433845",
      "5151896394146996044326930"
    ],
    [
      "156002504114722495",
      "-11095390122310394191422820"
    ],
    [
      "-126982638974824845",
      "137748914214530347631104020"
    ],
    [
      "187013395924133385",
      "12681930885593059563643170"
    ],
    [
      "-224752008071852655",
      "-134913036523838838447111930"
    ],
    [
      "116217419198615250",
      "-36989161261632967708445670"
    ],
    [
      "194788673250975795",
      "-18233956991309321728439820"
    ],
    [
      "90974719179658206",
      "52481941564233858410437704"
    ],
    [
      "97861292029406655",
      "-48349030405651203820285980"
    ],
    [
      "4653662385593971",
      "97645553541478262721931244"
    ],
    [
      "708046073926209465/4",
      "-50209979956772440696693515/8"
    ],
    [
      "429672365290883230",
      "227528119150619649768340480"
    ],
    [
      "-8518753334552855",
      "-103360907321932585810555070"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 409/34 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -96196961581357063033152T^8 - 399556103168445237840384T^7 + 121419290054525411589264T^6 + 1430959091691248074015632T^5 + 100688238281333139439320T^4 + 387367434659202151100832T^3 - 1953294802285379458973616T^2 - 733254399190976661626184T - 79743145896962463440187,\nA6 = 11484504086394253195526049377853696T^12 + 72121229539722792963703791386638848T^11 + 54055657239595166572471510008621696T^10 - 398904635104645281362553198961699200T^9 - 498516576461076920592919777700932080T^8 + 1133982302557837972386711623027647680T^7 + 1070918296969515869033113344560286480T^6 - 2589863488770145152071246194277744400T^5 + 73956315674627679114868875249120120T^4 + 1069188646911222614852645794843754400T^3 + 580961502887065292988342169113394080T^2 + 118245525237113913102523416049897560T + 8723796687794086545932578364805270.\nIt is a 2-neighbour of the fibration given in curve#4191 (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": "2026-10-27 01:58:58",
  "updated_at": "2026-10-27 01:58:58"
}