{
  "id": 4270,
  "curve_key": "143815268720921709597580046986496693056:-1722703414678139701804111519248732019612034999522801528704",
  "ainvs": [
    "0",
    "1",
    "0",
    "-2996151431685868949949584312218681105",
    "1993869692914513542756041558938890928271475367597015475"
  ],
  "rank_lower_bound": 24,
  "torsion": [],
  "naive_height": 263.58477890307785,
  "faltings_height": 19.74375344022916,
  "conductor": "47796897503943459568876405605909069872285309750145030520646927454057927262243899244920",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "31",
    "53",
    "67",
    "79",
    "89",
    "5569",
    "3092311524580964153545812774889",
    "159803738064166758505658320052397855293"
  ],
  "discriminant": "3935137512814823813464325117725198949797434070734424987458290504133331623301831232500241882964715715028000000",
  "regulator": "980661499815342142095122.23957893768277760215347500834029103093363578877909447732761159",
  "points": [
    [
      "939343313808670175",
      "91100770856231263657557390"
    ],
    [
      "939599982728767655",
      "-90608745946913680951564110"
    ],
    [
      "968486154716814715",
      "-23346268840323494142651750"
    ],
    [
      "965763749955863195",
      "-32599602933293297174431770"
    ],
    [
      "18668115606670213685/4",
      "-75752879012408881689676728975/8"
    ],
    [
      "1168213962181177115",
      "-296670232851540887441701350"
    ],
    [
      "968781220205709590",
      "-22170341752648786040095125"
    ],
    [
      "1039535808855597215",
      "51200153073745624577220750"
    ],
    [
      "1027018581538934015",
      "5654997469089131362110450"
    ],
    [
      "1041154495888081265",
      "-55022066257507238958309450"
    ],
    [
      "1636872793335601985",
      "1214623484340856484947057830"
    ],
    [
      "1649852092806030323",
      "-1241603825405946012783317466"
    ],
    [
      "-17594160670405461215/9",
      "-16645597688722639046469246550/27"
    ],
    [
      "1090800037168409555",
      "153460958733116780484844710"
    ],
    [
      "970758036138104135",
      "-12082810188358249392485070"
    ],
    [
      "7034835416240937595/9",
      "-9716240512574135200265597630/27"
    ],
    [
      "1048391578971882215",
      "71014470400950541230300750"
    ],
    [
      "132453241799791163",
      "1264651518863058607865112474"
    ],
    [
      "22406262183669079334/25",
      "-21100245304423219219725025473/125"
    ],
    [
      "8391618128543737715",
      "23828193517964433172900364250"
    ],
    [
      "12626761404426519590",
      "-44466967432355064773074333875"
    ],
    [
      "1390002026870384945",
      "-717526221420857541243466230"
    ],
    [
      "-866908718138165815",
      "-1984880588838458550216380370"
    ],
    [
      "958661139518021465",
      "-51139279638313663403153250"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 79/121 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -25598589065575488253872T^8 - 219912513106757586234048T^7 - 324549648424331055742464T^6 + 1523547434916270832355136T^5 - 2849165156820063127691880T^4 + 3746564993881929295112904T^3 - 973581348748449447744444T^2 - 862126587120769476566112T - 118556909623229874930432,\nA6 = 1625048868702522016795790220948864T^12 + 18521876511799709835187838396715264T^11 + 69457772033476867393403462775818496T^10 + 74100738882710387630246485913752320T^9 - 324420440712638126863027033199077920T^8 - 1791949805594601002560679464033967520T^7 + 4689003940396889037978292829416265040T^6 - 2864400878761409044683373393741992480T^5 - 91393345783003551423720760724759820T^4 - 338626380479684457921000808774737600T^3 + 374448354510478802333765563563322320T^2 + 177989462843015858245005305484080640T + 17806843321561611911434592141844480.\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": "2026-10-16 02:51:54",
  "updated_at": "2026-10-16 02:51:54"
}