{
  "id": 6165,
  "curve_key": "943324339496905054904061329789761:-6741060773700013205708917926099578642723264951009",
  "ainvs": [
    "1",
    "1",
    "1",
    "-19652590406185521977167944370620",
    "7802153673263895984694874651981095905397328157"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 227.7808888729286,
  "faltings_height": 17.04660764689542,
  "conductor": "435115839382894306387158286060774650624153704748902133729273287393899976638480289172690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "6963703",
    "54372998219597825543077138908347",
    "3482310011988839634083087533398258426977752873"
  ],
  "discriminant": "459482326388336387544839150080178031059106312214840653218112591487958375330235185366360640000000",
  "regulator": "2245649124894785075498013.19979385712290550045513899907524907069895561231664510985239",
  "points": [
    [
      "-86955941041203",
      "97521308806595417816601"
    ],
    [
      "4349386440176247",
      "-67849048604862448366299"
    ],
    [
      "-854639642230883",
      "-154834750486332054072439"
    ],
    [
      "112606844561197",
      "-74770083437981974888999"
    ],
    [
      "392164979933647",
      "-12466287751760114919349"
    ],
    [
      "31454403728943797",
      "5523584356167484260176601"
    ],
    [
      "-27924648872453",
      "91383387916469585454101"
    ],
    [
      "-349720619159953",
      "120964033460528478055851"
    ],
    [
      "352040241624247",
      "-30451275455271691502299"
    ],
    [
      "-339262680641703",
      "120126996820099014643101"
    ],
    [
      "18326290752130697",
      "-2408854833151639367684499"
    ],
    [
      "13679238940622797",
      "1516130083238431306936601"
    ],
    [
      "32200029841858797",
      "5723751287014832554924601"
    ],
    [
      "8381096797460797",
      "657117534178990870000601"
    ],
    [
      "-4048155772535735",
      "-144980977681154765755219"
    ],
    [
      "-130801937883871287/49",
      "69656365423473241168520463/343"
    ],
    [
      "71802636578892205",
      "19203741902460347865787001"
    ],
    [
      "-3419997766371203",
      "-187115896444120892365399"
    ],
    [
      "-449655341359705200723/108241",
      "-4744751464129092999523462724511/35611289"
    ],
    [
      "-1978462312691923",
      "-197331552861773086917159"
    ],
    [
      "-16397744211203",
      "-90135494746686501853399"
    ],
    [
      "-378831283835283",
      "-123259086533810995575079"
    ],
    [
      "4320365268782797",
      "-59479450260772575799399"
    ]
  ],
  "submitter": "apkorte",
  "history": [
    {
      "kind": "primes_recorded",
      "user": "Daniel Błażewicz",
      "at": "2026-10-30 03:52:55"
    }
  ],
  "commentary": "Specialization at T = 48/85 of a rank-17 fibration of X1008 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -2350252713284250372T^8 - 50405464050571118556T^7 - 952448555730502901313T^6 - 695049490520215525224T^5 - 2931749924460790132683T^4 - 2386411337210880522384T^3 + 2409436881372804430248T^2 + 4544024515422355802304T - 2684309556378273707952,\nA6 = 1416965056476304965893460864T^12 + 45023054173800546171881279808T^11 + 917608982150765091196202404680T^10 + 4283108867178449968605589545480T^9 + 53149163760305922465025229930778T^8 + 64588783908002903981500312561392T^7 - 30251100417436562854623526202130T^6 - 127076856645436090494117187739472T^5 + 56548211197412673092440132446600T^4 + 156704525825325938035598980257408T^3 - 11739117611564936890190411272416T^2 - 136493880790478548113078471588096T + 53534237645294085780370164274560.\nIt is a 2-neighbour of the fibration given in curve#3589: 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": "2026-10-30 03:52:31",
  "updated_at": "2026-10-30 03:52:55"
}