{
  "id": 6159,
  "curve_key": "3546400666570462127375674472656:-6676415805018011831392517247413416020930654400",
  "ainvs": [
    "0",
    "1",
    "0",
    "-73883347220217960986993218180",
    "7727333107659711288181154889630383989448864"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 211.03045794668097,
  "faltings_height": 15.31914133696459,
  "conductor": "3926046641084574152321158849702341670078001371260205141923329094823925574696",
  "bad_primes": [
    "2",
    "3",
    "17",
    "23",
    "16937",
    "87211",
    "97021",
    "285308551219757980245712093",
    "601908179713562561098137159667"
  ],
  "discriminant": "16436994288460819926329379071628171110063674101886421266334267681712584548658235939072",
  "regulator": "7737484678066917461957.100202739566303733762608671743997076995874938603478541358878",
  "points": [
    [
      "143624319731756",
      "-280289534426136311256"
    ],
    [
      "160530776191934",
      "-60671402062327276902"
    ],
    [
      "638084652022949/4",
      "213301382364506511423/8"
    ],
    [
      "178625733643214",
      "478857566957446620522"
    ],
    [
      "4081263310649774/25",
      "-16097473193154016305582/125"
    ],
    [
      "90591992953754",
      "-1333256800529044815582"
    ],
    [
      "56474680831766",
      "1932592666061439035406"
    ],
    [
      "153926704112534",
      "-42007226176994179698"
    ],
    [
      "68071572404572202",
      "17760092233624013201171346"
    ],
    [
      "1216665485006786",
      "-41458839789702140202906"
    ],
    [
      "606582943156949/4",
      "821665815014470553577/8"
    ],
    [
      "139649471340506",
      "-364696044377642017506"
    ],
    [
      "7228589094071606/49",
      "-67209635374189499736894/343"
    ],
    [
      "1884781718287265/16",
      "51938805982592717876313/64"
    ],
    [
      "4461467803348022",
      "297459669298498961968494"
    ],
    [
      "152351256719276",
      "85574055430587702456"
    ],
    [
      "130495653070124",
      "555070270903347798888"
    ],
    [
      "19463359405861859/121",
      "92596412371775011596108/1331"
    ],
    [
      "162342751806044",
      "107134856348039872992"
    ],
    [
      "115553184159419",
      "856040539460793141492"
    ],
    [
      "132088604137372",
      "-522290656036616008944"
    ],
    [
      "151905838045499",
      "96471858345707447388"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -47/26 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": "2026-10-29 19:32:44",
  "updated_at": "2026-10-29 19:32:44"
}