{
  "id": 6155,
  "curve_key": "1816169587643734709798461813806016:-67543846397269557152629549425463670004891818136064",
  "ainvs": [
    "0",
    "1",
    "0",
    "-37836866409244473120801287787625",
    "78175748144987900758810212457240059275602934375"
  ],
  "rank_lower_bound": 23,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 229.74611318966654,
  "faltings_height": 17.131487863180826,
  "conductor": "65469003729321126992574688995255164007952398763890089561456239252508767987094839680",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "29",
    "79",
    "113185621",
    "18785385693544260856406235549200074583950687043565875801172935607077"
  ],
  "discriminant": "826628063331304012319742840689079270569746741572582204993012072485229803904421328669265331200000",
  "regulator": "360347245077785792023793.802833179027553557155198234750118375784768695165882187840893",
  "points": [
    [
      "605722620133355",
      "235540531225904565095820"
    ],
    [
      "-6015326015826505",
      "-296845740651651251763180"
    ],
    [
      "213516524122904615",
      "-98620837298937137312892540"
    ],
    [
      "4627894848720203",
      "-46778561243115659982444"
    ],
    [
      "2359894295463485",
      "-45024802395402416780340"
    ],
    [
      "2364071940861425",
      "44035038788727422641800"
    ],
    [
      "-482460934745977",
      "-310351826717231631385764"
    ],
    [
      "2261260695508955",
      "64646991078495721407780"
    ],
    [
      "96667771603300073/16",
      "-16946625407125323004865091/64"
    ],
    [
      "25939783393841765/4",
      "2598793818950499860521305/8"
    ],
    [
      "823648574441975",
      "-218106001215811558809900"
    ],
    [
      "12909913713821275",
      "-1319601112241203833995100"
    ],
    [
      "20734368029062295",
      "-2864899247091672173443380"
    ],
    [
      "7483265229495425",
      "462698330799452650840800"
    ],
    [
      "5684797563351083",
      "216323806396745224988724"
    ],
    [
      "564539977929512075/289",
      "-531836908070858312572773900/4913"
    ],
    [
      "11610515845059863",
      "-1097276217257071420890804"
    ],
    [
      "2454724082966855",
      "-9382910280066652769820"
    ],
    [
      "209487258680966686715/37249",
      "-1495308489172645952134429179780/7189057"
    ],
    [
      "285580488197865905/256",
      "-791653297377161496214291305/4096"
    ],
    [
      "1935211840771325",
      "-110457464329889892047700"
    ],
    [
      "22194977805110795",
      "3189359120901440597137620"
    ],
    [
      "-6808373208586255",
      "-142085514264191222386680"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 113/7 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 18:22:58",
  "updated_at": "2026-10-29 18:22:58"
}