{
  "id": 6075,
  "curve_key": "5382757449957213903590041:-11135417419464369505335232546453405885",
  "ainvs": [
    "1",
    "0",
    "1",
    "-112140780207441956324793",
    "12888214605852193714305898987960672"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 170.83572903568574,
  "faltings_height": 12.214162254606793,
  "conductor": "146521621541575697378173499300203133993673935040333409356786",
  "bad_primes": [
    "2",
    "3",
    "31",
    "47",
    "71",
    "197311",
    "36340702200479",
    "32922132085592714755874703787782917"
  ],
  "discriminant": "18497055462881414561233166308409708002043553102198300251320773515944332",
  "regulator": "177091187555831386.2362428849646958081859478183409537304523533637643590198742",
  "points": [
    [
      "-50924460850",
      "135892854325973991"
    ],
    [
      "-31370715637",
      "-127965911529368760"
    ],
    [
      "244564707269",
      "9508629903273498"
    ],
    [
      "461461988459",
      "243734317925589912"
    ],
    [
      "-1205859433861/49",
      "42886013503120858020/343"
    ],
    [
      "164075761238171/529",
      "1084442764496091676836/12167"
    ],
    [
      "309383636429",
      "88359042296397018"
    ],
    [
      "391757533163",
      "170530742767886040"
    ],
    [
      "102173420225",
      "-49970417759954484"
    ],
    [
      "-359828807452",
      "-81548736883461825"
    ],
    [
      "4790938984757/49",
      "-18338284381536776490/343"
    ],
    [
      "50506919522",
      "85750600496842086"
    ],
    [
      "4885504220522",
      "10773714594273923991"
    ],
    [
      "-182070982951",
      "-165136737739596558"
    ],
    [
      "11917406654603/49",
      "-297281216550939972/343"
    ],
    [
      "-45620984665231/121",
      "-52776979568365855818/1331"
    ],
    [
      "1075350130697",
      "-1065743819011754574"
    ],
    [
      "1250807651534",
      "-1352603664693251097"
    ],
    [
      "-173843440027",
      "-164709769622274150"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 20/1 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": "2026-10-28 22:59:55",
  "updated_at": "2026-10-28 22:59:55"
}