{
  "id": 6077,
  "curve_key": "2522641414367523946192995121:-128289070150578810181233696736723137003305",
  "ainvs": [
    "1",
    "1",
    "1",
    "-52555029465990082212354065",
    "148482720081666539780817060540655890671"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 189.31020940995094,
  "faltings_height": 13.650164633251418,
  "conductor": "150170677834113186036706699512393314357381407912637152730354322",
  "bad_primes": [
    "2",
    "3",
    "7",
    "11",
    "13",
    "23",
    "41",
    "3923",
    "8494063",
    "3505594263855553",
    "226982661966361791718146479497"
  ],
  "discriminant": "-234202917606526280400426709922208131264849091986736703773749960846087388069888",
  "regulator": "1154999001869866158.59753282087037648704786686692143285212716628033807282166623",
  "points": [
    [
      "8043288044223",
      "15688330435366697392"
    ],
    [
      "4568432728753",
      "-1932470439567438256"
    ],
    [
      "4431798031071",
      "-1616681677819845584"
    ],
    [
      "6323411373711",
      "-8306663926227318368"
    ],
    [
      "5002894323495",
      "3282170778284127832"
    ],
    [
      "3732589652223",
      "-2078376640666225616"
    ],
    [
      "5793654193759",
      "6202362367862961584"
    ],
    [
      "-2451057353313",
      "-16204101279689983376"
    ],
    [
      "31676380475239/9",
      "-71991450187469787776/27"
    ],
    [
      "3273001085331",
      "3395906768745792676"
    ],
    [
      "-2101993839787",
      "-15800811102677253278"
    ],
    [
      "-7650982935073",
      "-10134621725090396432"
    ],
    [
      "-8374405218657",
      "1138970758569693424"
    ],
    [
      "6639741085409",
      "-9604774566735698066"
    ],
    [
      "9798700793159",
      "23965166356392017656"
    ],
    [
      "4997918208267",
      "3265102705543857784"
    ],
    [
      "13523357553599",
      "43714179909778330544"
    ],
    [
      "-2990974633732521/841",
      "-415622351490051044374864/24389"
    ],
    [
      "7128130324383",
      "11663857163646297712"
    ],
    [
      "1720561490079",
      "7946821978832108656"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -8/7 of a rank-17 fibration of X1092 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -906367358304324068310252T^8 - 7092594360115144947597168T^7 - 14978709734524328311342164T^6 - 1517328752523744361318344T^5 + 16445626070233551241776120T^4 + 31656989538932514546432384T^3 + 3170607514080799194804096T^2 - 20821372597943495849518272T - 9056516433253722389307312,\nA6 = 337611854459273162912229049690787604T^12 + 4055186600519069764816176019317421104T^11 + 16630161922875538866982567114625369976T^10 + 19534087387711880882915097539682432720T^9 - 33164430238644337752259032972461221020T^8 - 63692412215480873844213128903390312928T^7 + 64651978990562040281146555673727779952T^6 + 88488568678012147892356636187545056288T^5 - 63693457134721094796995914012618480800T^4 - 87430903964558167112366660980511247360T^3 + 10168572636345523801418545758328698624T^2 + 36650566934024985757498560520582105344T + 10594259331195802631445150476027999616.\nIt is a 2-neighbour of the fibration given in curve#728: 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 00:09:59",
  "updated_at": "2026-10-29 00:09:59"
}