{
  "id": 5559,
  "curve_key": "48109966170426192781525921:-392050499631297892608957608644804545265",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1002290961883879016281790",
    "453762152350955703309840242309759556"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 177.7289080097377,
  "faltings_height": 12.802710970529963,
  "conductor": "46605166195982783401379905313170285132169457798165042774174",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "29",
    "4057",
    "77863",
    "1214273",
    "104082677",
    "162614740016903",
    "453369790981816967"
  ],
  "discriminant": "-24507966107030207910171068371356404441158502463462276337285260752311999488",
  "regulator": "121491854808483632.8176114377632217092394417778325123593745519338920552787450",
  "points": [
    [
      "-121403013524",
      "757399541797602418"
    ],
    [
      "16429925356",
      "661285876857800818"
    ],
    [
      "813181575232",
      "-420054609453830546"
    ],
    [
      "-1140038803514",
      "-338699074238302154"
    ],
    [
      "-887564883101/4",
      "-6524962841630892217/8"
    ],
    [
      "-148235957396",
      "774002910488451106"
    ],
    [
      "-233455778036",
      "821601635211242626"
    ],
    [
      "2468183605732",
      "-3607760449230847286"
    ],
    [
      "-102905195442452/289",
      "4298539916223989443202/4913"
    ],
    [
      "407716656688",
      "335986913757823294"
    ],
    [
      "8501461533136",
      "-24624680205456963554"
    ],
    [
      "-1167816940784",
      "-177735088218342434"
    ],
    [
      "2336605850956",
      "-3296822827412771774"
    ],
    [
      "712406010160",
      "318254259779009086"
    ],
    [
      "3966688816948",
      "-7674135658996020422"
    ],
    [
      "-1174630191956",
      "-101882772345004430"
    ],
    [
      "231363584218",
      "-483997232709079466"
    ],
    [
      "-1090375552604",
      "500268143964638218"
    ],
    [
      "450962989048",
      "-305740790247469226"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 19/5 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -113946597679617331526187T^8 - 628704898397157619416528T^7 - 910139814353468861642484T^6 + 13879376823678260295456T^5 - 533762798296920925528530T^4 + 1639003787601085356814224T^3 + 806892413125232101174956T^2 - 592355532948433669282752T - 295458143973808062849867,\nA6 = 15882493844523546552540807840095910T^12 + 145809795943145321517489625166050800T^11 + 489200782557326126999832807296770620T^10 + 474439873253302462549441686771960000T^9 - 939321256931213164482716468158448790T^8 - 1775504390224299025107326496664527360T^7 + 1396226578858524162480471413923945800T^6 + 1631143206019716771050709031938957120T^5 - 432541045559235732878122118765459190T^4 - 878384718510400823408137143448720560T^3 - 116676491482650081744926274060252324T^2 + 185829851435689714140802850197329216T + 61035568685910358648726719363207174.\nIt is a 2-neighbour of the fibration given in curve#3900: 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": "2026-10-23 04:06:36",
  "updated_at": "2026-10-23 04:06:36"
}