{
  "id": 5952,
  "curve_key": "5082361146027886378093801601616:-11432462760026619034319233401093806000555849664",
  "ainvs": [
    "0",
    "0",
    "0",
    "-105882523875580966210287533367",
    "13232017083364142400832446066080793982124826"
  ],
  "rank_lower_bound": 21,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 212.10998620786305,
  "faltings_height": 15.478980234599243,
  "conductor": "26172162301409998012024965666090143891410658045555762405604832730760",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "31",
    "53",
    "542401",
    "4541527999",
    "1348413888248531307227",
    "146390351567191714643209"
  ],
  "discriminant": "334600841140686314792620251528573792191317189552014690281584086409813873788619380000000",
  "regulator": "26813795095583843076.726699004059911719676079345381726189082696155463670754281095",
  "points": [
    [
      "160063553903517",
      "620457004456249047750"
    ],
    [
      "293553520136517",
      "2728811721418336505250"
    ],
    [
      "210662075506755",
      "524837003560628423796"
    ],
    [
      "77982611326767",
      "-2334364168325523340500"
    ],
    [
      "808376361587713/64",
      "1765965316490543643941375/512"
    ],
    [
      "-191437575671403",
      "-5146459012599000126030"
    ],
    [
      "178789167934017",
      "-128319096713133777750"
    ],
    [
      "101795714442777",
      "1873092234589577109810"
    ],
    [
      "283909577520417",
      "2460769408521849256650"
    ],
    [
      "1519387618838653/9",
      "11077064828843640271750/27"
    ],
    [
      "197934813365137",
      "-170021394911027548070"
    ],
    [
      "284198869005042",
      "-2468761063660976988150"
    ],
    [
      "1085718655048785",
      "34323494114125504126566"
    ],
    [
      "553044143790415",
      "11127766454341631648164"
    ],
    [
      "230513836570467",
      "-1036030143275213883300"
    ],
    [
      "232601543578317",
      "-1090014268319589172950"
    ],
    [
      "165568826965117",
      "-489812310833112981350"
    ],
    [
      "232693488378927",
      "-1092394277729718867540"
    ],
    [
      "313336417996242",
      "3289140501582650065650"
    ],
    [
      "344346435085917",
      "-4195526495600893465350"
    ],
    [
      "138386808956517",
      "1108830758187518525250"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 11/3 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -21002811307157006823600T^8 - 124178507370130867554240T^7 + 49310208421370688028896T^6 + 684186462515449967548320T^5 - 347903063343023392990800T^4 + 865038291302878093532160T^3 - 4730559749562608875657216T^2 - 1057592985482409016246100T - 70547080864013046411667,\nA6 = 1113553877083860568742523460080000T^12 + 10884874496532731100952305583392000T^11 + 16025818242069165685904530244956800T^10 - 117712825348875017206735076768415360T^9 - 198718041681783370325910358312379136T^8 + 915547425460491331931148273660243840T^7 + 681145249962056049111823046340920640T^6 - 4213611997840624018803050780171853840T^5 + 2248778903441618677754791957860591444T^4 + 3103145171532247807286164719967775160T^3 + 1312278519504892012590363424552447828T^2 + 173499531556630156585519537608740300T + 7471605906530089270988904804006574.\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": "2026-10-26 08:42:03",
  "updated_at": "2026-10-26 08:42:03"
}