{
  "id": 5708,
  "curve_key": "57530129760060032467112896:-435649194988719757878304122691835933056",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1198544370001250676398185",
    "504223605310618723495073799186381083"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 177.94305311474898,
  "faltings_height": 12.620053364152081,
  "conductor": "472403774943229785498061552366085797586678297302100040",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "173",
    "10482979702973978760127",
    "6720456013996798144277599"
  ],
  "discriminant": "357731531567632250893870162626985569138546834027513417067437921780000000",
  "regulator": "2598311218710363.8132558696066656363372147125062757323841443634070299085172",
  "points": [
    [
      "570120419111",
      "78863071638395250"
    ],
    [
      "676697388611",
      "-55177823709029250"
    ],
    [
      "21493452002711",
      "99519046909192588050"
    ],
    [
      "682458957806",
      "-64200308552307765"
    ],
    [
      "668625950111",
      "-41977333114134750"
    ],
    [
      "480213431501",
      "-198509672424006270"
    ],
    [
      "-312495522139",
      "921003304961799750"
    ],
    [
      "1767643092851",
      "1977052237297152930"
    ],
    [
      "39488940296861",
      "-248055027694027116750"
    ],
    [
      "-72980992489",
      "768964140756499950"
    ],
    [
      "1521204688211",
      "-1483629618578219550"
    ],
    [
      "-906978420229",
      "-919341121702665330"
    ],
    [
      "596377277861",
      "-39370197956199750"
    ],
    [
      "677922303551",
      "57116214218192670"
    ],
    [
      "66724734257051",
      "-544969482694752133170"
    ],
    [
      "973761988091",
      "510352679745463410"
    ],
    [
      "-11895805904599/16",
      "63497092394507860125/64"
    ],
    [
      "-995082845989",
      "-843536361852751950"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 5/2 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -111272277595347481399552T^8 - 571677299335038766946944T^7 - 414437999094511764043024T^6 + 1035179743123152506406800T^5 + 662097824240016643327160T^4 + 815994324653724323045120T^3 - 1173674032798223873117584T^2 - 1437219526913596795113976T - 361162322085565372999627,\nA6 = 14017789577932496860029321164394496T^12 + 107552457791941270066673288429907968T^11 + 247298982788864524389713744611492352T^10 - 86954791407743286472040661661146880T^9 - 1006107482862739641862761048136361904T^8 - 241137273409585441201147837083740736T^7 + 2061063776469007784252972194463786352T^6 - 8144469449242082226324505727313744T^5 - 1635536224802875100792289970610279784T^4 - 164213104675413544335944722096034560T^3 + 887798893937215693740812283719232832T^2 + 504859995173227668638395021468280872T + 83905010208748238142485898220128646.\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": "2026-10-24 14:26:48",
  "updated_at": "2026-10-24 14:26:48"
}