{
  "id": 5942,
  "curve_key": "1513418781747025172766990197721:-2068700970966136683673287286110201186110027805",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-31529557953063024432645629119",
    "2394329827507110525529867069124396571256849"
  ],
  "rank_lower_bound": 22,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 208.6865000895187,
  "faltings_height": 15.363068072612153,
  "conductor": "13396978187120415472751957566876448609153151571183717279473750886538601098",
  "bad_primes": [
    "2",
    "7",
    "19",
    "29",
    "41",
    "47",
    "83",
    "4931",
    "119417382197",
    "6376700831951",
    "2891803755485558472023692070915740961"
  ],
  "discriminant": "-470563789110065751048959160740810200865782489814643802709163897449639845273410664140788",
  "regulator": "5621290319127023975295.690260906453029514683289997523044966801073564786365793632230",
  "points": [
    [
      "248223125895704",
      "3140407946637764085993"
    ],
    [
      "168123630535876",
      "-1358519066359410364581"
    ],
    [
      "213856071195621",
      "-2330692202191642288066"
    ],
    [
      "-116660759101179",
      "-2117751164747834697155"
    ],
    [
      "514930453127056",
      "11076747732273464812329"
    ],
    [
      "109996122890900",
      "-507010865638614771893"
    ],
    [
      "-1299079922593997/9",
      "53580227854047304652050/27"
    ],
    [
      "88000434450328",
      "548814244088762445545"
    ],
    [
      "-2552602072603264/25",
      "-266609682436108117783099/125"
    ],
    [
      "126039062622992",
      "650085277254389552425"
    ],
    [
      "70777082754243601/225",
      "16396647634830773099213231/3375"
    ],
    [
      "59209555795272",
      "857352803113518969743"
    ],
    [
      "26317838948973",
      "-1258081285711613468450"
    ],
    [
      "113253303183444628/49",
      "38004343937726921337599799/343"
    ],
    [
      "-142843714437724",
      "-1995870459426129712031"
    ],
    [
      "38290727991027",
      "1114980336768809528503"
    ],
    [
      "111199446030195",
      "513105028579710114902"
    ],
    [
      "-146928221359219",
      "-1963425407678572020971"
    ],
    [
      "64720831021813",
      "-790450754332314441090"
    ],
    [
      "2682114026254009/25",
      "62065719143850854202838/125"
    ],
    [
      "-137330702137040",
      "-2033294629431860892633"
    ],
    [
      "531064009381375",
      "-11637249010041153437418"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -5/6 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -70781753951590292657527T^8 - 367565467671631265368148T^7 - 564938152357888095468709T^6 + 861671225097878262924926T^5 + 883290795135789128496595T^4 + 1492235942354111474368304T^3 - 390179707279847183534299T^2 - 1933866828077577012667322T - 753991179760473695494012,\nA6 = 7240259042863556427532625579222554T^12 + 56530289701184340202303695554449444T^11 + 163263464615793597915652884274103291T^10 + 33336026591601761367769399981188740T^9 - 608655863176039416519152300146091520T^8 - 922975179177849633814913734492373280T^7 + 1471644379398400596650029609789831050T^6 + 1259508950348326801233446624368517040T^5 - 1608259867492513771432473315149086770T^4 - 1344292356731452517237148523695223300T^3 + 750512254493731351508294582787338435T^2 + 986666108581324895487891684114883660T + 253245346808298629177743261916441680.\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 01:15:02",
  "updated_at": "2026-10-26 01:15:02"
}