{
  "id": 4,
  "curve_key": "10070973336541588631748191975281:-23029049564574022388452675835133173395678625929",
  "ainvs": [
    "1",
    "0",
    "0",
    "-209811944511283096494753999485",
    "26653992551590286206010035905960909459942897"
  ],
  "rank_lower_bound": 15,
  "naive_height": 214.16163044680687,
  "faltings_height": 15.87181609687165,
  "conductor": "164007785374008600847294301252891222936905925387461785510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "31",
    "5451269",
    "1288878077393",
    "1443189199877",
    "39758801179649479"
  ],
  "discriminant": "284205064269551456641094292955182094002428922847801912953464227178522579040000000000000000",
  "regulator": "197339248536833.87234569574893649111280704605566198247249889501297495",
  "points": [
    [
      "501737473225534",
      "-6905875723539454906517"
    ],
    [
      "506962472826784",
      "-7112110805804266149017"
    ],
    [
      "723528240924034",
      "-15925174720190407416017"
    ],
    [
      "812523671448034",
      "-19814153331319366764017"
    ],
    [
      "-177569372855966",
      "7636180350046204211983"
    ],
    [
      "-419463909011966",
      "6392016193970552855983"
    ],
    [
      "-499080158224466",
      "-2656234672725490419017"
    ],
    [
      "-489670250151966",
      "-3461360602620746284017"
    ],
    [
      "-161285098583966",
      "-7503202055979337116017"
    ],
    [
      "576026995032034",
      "9845125145592749267983"
    ],
    [
      "569204876688994",
      "9573248090546012288143"
    ],
    [
      "437566790688034",
      "4315766925018741755983"
    ],
    [
      "383738756328034",
      "1627462454566927475983"
    ],
    [
      "380556863867362",
      "1386435548400000375823"
    ],
    [
      "373690874760034",
      "658176881176342211983"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Found by Mestre (1992). A historical rank ≥ 15 record, via Dujella's elliptic-curve rank-records tables.",
  "created_at": "2026-05-27 22:11:45",
  "updated_at": "2026-07-01 22:43:36"
}