{
  "id": 4175,
  "curve_key": "43696879516776758514112:-9125710210693774617228201210890624",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-910351656599515802377",
    "10562164596013837840658404817101"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "naive_height": 156.39469093646449,
  "faltings_height": 10.804111505886597,
  "conductor": "709486739958211139142167777070531368963706408",
  "bad_primes": [
    "2",
    "3",
    "13",
    "17",
    "23",
    "29",
    "157",
    "239",
    "6299",
    "14891",
    "4383071508659110290557591"
  ],
  "discriminant": "90850671391435354539572872164933853516996075293149197946160384",
  "regulator": "110375162066226482.8066887377704413062988676880990852525450322351716488",
  "points": [
    [
      "1854534249",
      "2979977275888574"
    ],
    [
      "15969942397",
      "311223679444686"
    ],
    [
      "18153508899",
      "136288197140974"
    ],
    [
      "57113519905",
      "12036214552234254"
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    [
      "155945027676",
      "60506209143915743"
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    [
      "747260144796",
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    [
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      "1250053223000454730897026/371694959"
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    [
      "-80494585202903/12321",
      "5509831701741518719646/1367631"
    ],
    [
      "-10365054855827/324",
      "15369349393768130657/5832"
    ],
    [
      "510754889701/25",
      "87582159035129226/125"
    ],
    [
      "591640316385/16",
      "335376781303025449/64"
    ],
    [
      "1297763958209/64",
      "339688216845450369/512"
    ],
    [
      "38377633027603/49",
      "237574358556098924802/343"
    ],
    [
      "227205368036595/29929",
      "10469684877534481936082/5177717"
    ],
    [
      "407225388375589/22801",
      "55377084100175911086/3442951"
    ],
    [
      "5420529962740541/319225",
      "1410311883784448191014/180362125"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = 7 of the K3 elliptic fibration y^2 + (Lx+B)y = x(x+D)(x+E) given in the commentary of database curve #3857; points from PARI ellrank.",
  "created_at": "2026-10-11 22:58:28",
  "updated_at": "2026-10-11 22:58:28"
}