{
  "id": 4078,
  "curve_key": "5955169978707979619295340340133836114848769418319009:-459439642209356287300483314102041140683375355076516957561567731041206457973873",
  "ainvs": [
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    "0",
    "0",
    "-124066041223082908735319590419454919059349362881646",
    "531758845149717925116300121723710847941442044136002832593534211537097604740"
  ],
  "rank_lower_bound": 20,
  "torsion": [
    2
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  "naive_height": 357.6482984668796,
  "faltings_height": 27.530454715523316,
  "conductor": "428610428388219248912417769724228361243960259613932319147782453962458759457805385527477270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "23",
    "37",
    "53",
    "61",
    "71",
    "79",
    "109",
    "137",
    "263",
    "317",
    "367",
    "661",
    "1109",
    "1237",
    "2141",
    "3253",
    "3881",
    "8011",
    "11027",
    "12781",
    "15731",
    "17483",
    "28001",
    "39023",
    "894227",
    "22707917"
  ],
  "discriminant": "63459447504799102863292256147010057536178349709496928220268873236565239447334194733857296612776664689614612874855195827692505821220757206591550259200",
  "regulator": "229676653253281008959036.074647951944341475534026264752044499123880521083225094",
  "points": [
    [
      "6344139792727965011797196",
      "78552475170257111104054721191398194"
    ],
    [
      "6230581666474965641621690",
      "792051188319558805663756309080385760"
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      "6244335090646645546693244",
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      "6259211570349900133086584",
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      "6544756981164401056053308",
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      "6612714384043993557422468",
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      "422555434538898459692986",
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      "4932629692385669178004604",
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      "5512987884717678165743996",
      "3916720441378800967834537425068409794"
    ],
    [
      "5601539081965749843286618",
      "3543854275248946762823062190411964646"
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    [
      "5954027814656164850298248",
      "2034486084831621543503723739865066946"
    ],
    [
      "6101126983894758557500708",
      "1386723373589166790450912359193544506"
    ],
    [
      "6113155516196273438531708",
      "1332876798945381100368861830411726786"
    ],
    [
      "2066443557154303439599868",
      "16858454202495138677817148911340401986"
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    [
      "8850199040788374470401148",
      "11267234811211080295899306393393246146"
    ],
    [
      "-1016779353531021070992910",
      "25629191304347152918413345204837910280"
    ],
    [
      "-115751108734402879081906628/9",
      "2286195628876847653995861911382011222/27"
    ],
    [
      "3223813941509603561015114507/484",
      "10069386212699873495994022718662247130233/10648"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "specialization at T = 2783/971425 of the rank-9 fibration of X808 given by:\ny^2 + 84(35397T^2 - 221T + 20)xy = x(x + (1139T + 115)(1269T - 59)(3776T + 34)(539T - 5))(x + 8(638T - 23)(250T - 1)(7811T + 499)).",
  "created_at": "2026-10-09 05:29:49",
  "updated_at": "2026-10-09 05:29:49"
}