{
  "id": 309,
  "curve_key": "6683899076449303155254597192364492663628825:10515872098771272639947813309510267017128395626861137289211391875",
  "ainvs": [
    "1",
    "0",
    "1",
    "-139247897426027149067804108174260263825601",
    "-12171148262466750740691943470052015013728330466029726884498652"
  ],
  "rank_lower_bound": 15,
  "torsion": [
    2
  ],
  "naive_height": 295.82482625128375,
  "faltings_height": 22.692710973656425,
  "conductor": "14736232836353426730586889330999407111621750064300242106070930802493850",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "37",
    "41",
    "67",
    "79",
    "97",
    "101",
    "103",
    "151",
    "229",
    "389",
    "857",
    "977",
    "983",
    "1499",
    "1531",
    "11719",
    "12907",
    "49639",
    "938573",
    "4153367"
  ],
  "discriminant": "108805746048883061193612306928010127310531083533286108872721769647652556904158900879842993759008627125609908132164015812250000",
  "regulator": "474127480377383785864.20755223411635893132159742175014720820682659761",
  "points": [
    [
      "417476533381735876627",
      "-1567389922802024902616992663114"
    ],
    [
      "13580713215478598882323",
      "-1582044898771593034949712886747018"
    ],
    [
      "35729115842572740083857/64",
      "4694856465890330255585827438133083/512"
    ],
    [
      "-6831837002591247631847/64",
      "622205546465850731255887962212257/512"
    ],
    [
      "45217890518455797390553/64",
      "-7967061107978184542849544737310143/512"
    ],
    [
      "-213293129493828877917353/961",
      "83208523138046682258484816354057826/29791"
    ],
    [
      "346002499441700055197692/121",
      "201731669795856202671162628019538241/1331"
    ],
    [
      "56977374367393099737748/121",
      "-6873807449291231757042867567962288/1331"
    ],
    [
      "4010446973304367153050763/169",
      "8030364686397976757935409794061557742/2197"
    ],
    [
      "9381785176543140026035759/169",
      "-28735476228620029072986061579098599626/2197"
    ],
    [
      "1462525692414421670628763/1369",
      "1647849426236391674372613810260726558/50653"
    ],
    [
      "-5679055972988851923621653/26569",
      "-12116070391266908198024640288072161902/4330747"
    ],
    [
      "-1121581080347924732470229/3721",
      "352795474595347348115654922139783886/226981"
    ],
    [
      "-46416368114055357305883497/146689",
      "25626148534805874399586744718663739382/56181887"
    ],
    [
      "-382777754516683952410076/1369",
      "-112172516271497474124380291760240049/50653"
    ]
  ],
  "submitter": "7fff-zip",
  "commentary": null,
  "created_at": "2026-08-24 00:23:34",
  "updated_at": "2026-08-24 00:23:34"
}