{
  "id": 4269,
  "curve_key": "860145012705924993804762567537551016641473:-302906435394031598162143035074100793516976095592986289055574945",
  "ainvs": [
    "1",
    "0",
    "0",
    "-17919687764706770704265886823698979513364",
    "350586152076425460834320390688705909752626101552870327003024"
  ],
  "rank_lower_bound": 14,
  "torsion": [
    2,
    2
  ],
  "naive_height": 289.67375886367853,
  "faltings_height": 22.198319307151785,
  "conductor": "2029002416341262551558890376876260685313306986997405814",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "19",
    "41",
    "61",
    "89",
    "127",
    "199",
    "269",
    "271",
    "283",
    "293",
    "383",
    "443",
    "617",
    "773",
    "883",
    "1249",
    "1289",
    "1307",
    "45673"
  ],
  "discriminant": "315176793892270922360434804847978261806955483152613374454606561871597256154463045907975556675309327733745844328114416062464",
  "regulator": "39089511090423.7549688370287674270502587368899389660955250016064986",
  "points": [
    [
      "122733725362400010184",
      "6622116830633155018684806412"
    ],
    [
      "19467426095698817884",
      "95465874600355425604485240904"
    ],
    [
      "19680603477105202360",
      "74422410483189869248871057692"
    ],
    [
      "5723950858244824180",
      "498199033747055074571973012508"
    ],
    [
      "6897113247117147688",
      "476781011644273413695124731116"
    ],
    [
      "-3289072746247952360",
      "639913843840931997143409958588"
    ],
    [
      "-7504848148508857220",
      "696166642385599694994298944808"
    ],
    [
      "122759933899526166136",
      "27547027955657962231861817692"
    ],
    [
      "14333957400727393534",
      "310919924373324691343419320904"
    ],
    [
      "18235544865103521688",
      "172843398899871089073000457516"
    ],
    [
      "19405811678093074560",
      "100737350559660886326621134892"
    ],
    [
      "-142624938899163173270",
      "71568868563189721026397404862"
    ],
    [
      "-31283465470070843912",
      "938381776784614974305829709276"
    ],
    [
      "301559104009923748600",
      "4729681887984401027284987956268"
    ]
  ],
  "submitter": "wgxli",
  "history": [],
  "commentary": "Specialization at T = 180781/50546 of the rank-5 fibration of X312 given by:\r\ny^2 = x(x - (29T + 2)(400T + 49)(221T + 86))(x - T(8T + 53)(25T + 88)(392T + 221)).",
  "created_at": "2026-10-16 00:59:32",
  "updated_at": "2026-10-16 00:59:32"
}