{
  "id": 3613,
  "curve_key": "3903454744754567064284414416:-277365816553605898371378444278715854966464",
  "ainvs": [
    "0",
    "1",
    "0",
    "-81321973849053480505925300",
    "321025250640720460234849440829085820000"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "naive_height": 190.85231179811646,
  "faltings_height": 13.886114830133716,
  "conductor": "613662111701893885107735999793593321355118146923962938690680",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "19",
    "53",
    "71",
    "40444406887404089",
    "12367039174898142442876476336022831"
  ],
  "discriminant": "-10101282699946150736973387858889560363365402529339851351117173755399668531040000",
  "regulator": "2443968229711946274117014.458837541608162124677744026085659292826773970095271",
  "points": [
    [
      "-2953783184288383727051525/1255477671361",
      "31434551286944437739255687830962099000/1406738876684244641"
    ],
    [
      "-64944718668245545865/7284601",
      "361153887211264916227485145590/19661138099"
    ],
    [
      "-684089222834494100/267289",
      "3128046434867764846023471000/138188413"
    ],
    [
      "1052360178759916/25",
      "33421211326032085248264/125"
    ],
    [
      "60642805546304331/4225",
      "12617301557664678853176804/274625"
    ],
    [
      "71398598483474860/6889",
      "13905860789422558506658680/571787"
    ],
    [
      "3533850457931517100/537289",
      "3311020192904233428864187800/393832837"
    ],
    [
      "4986553838529257215/1681",
      "11135219040503234885690963910/68921"
    ],
    [
      "21136233367864131400/5387041",
      "98732793918997256753104718400/12503322161"
    ],
    [
      "240619181977233026812/877969",
      "3730469792722051873934502196992/822656953"
    ],
    [
      "298372103304871917850/1062961",
      "5151292885191342348158756487750/1095912791"
    ],
    [
      "6010253816637724059400/15155449",
      "465830612846972002147753609308000/59000162957"
    ],
    [
      "6235584874581412437685/627101764",
      "349581709171997318709987250909095/15703882374088"
    ],
    [
      "12937495002834107684355/587044441",
      "1366686212642430760144361748714120/14223499760989"
    ],
    [
      "13582952902738805399515/337126321",
      "1546857319466904786133983790374060/6189976379881"
    ],
    [
      "37618084646681737366987/15543356929",
      "22796211450241137113498097242633052/1937836938409217"
    ],
    [
      "39112145221764286539400/5624850001",
      "4041037268409196829505607708575600/421858125224999"
    ],
    [
      "44667067298695942984975/9063230401",
      "5453234616252507242753744496740250/862828597405601"
    ],
    [
      "854548567430628169733725/224746157476",
      "870732001379797264164861192694888125/106546309859277224"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at T = -15/4 of the rank-17 fibration of X1008, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #751 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:19:24",
  "updated_at": "2026-09-29 19:19:24"
}