{
  "id": 5548,
  "curve_key": "76749430799289528427763353708321:-672850507778142664227604958416550974665443736625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1598946474985198508911736535590",
    "778762161780257579980855045697058255810663396"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 220.25570472317398,
  "faltings_height": 16.115396466395072,
  "conductor": "8677551978688959744721052117666650968801190477243895647930960878",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "29",
    "41",
    "47",
    "79",
    "89",
    "94529",
    "125887",
    "470831",
    "6244347101",
    "4680721312117450811129881"
  ],
  "discriminant": "-368745720362423219890348942398080231927373545138942663009880667226992068827076356481957888",
  "regulator": "440882540984883741.950751358174415911477197127174937537949264617286152397021983",
  "points": [
    [
      "818956602960454",
      "4308169133732844955246"
    ],
    [
      "-1431874966541096",
      "11512131136784976851146"
    ],
    [
      "18152204883662524/25",
      "95414444809471109206322/125"
    ],
    [
      "5112051738383968",
      "-355244265269146022197526"
    ],
    [
      "606625636774444",
      "-5659968069347610718070"
    ],
    [
      "618737802711406",
      "5129222683913128436356"
    ],
    [
      "635686880794252",
      "-4383211603849135106966"
    ],
    [
      "738355474223836",
      "836451365083764881626"
    ],
    [
      "405531718438588",
      "-14036764933267340332166"
    ],
    [
      "735970001282908",
      "790587998955335642698"
    ],
    [
      "670422231351250",
      "2850416403949994063086"
    ],
    [
      "630388937117716",
      "-4616750936069890205462"
    ],
    [
      "20380927323037750",
      "-2904146210045188147560164"
    ],
    [
      "1466336522163436",
      "-39837187613069425545974"
    ],
    [
      "732853314777052",
      "-751921025646950041526"
    ],
    [
      "1083989836648600",
      "-17867437693583833912886"
    ],
    [
      "89298993607323724/121",
      "-1103384783165386133681794/1331"
    ],
    [
      "723883440237244",
      "794635862846888963530"
    ],
    [
      "-302461004119052",
      "35138457448505744709538"
    ],
    [
      "-152431663412420",
      "-31921002730193874453254"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -5/69 of the rank-17 fibration of X1008 given in curve#3589. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-23 01:09:30",
  "updated_at": "2026-10-23 01:09:30"
}