{
  "id": 6195,
  "curve_key": "31004873786334056871671771761:-5525476001977738937327021359681191410943241",
  "ainvs": [
    "1",
    "0",
    "0",
    "-645934870548626184826495245",
    "6395226854140847719926321595597087851025"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 196.8358866072936,
  "faltings_height": 14.27581168072534,
  "conductor": "186145258953442579858523828625110",
  "bad_primes": [
    "2",
    "5",
    "11",
    "13",
    "17",
    "23",
    "31",
    "83",
    "131",
    "181",
    "3541",
    "1541074382026489"
  ],
  "discriminant": "-420041500701545602610929772166893436418613189173303320298243398803968000000000000",
  "regulator": "97847839.29881679119505048772770377418699785496549948854588",
  "points": [
    [
      "-13153921001470",
      "112320252052687795455"
    ],
    [
      "-3843133357598",
      "93919535966063069887"
    ],
    [
      "90882204450",
      "79602283965902785855"
    ],
    [
      "6255848630640",
      "50982177403230897305"
    ],
    [
      "15052042729090",
      "9101555283667945855"
    ],
    [
      "16453381797890",
      "14885248598673741055"
    ],
    [
      "18652786616930",
      "28922980647864007615"
    ],
    [
      "34659550258370",
      "160135527184398053055"
    ],
    [
      "179168364603980",
      "2375331901991694300565"
    ],
    [
      "1384800148816610/49",
      "35500862383820757341865/343"
    ]
  ],
  "submitter": "Andrii Prokhorenkov",
  "history": [],
  "commentary": "Specialization at T = 5239/3439 of the elliptic fibration of X648 given by:\ny^2 + (Lx+B)y = x^3,\nwhere\nL = 3885067921T^2 - 14778309212T + 14171920816,\nB = 4936839685420991948803368000T^5 - 37762139727356747035718880000T^4 + 97681596151298882036363082000T^3 - 104946797327065126983361746000T^2 + 40090501217702000033914176000T.",
  "created_at": "2026-10-30 15:40:51",
  "updated_at": "2026-10-30 15:40:51"
}