{
  "id": 735,
  "curve_key": "5893285203340096877603879631328561:-454805583197184472561163393435654200882318849376809",
  "ainvs": [
    "1",
    "0",
    "0",
    "-122776775069585351616747492319345",
    "526395350922667203381059708825820468144096530537"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "naive_height": 233.28790900334874,
  "faltings_height": 17.278497400573983,
  "conductor": "1815436548573871882271810231932931339840134069673695222694630595510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "19",
    "29",
    "41",
    "59",
    "97",
    "2859137",
    "875435282615586462965097331992891038830823172451"
  ],
  "discriminant": "-1255524860496404041339919526715401858321042056672825094118416026325509307285490145973711360000000",
  "regulator": "1109587422089427432.32640199927404202908593401462523859195613702757570250863210",
  "points": [
    [
      "-12764350695458866",
      "-117825097573695156892237"
    ],
    [
      "-110539812835998374/9",
      "-11504787835279316233210439/27"
    ],
    [
      "-3532900334322407464/289",
      "-2199619652760180395337136301/4913"
    ],
    [
      "-10982967466937926",
      "-741634620259801394859877"
    ],
    [
      "-10778781361429486",
      "-772966755699875726184757"
    ],
    [
      "-9620216709360376",
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    ],
    [
      "9362541474073688039/5476",
      "-229757652001889507807081047943/405224"
    ],
    [
      "3876421835185682",
      "-329712602243806909828405"
    ],
    [
      "304166893386438686/49",
      "-20154148726831806625230151/343"
    ],
    [
      "56131302559111666/9",
      "-1541155151533508181820319/27"
    ],
    [
      "6402704308585994",
      "-52615685884698328523077"
    ],
    [
      "7832488525188362",
      "-212730367850396509747525"
    ],
    [
      "9572262199783604",
      "-477737440907691060150517"
    ],
    [
      "19384270952327228",
      "-2330256673266826860485029"
    ],
    [
      "37296229629855764",
      "-6915682639370567170263007"
    ],
    [
      "55601184018723752",
      "-12868195635781433096407435"
    ],
    [
      "108481624363224362",
      "-35550634907793508995211525"
    ],
    [
      "6209906915228474",
      "-58611421435423497470677"
    ],
    [
      "6398500317489014",
      "-52610637590405654589757"
    ],
    [
      "6307588257913274",
      "-54052096076350389606997"
    ]
  ],
  "submitter": "Valery Asiryan",
  "history": [],
  "commentary": "Specialization T=-12/31 of the family identified by wgxli in the commentary to curve #302. Starting from 17 reconstructed generic sections, minimized quartic searches produced a set of 20 points certified independent by exact quadratic-character certificates.",
  "created_at": "2026-09-16 17:20:30",
  "updated_at": "2026-09-16 17:20:30"
}