{
  "id": 4953,
  "curve_key": "0:58552349743083287370528",
  "ainvs": [
    "0",
    "0",
    "0",
    "0",
    "-67768923313753804827"
  ],
  "rank_lower_bound": 12,
  "torsion": [],
  "family": "mordell",
  "families": [
    "mordell"
  ],
  "naive_height": 104.84841634872154,
  "faltings_height": 6.795023938185091,
  "conductor": "226796393437305875506046058539220172836",
  "bad_primes": [
    "2",
    "3",
    "751",
    "443837",
    "7530145723"
  ],
  "discriminant": "-1984014849789551798926890920101098071969328",
  "regulator": "72668711198990503.978593593817757236271354508190653030328413861",
  "points": [
    [
      "2509960585682710401/37699600",
      "-3976494193290492754058844351/231475544000"
    ],
    [
      "2499697786817638401/29749350400",
      "3951904592425984541748582399/5131167956992000"
    ],
    [
      "2527598506376408433/42686039236",
      "-4017827106319250127385607895/8819191822393016"
    ],
    [
      "2473751670088561323/68947731241",
      "3887901862773585964924897980/18104226321530539"
    ],
    [
      "2378830314069988593/162597658756",
      "3629060890694437422363847785/65564904330816904"
    ],
    [
      "2091080919036049107/352673262769",
      "2484113684398160755244141880/209439601847786647"
    ],
    [
      "2011840081833196401/395854888900",
      "1984730934655660155550845399/249060020449213000"
    ],
    [
      "2694099866929372401/203897402500",
      "-4356578714015968313591187351/92069872098875000"
    ],
    [
      "2985924537477622401/384028090000",
      "-4773218393510607042779406399/237982207373000000"
    ],
    [
      "3333488849233894401/553476481600",
      "-5054899365151458364687398399/411764363251136000"
    ],
    [
      "8869251609450296979/1110715749025",
      "24593193931089720125409955308/1170588881476192625"
    ],
    [
      "2769778254588637565479/196748733691225",
      "143988507936737280104674538545442/2759738414097711075875"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 3-isogeny from curve #4677, submitted by dujella: https://elliptic-rank.icarm.cloud/curve/4677.\r\n\r\nThe source model is y^2 = x^3 + 2509960122731622401. Its public entry supplies twelve rational points and no commentary identifying an earlier source.\r\n\r\nApplied the degree-3 isogeny X = (x^3 + 4B)/x^2, Y = y*(x^3 - 8B)/x^3 with B = 2509960122731622401. The resulting model is Y^2 = X^3 - 67768923313753804827.\r\n\r\nTwelve supplied rational points transported through this map and checked exactly on the target curve. Rational torsion trivial. Same rank and conductor as the source; conductor 226796393437305875506046058539220172836. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:43:48",
  "updated_at": "2026-10-20 23:43:48"
}