{
  "id": 4961,
  "curve_key": "2463146815325005489:3605482955755262528054062487",
  "ainvs": [
    "1",
    "0",
    "0",
    "-51315558652604281",
    "-4173012684548591147038855"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 127.04391419876416,
  "faltings_height": 8.541088412846081,
  "conductor": "350994032023955239500892170090",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "41",
    "79",
    "313",
    "439",
    "2017",
    "7753",
    "949214641"
  ],
  "discriminant": "1125365491804656359476308542567827131186257453040000",
  "regulator": "74859666414.2476873256562135061970308664531303107519015993486",
  "points": [
    [
      "-109188382",
      "358237547891"
    ],
    [
      "-121745032",
      "519594032141"
    ],
    [
      "-148818782",
      "409723339891"
    ],
    [
      "301971218",
      "2804648336891"
    ],
    [
      "-102278782",
      "74529371891"
    ],
    [
      "344097614",
      "-4348927461205"
    ],
    [
      "1157011118",
      "-38540374282009"
    ],
    [
      "779836118",
      "-20738331157009"
    ],
    [
      "-140928382",
      "-509688612109"
    ],
    [
      "-123003146",
      "527273680015"
    ],
    [
      "-139502926",
      "520437122675"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4897, submitted by Ritik Jain: https://elliptic-rank.icarm.cloud/curve/4897.\r\n\r\nThe source model is y^2 + x*y = x^3 - 10455088461805561*x + 334576760664626995112441. Its public entry supplies eleven rational points and no commentary identifying an earlier source.\r\n\r\nApplied the degree-2 isogeny with kernel generated by the rational order-2 point (78797594, -39398797), then converted the target to its minimal model y^2 + x*y = x^3 - 51315558652604281*x - 4173012684548591147038855.\r\n\r\nEleven supplied rational points transported through this map and checked exactly on the target curve. Rational torsion Z/2Z. Same rank and conductor as the source; conductor 350994032023955239500892170090. Source-attributed existing curve.",
  "created_at": "2026-10-20 23:55:07",
  "updated_at": "2026-10-20 23:55:07"
}