{
  "id": 5056,
  "curve_key": "14299695466983880662698305162702128:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-297910322228830847139548024222961",
    "0"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 235.93663892948248,
  "faltings_height": 17.729626989098364,
  "conductor": "9533130311322587108465536775134752",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "37",
    "41",
    "43",
    "47",
    "71",
    "127",
    "2287"
  ],
  "discriminant": "1692141309090934248752193089070736499339342656265532089786496963378390689579378328252736975135339584",
  "regulator": "754395768.2723718960224471664625964240889361569012822",
  "points": [
    [
      "5536145766238839024/25",
      "12986378870816463073220445732/125"
    ],
    [
      "590198031106914048",
      "453221852098920402517791408"
    ],
    [
      "2520269289388217803568496/61952641",
      "3623039662394469615405919115527723500/487629237311"
    ],
    [
      "-1801348406683558779770087/217149696",
      "4411305307806368373991431438290623747/3199917920256"
    ],
    [
      "-298749252018612589008806775/17567381764",
      "896099450701275193906046039669392417245/2328415913764088"
    ],
    [
      "72251309799151894845131100/124609",
      "614141699742771648011399057013299864070/43986977"
    ],
    [
      "-1846599421493957551239/10432900",
      "7737690092508460865430136413731259/33698267000"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 17260078859287719, rank 7 example from Watkins, Donnelly, Elkies, Fisher, Granville, Rogers, 'Ranks of quadratic twists of elliptic curves', Publ. Math. Besancon 2014, doi:10.5802/pmb.9; points from https://magma.maths.usyd.edu.au/~watkins/PTS.r6r7.",
  "created_at": "2026-10-21 01:50:31",
  "updated_at": "2026-10-21 01:50:31"
}