{
  "id": 4887,
  "curve_key": "-53286521861360935793712:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "1110135872111686162369",
    "0"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2
  ],
  "family": null,
  "families": [
    "quartic"
  ],
  "naive_height": 156.98991113677127,
  "faltings_height": 11.150733006372429,
  "conductor": "71048695815147914391616",
  "bad_primes": [
    "2",
    "11",
    "41",
    "73",
    "83",
    "89",
    "137"
  ],
  "discriminant": "-87560530276149265457820281772670615223524526599564590506911322176",
  "regulator": "228061682.33464370900764587061949281533206327642152",
  "points": [
    [
      "2158006912648609/176400",
      "290854140748391552484977/74088000"
    ],
    [
      "322482473093209/28224",
      "17852639961296943813725/4741632"
    ],
    [
      "7835451774232914601/1038128400",
      "99274503855775601553616220651/33448497048000"
    ],
    [
      "3203594864010621025/93547584",
      "8000085856333247055923231215/904792232448"
    ],
    [
      "908802237444409/8020224",
      "8055857428983897637653395/22713274368"
    ],
    [
      "693456018449182760464/21498890625",
      "26254283031737787647675214117188/3152274837890625"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Obtained by a rational 2-isogeny from curve #4723, submitted by David Renshaw and sourced to Watkins et al.'s electronic data PTS.r6r7: http://magma.maths.usyd.edu.au/~watkins/PTS.r6r7, accompanying Section 15 of Ranks of quadratic twists of elliptic curves (2014): https://doi.org/10.5802/pmb.9. Six rational points transported through the isogeny and checked exactly. Rational torsion C2. Same rank and conductor as the source. Source-attributed existing curve.",
  "created_at": "2026-10-20 22:31:00",
  "updated_at": "2026-10-20 22:31:00"
}