{
  "id": 317,
  "curve_key": "207161417089083523968289:-93229599617770243340100075038815537",
  "ainvs": [
    "1",
    "0",
    "0",
    "-4315862856022573416006",
    "107904629186874422701928761288036"
  ],
  "rank_lower_bound": 16,
  "torsion": [],
  "naive_height": 161.06335570488255,
  "faltings_height": 11.292232055195537,
  "conductor": "382724524351827852913185875134830026418690856518876504970",
  "bad_primes": [
    "2",
    "5",
    "11",
    "23",
    "29",
    "9377404282283",
    "556269352188281130391524829339614864907"
  ],
  "discriminant": "115017721248537024791512873609799594141037969992867713718881894400",
  "regulator": "1522807205165362.956219376809242957391278748925554379651079502171632000",
  "points": [
    [
      "350823376408844/5041",
      "-4304074360072412521722/357911"
    ],
    [
      "41613352696",
      "-606442401259298"
    ],
    [
      "43754416876",
      "1682882181574762"
    ],
    [
      "-514519682456/9",
      "-349744460202098386/27"
    ],
    [
      "42850357588",
      "1283793738135010"
    ],
    [
      "5575404693310/9",
      "13093570471884083482/27"
    ],
    [
      "24735711016",
      "4035253563971182"
    ],
    [
      "70005766238893/1296",
      "265514088956225527675/46656"
    ],
    [
      "-75671565400",
      "-1087750532760594"
    ],
    [
      "169221880657869/16",
      "-2201286064287084439973/64"
    ],
    [
      "431937596876",
      "-280767657962153238"
    ],
    [
      "2283920593876/81",
      "2141528641062149458/729"
    ],
    [
      "32362547578701884/351649",
      "4616814020286500130366474/208527857"
    ],
    [
      "59381760629636064/1297321",
      "-3695917007568875981110418/1477648619"
    ],
    [
      "5970160613604639/114244",
      "193370327124387817329229/38614472"
    ],
    [
      "-57052998624",
      "-12977933128655338"
    ]
  ],
  "submitter": "Jack Cheng",
  "commentary": "A new canonical curve from the Mestre-Fermigier family on [348,-600,-216,492,876,-900] at the fresh integer shift t=781. Completing p6(x-t)p6(x+t) and removing square content gives Y^2=4001161*x^4-60808320*x^3-1036031133986*x^2-38029624675200*x+46823070345440729. Its 11 generic construction directions are enlarged by five independent points found in hyperellratpoints(Q,[1000000,2000]), with primitive-quartic sources (-293,6467696), (536,222888923), (-1169/3,119790416/9), (4739/3,42286639784/9), and (1631/9,8043119288/81); these map respectively to the final five displayed witnesses. The ICARM exact Cremona/Brumer verifier certifies all 16 points. No parity or BSD assumption is used.",
  "created_at": "2026-08-24 08:01:40",
  "updated_at": "2026-08-24 08:01:40"
}