{
  "id": 63,
  "curve_key": "82493423699285283661595499950745752858794321:-385065468974883849402843214871548112294742551077469184169304929369",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1718612993735110076283239582307203184558215",
    "445677626128337788660554947611110167094039534522619288819463817"
  ],
  "rank_lower_bound": 18,
  "naive_height": 303.36387744953214,
  "faltings_height": 23.330153180013127,
  "conductor": "113867782999071766513257245176182365522858404266111886760688305190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "19",
    "23",
    "71",
    "127",
    "151",
    "179",
    "241",
    "281",
    "449",
    "503",
    "1223",
    "1361",
    "1399",
    "2017",
    "2083",
    "2293",
    "2843",
    "5651",
    "74923",
    "436549"
  ],
  "discriminant": "239065937769943972318715082774604147597436659174149372442869290187913170319391241801587631661352787169448770987206379287600000000",
  "regulator": "36389786154315993359.606350911054022215893750090730455834360025330154869588",
  "points": [
    [
      "-916413066082020853346",
      "-35369782405684521707886952377707"
    ],
    [
      "195434116396250243974",
      "10828966775531818886070739823413"
    ],
    [
      "1265034698502036374374",
      "17205341075829552264529317189013"
    ],
    [
      "2216840056561938704974",
      "86776618821766613189523105183613"
    ],
    [
      "1317460353165617357158",
      "21637731566353513111501700533141"
    ],
    [
      "-419919197918370459176",
      "-33065253185351621643390087304037"
    ],
    [
      "-29666703514651498703639/64",
      "-17307761259547457289873127491657319/512"
    ],
    [
      "1028534464393349854573171/4",
      "1043092047443803329899021606077145579/8"
    ],
    [
      "-4727498668121314310834/9",
      "-936668010323115521156024630441249/27"
    ],
    [
      "2529716865202204892214",
      "110846353150164494211027781928133"
    ],
    [
      "1199344199314248064924",
      "10470797020157142702308988437263"
    ],
    [
      "5710166898431918122165966/9",
      "13644960301239082757781340351692685151/27"
    ],
    [
      "-1338652300506182722676",
      "-18640047007082369619825194657537"
    ],
    [
      "5372757156747175085983246/1369",
      "11786893726772068452866617397651512729/50653"
    ],
    [
      "29128426914241943990086/25",
      "624790324363217559708520261779569/125"
    ],
    [
      "4983719710548842292787296/1849",
      "9864984392366637148101983568300087321/79507"
    ],
    [
      "10589515239193964535623854/961",
      "34220949959199862455549906395740174723/29791"
    ],
    [
      "1023941243985123630141565744/259081",
      "31035258051713148261108384857840848626527/131872229"
    ]
  ],
  "submitter": "David Renshaw",
  "commentary": "Provenance: Elkies, 2009, as listed on Andrej Dujella’s high-rank elliptic-curve tables for torsion group Z/2Z. Dujella’s rank-18 page lists this curve and the 18 independent points submitted here.",
  "created_at": "2026-05-29 04:07:17",
  "updated_at": "2026-07-01 22:33:41"
}