{
  "id": 3115,
  "curve_key": "1918758897226803424944927377677318251806594241:80771558063375596498001838379108048792277560504587792146699811171039",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-39974143692225071353019320368277463579304047",
    "-93485599610388421872677319402859407612112625383551208581674399881"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "naive_height": 312.8040232621975,
  "faltings_height": 23.994447588412587,
  "conductor": "2329609314357493409271842921820896872147183012290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "23",
    "29",
    "61",
    "71",
    "79",
    "199",
    "601",
    "619",
    "859",
    "1123",
    "7207",
    "191413",
    "3560785447"
  ],
  "discriminant": "312573307088884863253575885734840703026547488517541812958733508484047136504307334765262472281788273863176812166584057334480896000000",
  "regulator": "3786698286834.34068489090647325297972506327160175878010871107",
  "points": [
    [
      "-3820960803782437245293",
      "-58898189468648535408490003509594"
    ],
    [
      "-4036260076497007842573",
      "-45870816456455952722736719565914"
    ],
    [
      "7351306746245758740627",
      "-99646384490227694728068088250714"
    ],
    [
      "-3717081800981354887173",
      "-61186346688090184471896574410914"
    ],
    [
      "-5780806276364674591550237/1369",
      "-215618147625050560212265599905169842/50653"
    ],
    [
      "1406786692009528931645727",
      "-1668545229120370129145845825488613814"
    ],
    [
      "5035043284564019992315172227153814061/91542261043984",
      "-11219997428118984006861610980366224289045202116974240441/875855482033320883648"
    ],
    [
      "-3414513869223011776181",
      "-56543573819851229319322226977242"
    ],
    [
      "188573855300136391141742271925454263441773/25552860783533835049",
      "-14964847423934676186475483967531732524308926763298016870825752/129169296205645829232612299093"
    ],
    [
      "-7833415626001196166442727853/2343961",
      "-189246719535780898498030973258581129068374/3588604291"
    ],
    [
      "55017757660089931182454869601258473/575569547569",
      "-12875938673891333736830894226118755977180499851016658/436663319667340247"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z4old9101112-007, rational kernel x=2111993798863171867827. Source: https://dujella.github.io/tors/z4old9101112.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:37:59",
  "updated_at": "2026-09-26 20:37:59"
}