{
  "id": 2723,
  "curve_key": "9702633527542183061008649210247810013213128703921:-30222089139289521932972217443002380310269083721214480484393737025384020969",
  "ainvs": [
    "1",
    "0",
    "0",
    "-202138198490462147104346858546829375275273514665",
    "34979269837140650385384494084551028931706588203982251287822589358438617"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    10
  ],
  "naive_height": 338.3894454301784,
  "faltings_height": 25.850669154233962,
  "conductor": "15193969795647382423209109974390",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "19",
    "23",
    "37",
    "47",
    "83",
    "269",
    "317",
    "571",
    "641",
    "659",
    "390001"
  ],
  "discriminant": "24245206327522789654784127343915552622546704716100437407309122024840280691220119820777537519461675437386633088780791861889526097762713600000",
  "regulator": "6814541.865516143539185602754435532272718597064",
  "points": [
    [
      "47562413266946162062040056049702208330738778/66103956816964716169",
      "275113579858945331488197914169361058897711278158195980477729502529/537453857179830266520246035803"
    ],
    [
      "13440736921603262145027838530754623747802/47666575442058169",
      "-208429144591835735641819999183553392457494768894867453258663/10406889119559854095476947"
    ],
    [
      "123782311552578192845827408894869379103457408603502/34381240809632044844408281",
      "1366910733929288893445275178859908487291269215490034667063462487793539624725/201596189655664066874438584074890990179"
    ],
    [
      "249308336890730379911847604803754614075980087777137/304911686631524918886666496",
      "3435404984582413523921674498343176149515544357895800994116043665857860219505/5324282682420116454602245077481602707456"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z10-023, rational kernel x=-2068478264036700474688465/4. Source: https://dujella.github.io/tors/z10.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 20:19:24",
  "updated_at": "2026-09-26 20:19:24"
}