{
  "id": 235,
  "curve_key": "291537614333703744:-151865295230477283557887872",
  "ainvs": [
    "0",
    "0",
    "0",
    "-6073700298618828",
    "175770017627867226340148"
  ],
  "rank_lower_bound": 15,
  "naive_height": 120.64183628862605,
  "faltings_height": 7.97610173327405,
  "conductor": "690285168700675717325304943706298441927480",
  "bad_primes": [
    "2",
    "3",
    "5",
    "37",
    "61",
    "1061",
    "11174227",
    "71657492841305578040354317"
  ],
  "discriminant": "993016632286044059915490679818132686619195628800",
  "regulator": "1930058946037.1760717909398678090108062436141414502209083178458576916",
  "points": [
    [
      "33929674",
      "93551911110"
    ],
    [
      "55028554",
      "90428617530"
    ],
    [
      "51848404",
      "15497923230"
    ],
    [
      "51767374",
      "8936997390"
    ],
    [
      "20389894",
      "245774216430"
    ],
    [
      "34564594",
      "84437781030"
    ],
    [
      "53046094",
      "53382700530"
    ],
    [
      "26873404",
      "-178763660730"
    ],
    [
      "-29739926",
      "574541160390"
    ],
    [
      "65790004",
      "246863819070"
    ],
    [
      "-36266726",
      "590205480390"
    ],
    [
      "-6254546",
      "462075298830"
    ],
    [
      "70278844",
      "309891494970"
    ],
    [
      "31681258",
      "123069479994"
    ],
    [
      "57653926",
      "131291923986"
    ]
  ],
  "submitter": "RoyManami",
  "commentary": "Rank-15 naive-height record: h=120.642 (beats 127.132). New 3-parameter sub-family of Mestre locus 12*p5=5*p2*p3: six roots = union of two depth-2 cubics with (p-r)(q-s)=0 (equal product), beyond Mestre (u,v) slice. Sextuple {0,7,133,136,430,434}, T=162; base-point injection + Neron-Tate independence (15 indep).",
  "created_at": "2026-06-26 01:21:19",
  "updated_at": "2026-07-01 22:41:38"
}