{
  "id": 5855,
  "curve_key": "6117392675340211330546000:-28752191087128769476837247887757310400",
  "ainvs": [
    "0",
    "1",
    "0",
    "-127445680736254402719708",
    "33277998943393593889797692846960688"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 172.50355464770252,
  "faltings_height": 12.418689076987285,
  "conductor": "763637306803889757227254912087618163457944258334442200",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "23",
    "53",
    "149",
    "1787",
    "1071067",
    "235048549",
    "11898918791934728943218743"
  ],
  "discriminant": "-345926161375474441467893249980877513982914324402883732669591526218720000",
  "regulator": "1669187430791097.2412946187728207948180471969417321531305756625998044717431",
  "points": [
    [
      "3030856429668",
      "-5242969625256580140"
    ],
    [
      "892757989032",
      "-794382142912980732"
    ],
    [
      "242011005303",
      "-128876542701039210"
    ],
    [
      "167421918948",
      "-128971514166769260"
    ],
    [
      "-170167361682",
      "223690790254079610"
    ],
    [
      "228402634758",
      "126823989537858690"
    ],
    [
      "62656219518",
      "159808354902694890"
    ],
    [
      "620393011998",
      "-439309797290199990"
    ],
    [
      "-68154815046",
      "204077071850196006"
    ],
    [
      "-218737437852",
      "225143097979462740"
    ],
    [
      "-187394966076",
      "224899872562863036"
    ],
    [
      "388411705518",
      "-205849006516504890"
    ],
    [
      "58600843945242/49",
      "-432691791631485688170/343"
    ],
    [
      "465606176037/4",
      "-1131944497081397055/8"
    ],
    [
      "-53417407422",
      "199833416945178210"
    ],
    [
      "205895207607",
      "125562836560202118"
    ],
    [
      "187329648804",
      "-126402099647744844"
    ],
    [
      "-435041599926",
      "-79910445489337386"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 1/5 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -129077164062048809835900T^8 + 378319182388641891290880T^7 + 136088129918041916509980T^6 - 755961738076060064377560T^5 + 619450622573441931032760T^4 - 1170861959203596215660160T^3 - 1734751811488996657912320T^2 + 1314050376486783211611840T - 219065110811691252584112,\nA6 = 18245050345346515787515057919752500T^12 - 83505322013254826025359146692690000T^11 - 2407103439528010819936132599838344T^10 + 465220783429849849086641780587731600T^9 - 185239629309258027189063745343474940T^8 - 1503733795718269687786747306505656800T^7 + 626403979186422524394828379594167600T^6 + 2519798602559624814688441138399867488T^5 - 832465009702733039267308016691100320T^4 - 905573011434584900869203229631278080T^3 + 930446348033589270658482617988215040T^2 - 337397396218794978267255003741415680T + 42647307174629128234916120026233216.\nIt is a 2-neighbour of the fibration given in curve#3900: its Mordell-Weil lattice (rank 17, no reducible fibres) is a root-free Kneser 2-neighbour of that fibration's, realised by the pencil |O + P - F| for a section P of height 12. Constructed and searched by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.",
  "created_at": "2026-10-25 13:08:31",
  "updated_at": "2026-10-25 13:08:31"
}