{
  "id": 5941,
  "curve_key": "37912449034833024916436720798656:-231863475830916313680975819348109507643008746880",
  "ainvs": [
    "0",
    "1",
    "0",
    "-789842688225688019092431683305",
    "268360504433930655331344456423564825257736059"
  ],
  "rank_lower_bound": 20,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 218.13849695565352,
  "faltings_height": 16.026546590569033,
  "conductor": "139288241603354846841940783546467683574322993492407312861366648",
  "bad_primes": [
    "2",
    "3",
    "7",
    "13",
    "19",
    "23",
    "97",
    "103",
    "109",
    "113",
    "11626251838739",
    "6044018522463029",
    "2411031762496915969"
  ],
  "discriminant": "424149857037486985174332835458424040307717256143131788269916241026697113952672218077910272",
  "regulator": "294352412571209509.846823888508400220542995844990837052173056972245243114870116",
  "points": [
    [
      "437240784301199",
      "-2569152388069282699242"
    ],
    [
      "817867765053971",
      "13017359964717028077066"
    ],
    [
      "-90245172429235",
      "-18409373158543186989078"
    ],
    [
      "11869434965796374/25",
      "77290026882824721668157/125"
    ],
    [
      "7647231151775909/25",
      "-930201890152782844431198/125"
    ],
    [
      "993822587001395",
      "21563371889916670004022"
    ],
    [
      "-257181846529249",
      "21318608177215583363766"
    ],
    [
      "392570642341691",
      "-4334880119740254618534"
    ],
    [
      "4814165022824243",
      "-328694243956886067757770"
    ],
    [
      "16127564908063877",
      "2045063114231898900135906"
    ],
    [
      "204645318984647",
      "10737475563037040110566"
    ],
    [
      "571439439472715",
      "1900739102356675659078"
    ],
    [
      "914732837386454",
      "17642434820471856204537"
    ],
    [
      "471528704754557",
      "-875429032673598584454"
    ],
    [
      "441419648484131",
      "2391572217335785382934"
    ],
    [
      "478212162112862",
      "-94700955253015213011"
    ],
    [
      "725696966920571",
      "-8795014089237006742566"
    ],
    [
      "1031188453707743",
      "-23460556297091408511030"
    ],
    [
      "789826160375702",
      "-11714763266062882633881"
    ],
    [
      "1046971235882294",
      "-24270437988102522423753"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 235/73 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -70781753951590292657527T^8 - 367565467671631265368148T^7 - 564938152357888095468709T^6 + 861671225097878262924926T^5 + 883290795135789128496595T^4 + 1492235942354111474368304T^3 - 390179707279847183534299T^2 - 1933866828077577012667322T - 753991179760473695494012,\nA6 = 7240259042863556427532625579222554T^12 + 56530289701184340202303695554449444T^11 + 163263464615793597915652884274103291T^10 + 33336026591601761367769399981188740T^9 - 608655863176039416519152300146091520T^8 - 922975179177849633814913734492373280T^7 + 1471644379398400596650029609789831050T^6 + 1259508950348326801233446624368517040T^5 - 1608259867492513771432473315149086770T^4 - 1344292356731452517237148523695223300T^3 + 750512254493731351508294582787338435T^2 + 986666108581324895487891684114883660T + 253245346808298629177743261916441680.\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": "2026-10-26 01:06:26",
  "updated_at": "2026-10-26 01:06:26"
}