{
  "id": 5682,
  "curve_key": "875481790219972535372054401:-25172140598681335850675252282408135841601",
  "ainvs": [
    "1",
    "0",
    "0",
    "-18239203962916094486917800",
    "29134421989212989152766113800468840000"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 186.1104497522245,
  "faltings_height": 13.421366178923224,
  "conductor": "68419229104773713711176014223101215945773270471939176270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "47",
    "167",
    "5519356019",
    "63198851032012151243565340592009585083"
  ],
  "discriminant": "21639140059791341059902619587510851987210465772708438242536321703043072000000",
  "regulator": "14033537026514259.76977858071144764694295314627070023542521715300134309389190",
  "points": [
    [
      "-3981263396400",
      "6216483948536266200"
    ],
    [
      "4112504508960",
      "4866119711206003800"
    ],
    [
      "8733717954000",
      "-23152270046947237800"
    ],
    [
      "353176981200",
      "4768312749869482200"
    ],
    [
      "-1441107244440",
      "-7240592743323696360"
    ],
    [
      "2038252640400",
      "-652828407125797800"
    ],
    [
      "30765728677200",
      "-169081886274809317800"
    ],
    [
      "1748907510480",
      "1607819143637320920"
    ],
    [
      "1444296506832",
      "2409230473537593816"
    ],
    [
      "2866472427600",
      "636463838225338200"
    ],
    [
      "-1347358295790",
      "7159833425226021300"
    ],
    [
      "175843982082000/121",
      "3176992363654732888200/1331"
    ],
    [
      "-2711793834270",
      "-7658544418349911830"
    ],
    [
      "1224845769060",
      "2937988762679485800"
    ],
    [
      "2798469003600",
      "-92660445847333800"
    ],
    [
      "3117445201350",
      "-1603586261397138300"
    ],
    [
      "1947968197200",
      "-998376694082879400"
    ],
    [
      "24611562000",
      "5355888485225275800"
    ],
    [
      "4414730724900",
      "-5886909364716264600"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -5/1 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -4247232044073407555787T^8 + 31562440352380138911048T^7 - 1079699554459262036768544T^6 + 808673010384011405337504T^5 - 370492253920133220842280T^4 - 583074314969616668304144T^3 + 1749298418924942437857936T^2 + 6981774061823935535232T - 733152591313571732712192,\nA6 = 99353320243156880097765275026566T^12 - 1192047168420920079142624551372696T^11 + 51816962014333011197785218484470384T^10 - 160733095313938224161654547702105120T^9 + 1161258380951665950605765814917343480T^8 - 500375410396179478662655437513305328T^7 - 2173656091315178125605895871772822192T^6 + 963181788398399075637606795285979968T^5 + 1772421005485324185894755005716179280T^4 - 460279153080260982936199267860712320T^3 - 927109903404780261014801473928185344T^2 + 58145438007481575316035550439430144T + 241998303936746269490887631501697024.\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": "2026-10-24 08:36:05",
  "updated_at": "2026-10-24 08:36:05"
}