{
  "id": 6009,
  "curve_key": "3858900569127511358333376:-7574287367459910033412859204900582400",
  "ainvs": [
    "0",
    "0",
    "0",
    "-80393761856823153298612",
    "8766536304930451427561179635301600"
  ],
  "rank_lower_bound": 18,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 169.83727364433636,
  "faltings_height": 11.919067280782453,
  "conductor": "2354216583461161104471181115871596952153776736160963136",
  "bad_primes": [
    "2",
    "7",
    "13",
    "23",
    "239",
    "65326913515681309",
    "86589218375050156914025100411"
  ],
  "discriminant": "54107425017218588138183099114632562860151199742853781629498513723392",
  "regulator": "23959267775614549.944139612236584564557965405964299357270802671180423213176",
  "points": [
    [
      "156883748125",
      "3919758324237665"
    ],
    [
      "318600797528",
      "124471126688940304"
    ],
    [
      "159636990162",
      "-949833385683728"
    ],
    [
      "-324574406598",
      "25823482310406872"
    ],
    [
      "143804542388",
      "-13393641762216404"
    ],
    [
      "158762516350",
      "2171356699109480"
    ],
    [
      "158879758804",
      "2039915058371996"
    ],
    [
      "61188295181",
      "-63847227878619913"
    ],
    [
      "246022786750",
      "-62280913992136840"
    ],
    [
      "177124265786",
      "-9152640728672168"
    ],
    [
      "167991607762",
      "-1407282660804272"
    ],
    [
      "193793725684",
      "-21560343394044364"
    ],
    [
      "105442021334",
      "38235612191895664"
    ],
    [
      "159223537941",
      "1616709078284573"
    ],
    [
      "45336019394662/361",
      "-175002153838064464352/6859"
    ],
    [
      "-2511419975675/9",
      "-2627699234959510075/27"
    ],
    [
      "1763036255188/9",
      "624610692827001244/27"
    ],
    [
      "159859549044",
      "-220501842786316"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = 0/1 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -7760309087359314183600T^8 + 119026997715519499556160T^7 - 1153373924390107974174144T^6 + 2487025529977453776585216T^5 - 3661714748108170932991560T^4 + 1974920503429370676448440T^3 + 1022466571703719091443964T^2 + 405620581566251073119344T - 1286300189709170452777792,\nA6 = 264858137926126918747215127920000T^12 - 6183711970751924651607354681696000T^11 + 81178268015262088437641813152396800T^10 - 478686331323910127099177745304273920T^9 + 2005108572441196128294357056113536864T^8 - 3279557226608882175286227464412177888T^7 + 1865313942900757552134099206544410352T^6 - 915373920036612203329630698180943776T^5 + 2248150939946977357222177775373137844T^4 - 1203506060647437664686363673157004240T^3 - 593281745909986606769035134794080016T^2 - 270618994174348662640690696819440256T + 561058323515548891363915496659302400.\nIt is a 2-neighbour of the fibration given in curve#4191 (itself a 2-neighbour of the fibration 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": "2026-10-27 22:48:23",
  "updated_at": "2026-10-27 22:48:23"
}