{
  "id": 4273,
  "curve_key": "9014737644748972257047590735289894801281:-855725956420217428625679323290532123735731685399115412893505",
  "ainvs": [
    "1",
    "0",
    "0",
    "-187807034265603588688491473651872808360",
    "990423560671547949782589371323389658970092939000208993856"
  ],
  "rank_lower_bound": 25,
  "torsion": [],
  "naive_height": 275.9990381427588,
  "faltings_height": 20.72065027490183,
  "conductor": "17134222746387774970099915813476227048841598658950608099457561222375948826440847228073750929265414",
  "bad_primes": [
    "2",
    "3",
    "7",
    "41",
    "73",
    "1471",
    "36187140582315791",
    "2560598347654085510138906761380200366284296076666135789818938328782176279"
  ],
  "discriminant": "185302508309072474721711085693066416029736402378764218412967062072319829652551831902045227662998214205891613622272",
  "regulator": "1083616344002359656365285397.461952016202985813751003441369110760550297372760869116403215",
  "points": [
    [
      "10598949031235323936",
      "13803193514854316911692683608"
    ],
    [
      "8015015501234185936",
      "188840089745516162486603608"
    ],
    [
      "33256609107063808720",
      "177556966221608483869269409624"
    ],
    [
      "7587855471947503720",
      "1498627768180368134460874624"
    ],
    [
      "8481568266835779712",
      "2768385303986588671104136024"
    ],
    [
      "7448624967717269212",
      "-2187260892342016395883901336"
    ],
    [
      "-13592558631541176320",
      "32122772194566194779582188376"
    ],
    [
      "5245768336684499878",
      "12230489284936059737200174468"
    ],
    [
      "7490374866125553208",
      "1982754082348556875628103448"
    ],
    [
      "12789164471914848208",
      "-26083694892711636363800271656"
    ],
    [
      "8403087911186816688",
      "-2371166543017811292519121416"
    ],
    [
      "-3152574069415117520",
      "-39384852235147303507153274024"
    ],
    [
      "511133146790119041568",
      "-11551716603063282838234346014376"
    ],
    [
      "6590391547267943662",
      "-6240501908010722097445248956"
    ],
    [
      "3979756358617224712",
      "17493728486752802484637303264"
    ],
    [
      "8338018774144176112",
      "2040923608149736557711667384"
    ],
    [
      "8963014444451716756",
      "-5211122084512894790885389592"
    ],
    [
      "6480367841454429616",
      "6746037906351559726340208376"
    ],
    [
      "7786136362890277408",
      "-398102691451671107367103352"
    ],
    [
      "9072873840318107836",
      "5772880451922783569776494556"
    ],
    [
      "-4177140832302731312",
      "-41255728414362650969759925416"
    ],
    [
      "2978481322104012076",
      "21388477507807540544746177516"
    ],
    [
      "188676800077588249936/25",
      "-212819984096953989635313737224/125"
    ],
    [
      "6470777701925388112",
      "-6789969938998026271499318696"
    ],
    [
      "12084447491830344766",
      "-22036741254008064806236610492"
    ]
  ],
  "submitter": "apkorte",
  "history": [],
  "commentary": "Specialization at T = -715/1029 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where\nA4 = -9801785533668367408277499T^8 - 121843241966486333706286824T^7 - 383434732762042957835672232T^6 - 85754468638713501529031952T^5 - 584201627367901316547607440T^4 + 1235140044591109335942134016T^3 + 994771523582906627448194816T^2 - 550790635100880788122728032T - 647714191600162651688347312,\nA6 = 12142329458953725303990225302566830294T^12 + 247791101750863056653001398463488667192T^11 + 1886090538602583189200926091842195641480T^10 + 5912076790668428510577901681319655809040T^9 + 1282952245208814516295621371483268940160T^8 - 25791045529140834460411754210526102555072T^7 + 619130399100809058015628676691838434624T^6 + 31601519751505535243254509940106610677280T^5 + 10405299225003196422075679041028274690640T^4 - 27172444692997266799042742904489658895040T^3 - 13432438015701644454859263568215615214016T^2 + 8212424024664720375926323815936672405632T + 6370397708074310285430666560056789129600.\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": "2026-10-16 04:14:48",
  "updated_at": "2026-10-16 04:14:48"
}