{
  "id": 5289,
  "curve_key": "1926507023825612187469318081:-93099811147452445832095563520162973487521",
  "ainvs": [
    "1",
    "1",
    "1",
    "-40135562996366920572277460",
    "107754411050275459524788045635135362965"
  ],
  "rank_lower_bound": 19,
  "torsion": [],
  "family": null,
  "families": [],
  "naive_height": 188.66898156511473,
  "faltings_height": 13.690718695875175,
  "conductor": "245652734983669985750310124001832617709974624007847366230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "23",
    "29",
    "103375858763",
    "953177373205303",
    "666254344255314933502961"
  ],
  "discriminant": "-878171409753843593164196007178656408029927242223354575427441023941931008000000",
  "regulator": "14109775074474864.26065329552739239712822286479500183660112592455113663633876",
  "points": [
    [
      "14804256445053",
      "52518246981898135873"
    ],
    [
      "2281061006653",
      "5298267409796275073"
    ],
    [
      "5021097276353",
      "-5728774328937478927"
    ],
    [
      "1827583594565107/729",
      "-94173952552895645281531/19683"
    ],
    [
      "13669204620087/4",
      "-25930588877213528041/8"
    ],
    [
      "6591943390893",
      "11385403978817661073"
    ],
    [
      "4069293813693",
      "3437303336161443073"
    ],
    [
      "23823263153853",
      "-112571929044646388927"
    ],
    [
      "278301209122038877/91809",
      "103882492758669038949825871/27818127"
    ],
    [
      "159030955734579/25",
      "-1310130855450379362277/125"
    ],
    [
      "399795883099413/121",
      "4457084190992333266163/1331"
    ],
    [
      "4525234992303",
      "-4335690865460833427"
    ],
    [
      "121388617178437/9",
      "-1213509983567948213029/27"
    ],
    [
      "13428089290487/4",
      "-26352364524056130941/8"
    ],
    [
      "21227035526453",
      "93917093455618625473"
    ],
    [
      "10558573301123",
      "29344270460089500703"
    ],
    [
      "10590384072123",
      "-29503920061389895577"
    ],
    [
      "18266056305687/4",
      "35508220979013116459/8"
    ],
    [
      "18970662031907/4",
      "39257936991486617309/8"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "fiber of the x1152 K3 fibration family (file 063_x1152_A_0003.fiber), E(u): y^2 = x^3 + A(u)*x + B(u), specialized at T = u = -4/55. A(u) = (-9585496518629293615819721472)+(-536501816413053749656301196288)*u^1+(-12368010625534698965575586486784)*u^2+(-153670852784977847815038932888064)*u^3+(-1126077980994120736641769318298880)*u^4+(-4916607522934484171617568222893056)*u^5+(-12090799466059737633435362494243584)*u^6+(-14587262243584009021750010492175552)*u^7+(-6844291761509816231381594824587312)*u^8 ; B(u) = (374502094435674025104043654117865569935360)+(33193601381088363486746606727381236442316800)*u^1+(1289004250376379330798378598319831835979161600)*u^2+(28827565230794722135124600956050588624882278400)*u^3+(411108117101856888285966528948531742337079951360)*u^4+(3917967010548910874456925019692368143550867005440)*u^5+(25483742971305896595171553802128442605475798507520)*u^6+(113730906815932001693278266355855041235272854799360)*u^7+(345910796938972022540354749372936686129388052501760)*u^8+(702809951568307885052748475426214338146465682967040)*u^9+(911994372915445045966812634121039331292285376811264)*u^10+(677012143418988419778649816019731910499434169371904)*u^11+(216718499633097826210902038787366269826187097759616)*u^12. Rank exactly 19: 19 independent witness points (17 from mod-p Shioda fake 2-descent section lift, 2 more from kappa(z*)-covers of the 20 shallowest 2*Lambda_17 coset classes, ratpoints H=1e6, exact halving), canonical height Gram det != 0; Bober analytic rank bound 19 (kappa=2.8, GRH), rank is exactly 19.",
  "created_at": "2026-10-21 12:16:35",
  "updated_at": "2026-10-21 12:16:35"
}