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This builds on prior work of Zywina which gives a method for computing the image of the adelic Galois representation associated to <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper E\">\n  <mml:semantics>\n    <mml:mi>E<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">E<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>. Running this algorithm on all elliptic curves presently in the <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L\">\n  <mml:semantics>\n    <mml:mi>L<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">L<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>-functions and Modular Forms Database and the Stein\u2013Watkins Database gives strong evidence for the conjecture that <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper E\">\n  <mml:semantics>\n    <mml:mi>E<\/mml:mi>\n    <mml:annotation encoding=\"application\/x-tex\">E<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> gives rise to an isolated point on <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper X 1 left-parenthesis upper N right-parenthesis\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:msub>\n        <mml:mi>X<\/mml:mi>\n        <mml:mn>1<\/mml:mn>\n      <\/mml:msub>\n      <mml:mo stretchy=\"false\">(<\/mml:mo>\n      <mml:mi>N<\/mml:mi>\n      <mml:mo stretchy=\"false\">)<\/mml:mo>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">X_1(N)<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> if and only if <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"j left-parenthesis upper E right-parenthesis equals negative 140625 slash 8 comma negative 9317\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mi>j<\/mml:mi>\n      <mml:mo stretchy=\"false\">(<\/mml:mo>\n      <mml:mi>E<\/mml:mi>\n      <mml:mo stretchy=\"false\">)<\/mml:mo>\n      <mml:mo>=<\/mml:mo>\n      <mml:mo>\u2212<\/mml:mo>\n      <mml:mn>140625<\/mml:mn>\n      <mml:mrow class=\"MJX-TeXAtom-ORD\">\n        <mml:mo>\/<\/mml:mo>\n      <\/mml:mrow>\n      <mml:mn>8<\/mml:mn>\n      <mml:mo>,<\/mml:mo>\n      <mml:mo>\u2212<\/mml:mo>\n      <mml:mn>9317<\/mml:mn>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">j(E)=-140625\/8, -9317<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>, <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"351 slash 4\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mn>351<\/mml:mn>\n      <mml:mrow class=\"MJX-TeXAtom-ORD\">\n        <mml:mo>\/<\/mml:mo>\n      <\/mml:mrow>\n      <mml:mn>4<\/mml:mn>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">351\/4<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>, or <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"negative 162677523113838677\">\n  <mml:semantics>\n    <mml:mrow>\n      <mml:mo>\u2212<\/mml:mo>\n      <mml:mn>162677523113838677<\/mml:mn>\n    <\/mml:mrow>\n    <mml:annotation encoding=\"application\/x-tex\">-162677523113838677<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula>.<\/p>","DOI":"10.1090\/mcom\/3956","type":"journal-article","created":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T14:00:09Z","timestamp":1714053609000},"page":"447-473","source":"Crossref","is-referenced-by-count":2,"title":["Towards a classification of isolated \ud835\udc57-invariants"],"prefix":"10.1090","volume":"94","author":[{"given":"Abbey","family":"Bourdon","sequence":"first","affiliation":[]},{"given":"Sachi","family":"Hashimoto","sequence":"additional","affiliation":[]},{"given":"Timo","family":"Keller","sequence":"additional","affiliation":[]},{"given":"Zev","family":"Klagsbrun","sequence":"additional","affiliation":[]},{"given":"David","family":"Lowry-Duda","sequence":"additional","affiliation":[]},{"given":"Travis","family":"Morrison","sequence":"additional","affiliation":[]},{"given":"Filip","family":"Najman","sequence":"additional","affiliation":[]},{"given":"Himanshu","family":"Shukla","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2024,4,25]]},"reference":[{"key":"1","unstructured":"[Avi] J. 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